The Pennsylvania State University
The Graduate School
Department of Industrial and Manufacturing Engineering
DEVELOPMENT OF OPERATIONAL STRATEGIES FOR AN ON-DEMAND FOOD
DELIVERY SYSTEM IN HEALTH CARE
A Thesis in
Industrial Engineering and Operations Research
by
Caitlin Cronk
2012 Caitlin Cronk
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
May 2012
The thesis of Caitlin Cronk was reviewed and approved* by the following:
Deborah J. Medeiros
Associate Professor of Industrial Engineering
Thesis Advisor
Jack C. Hayya
Professor Emeritus of Supply Chain and Information Systems
Paul Griffin
Professor of Industrial Engineering
Head of the Harold and Inge Marcus Department of Industrial and Manufacturing
Engineering
*Signatures are on file in the Graduate School
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ABSTRACT
As hospitals strive to improve measures of service for patients under their care, every
element of the patient care process is examined for opportunities to improve the quality of care
and the presence of a patient-centered approach. Some hospitals have implemented an “on-
demand” style food service system in an effort to be more patient-centric. This system allows
patients to order from a menu and have it delivered to their room, much like a hotel room service
system. Geisinger Medical Center, in Danville PA, is among the hospitals looking to improve
their inpatient food service to better meet the needs of patients by implementing such an on-
demand delivery style system.
This research develops operational recommendations for an on-demand food delivery
system for the inpatients at Geisinger Medical Center. The recommendations made will allow the
system to achieve service level standards set by Geisinger’s Guest Service management team.
Specifically, several combinations of meal delivery cart capacities and dispatching strategies were
analyzed for effectiveness with the use of a discrete event simulation model. The model captures
all material handling and routing throughout the Geisinger Medical Center facility and was used
to understand how different delivery strategies affect operational performance and service levels.
To reduce the percent of meals delivered late, more resources will be required, however,
they will not necessarily be utilized efficiently. The operational strategy that allowed for the best
balance between resource utilization and patient service levels used twelve-tray delivery carts,
and a dispatch timer setting of ten minutes, provided the meal preparation required less than
fifteen minutes. This policy suggests that approximately 94.3% of patients will receive their
meals within 45 minutes of placing an order. The results also provide an expectation for the
number of carts needed, as well as information to assist planning for host staffing levels
depending on the operational policy chosen.
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TABLE OF CONTENTS
LIST OF FIGURES ................................................................................................................. vi
LIST OF TABLES ................................................................................................................... vii
ACKNOWLEDGEMENTS ..................................................................................................... viii
Chapter 1 Introduction ............................................................................................................. 1
1.1 Motivation .................................................................................................................. 1 1.2 Scope .......................................................................................................................... 1 1.3 Objectives................................................................................................................... 2 1.4 Organization ............................................................................................................... 2
Chapter 2 Literature Review .................................................................................................... 4
2.1 Current Hospital Food Service Practices ................................................................... 4 2.1.1 Quality considerations in food service ............................................................ 4 2.1.2 The restaurant style system ............................................................................. 5
2.2 The Vehicle Routing Problem .................................................................................... 7 2.2.1 Capacitated vehicle routing problem ............................................................... 7 2.2.3 Vehicle routing problem with time windows .................................................. 8 2.2.4 Vehicle routing problem with time windows and multiple trips ..................... 9 2.2.5 Stochastic vehicle routing problem ................................................................. 10
2.3 The Pickup and Delivery Problem ............................................................................. 13 2.3.1 1-M-1 pickup and delivery problem ................................................................ 13 2.3.2 A tabu search algorithm for VRP with backhauls ........................................... 15
2.4 Order Batching ........................................................................................................... 17 2.4.1 A GA-based order batching method ................................................................ 18
Chapter 3 Model Development ................................................................................................ 21
3.1 Introduction ................................................................................................................ 21 3.2 System Description .................................................................................................... 21
3.2.1 Meal order arrival process ............................................................................... 22 3.2.2 Meal delivery process ...................................................................................... 23
3.3 Modeling Approach ................................................................................................... 26 3.3.1 Modeling assumptions ..................................................................................... 28
Chapter 4 Analysis of Results .................................................................................................. 30
4.1 Introduction ................................................................................................................ 30 4.2 Experimental Plan ...................................................................................................... 30
4.2.1 Performance Measures .................................................................................... 30 4.2.2 Experimental design ........................................................................................ 33
4.3 Results ........................................................................................................................ 34 4.4 System Limitations .................................................................................................... 39 4.5 Recommendations ...................................................................................................... 40
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Chapter 5 Conclusions and Future Research ........................................................................... 42
References ................................................................................................................................ 44
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LIST OF FIGURES
Figure 1. Illustration of Double Path Solution to VRPB, (Berbeglia et al. 2007).................... 14
Figure 2. Food Order Arrival Logic ......................................................................................... 23
Figure 3. Food Cart Routing Logic .......................................................................................... 25
Figure 4. Simul8 Modeling Environment ................................................................................ 27
Figure 5. Food Service Logic Modules .................................................................................... 27
Figure 6. Resource Performance Measures Plot for Twelve Tray Cart Scenarios ................... 36
Figure 7. Service Performance Measures Plot for Twelve Tray Cart Scenarios...................... 37
Figure 8. Cart Usage Profile Plot for each Twelve Tray Cart Scenario ................................... 38
Figure 9. Average Number of Carts in Use throughout a Day for all Twelve Tray Cart
Options ............................................................................................................................. 39
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LIST OF TABLES
Table 4-1. List of System Performance Measures (bold measures represent key
performance measures) .................................................................................................... 32
Table 4-2. Experimental Scenarios .......................................................................................... 33
Table 4-3. Experimental Results .............................................................................................. 34
Table 4-4. Average Number of Carts Filled to Capacity for Each Scenario ............................ 36
viii
ACKNOWLEDGEMENTS
I would like to thank, Dr. Deborah Medeiros for her support and guidance. She has been
not only a good thesis advisor, but also a great teacher and mentor to me throughout my time in
graduate school. In addition, I would like to thank Dr. Jack Hayya for the input he provided to
improve this document, as well as Seth Hostetler for his time and patience in helping me to learn
Simul8, and for acting as a great resource and sounding board throughout the duration of my
research work.
I would also like to thank the Supply Chain and Guest Services groups at Geisinger
Medical Center for providing me the opportunity to work with them on my thesis research. The
practical experience I gained by working with a top performing innovative hospital has proven to
be invaluable.
Finally I would like to thank my friends and family for their never-ending support in my
academic ventures. My family for continually encouraging me through the years, and my friends
for making sure I had fun along the way.
Chapter 1
Introduction
1.1 Motivation
This research is motivated by the growing interest in improving patient services within a
hospital environment. Food services are one additional element of caregiving which can be
examined for ways to improve a patient-centered experience. In an effort to enhance its food
service to inpatients, Geisinger Medical Center (GMC) is working to develop an on-demand food
delivery system that will allow for more flexibility in meal choices and delivery times.
The implementation of such an on-demand style food delivery system will require an
understanding of the strategic operational changes required to transition from their currently
utilized traditional food service system. Resource usage may require shifts in size and schedule,
and strategies for routing the food deliveries will likely change. Specifically, it is important to
consider questions, such as how to group orders together, how many delivery carts should be
used, or how long a partially filled cart should wait for additional meals before commencing
delivery.
1.2 Scope
Geisinger Medical Center is currently in the process of developing a discrete event
simulation model to capture all material handling throughout the facility. This research
capitalizes on the opportunity to include food delivery operations in the overall model and
analyze how to best structure operational policies while considering the facility layout as well as
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traffic and routing challenges. Using the simulation model, several food delivery cart capacities
and order batching strategies will be tested and analyzed for their effect on customer service
levels. The results of the analysis will yield recommendations for management regarding the best
strategies to achieve high patient service levels.
Whereas the modeling and analysis pertaining to this research is specific to GMC’s
inpatient system characteristics, the approach is one that can be applied to any hospital looking to
implement an on-demand food delivery system within their inpatient units. Therefore, this
research provides the opportunity for the generalization of modeling and quantitative analytical
techniques used to evaluate such operational strategies.
1.3 Objectives
The goal of this research is to develop and analyze operational policies of on-demand
distribution of food to inpatients at Geisinger Medical Center in Danville, PA. Specifically, it
will aim to provide recommended resource requirements and routing strategies to allow for the
achievement of high patient service levels. The objectives will be approached by simulating and
analyzing the various operational strategies in a discrete event simulation model representing the
food delivery process at GMC.
1.4 Organization
Chapter 2 provides a literature review of relevant research topics in the areas of hospital
food delivery, vehicle routing algorithms, pickup and delivery algorithms, and batching
strategies. Chapter 3 includes a description of the system parameters and constraints, as well as
data used for modeling and evaluation. This chapter also discusses the modeling approach used
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to represent the food delivery system in a discrete event simulation. Chapter 4 contains the
experimentation methodology used to evaluate the scenarios. Results of the evaluation will also
be provided in this chapter, followed by recommendations for successful implementation of an
efficient on-demand food delivery model. Finally, Chapter 5 will provide a summary of
conclusions and will outline opportunities for future work.
Chapter 2
Literature Review
2.1 Current Hospital Food Service Practices
There are two predominant methods used by hospital food service providers to distribute
food to inpatients, the conventional method (often referred to as “plated”) and the cook-chill
method. In the conventional system, food is prepared hot and immediately served to patients [1].
In the cook-chill system, food can be prepared in advance, chilled, and then reheated just before it
is served to the patients. A third method, referred to as “hotel-style room service,” has been
introduced into hospital systems and studied for its effect on patient satisfaction [2] [3]. In 2000,
a survey conducted on current and future hospital food service trends found the conventional
method to be used in 81% of the 200 US hospitals surveyed. Reheating methods, such as the
cook-chill system, were found to be used in 6% of hospitals where the food is heated in the
kitchen, and 8% where the food is heated in the galleys [4]. The survey does not mention the use
of a hotel style delivery system, suggesting that it is either relatively new or uncommonly used in
US hospital systems.
2.1.1 Quality considerations in food service
There have been various studies examining the impact of food service delivery methods
on quality indicators of inpatient food. The common quality indicators studied in the surveys
include: cost, temperature, texture, menu style, and flavor. One study found that a “bulk trolley”
system, where food was served from a portable heated system, resulted in improved texture of all
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foods, more acceptable temperatures for some and better flavor for other foods, when compared
with the conventional “plated” system [5]. In contrast however, Mibey and Williams (2002) state
that research has shown that a central plating system, found in the conventional meal delivery
method, allows for better portion control, food quality, and diet monitoring.
Cook-chill systems, which can either be used to serve food in a bulk or plated method,
have been evaluated on common quality indicators as well. This system has been found to have
conflicting ratings. While managers have been found to be more satisfied with the conventional
system because of the perceived improvement in texture, food quality, and a reduction of
leftovers, they noted an improvement with the cook-chill system on measures of cost, waste,
labor utilization, and space [6] [7].
The effect of cook-chill versus conventional systems on labor utilization has been
disputed by several researchers in the field. In a study conducted on the food service trends in
New South Wales hospitals, researchers found that a cook-chill system allowed for a higher beds-
to-fulltime employee ratio. This, however, was noted by Mibey and Willams (2002) to be a
considerably “crude” indicator of resource utilization, which is further supported by their claim
that other researchers have found contradicting results. Additionally, Assaf et al. noted a similar
controversy of the notion of reduced skill requirements necessary in the cook-chill method [6].
Therefore, the measure of productivity in terms of employee utilization and skill requirements
cannot be considered a high priority quality indicator.
2.1.2 The restaurant style system
The restaurant style system (also referred to as hotel-style room service) has been found
to provide significant benefits to the patient. In this system, the patients are presented with more
options at meal time, have the ability to receive food at their personally preferred time, and can
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order their meal much closer to the time of consumption when compared with more traditional
systems [1]. A study focused on the pediatric oncology patients found that providing a restaurant
style food delivery system to the patients resulted in an improvement of dietary and caloric
intake, along with an increase in patient satisfaction. The study also found that the restaurant
style service increased the efficiency of the meal delivery system because patients were ordering
fewer times per day, but consuming more of the food at each meal [2]. These results suggest that
not only can this new approach to hospital food delivery support faster patient recovery, but can
also potentially allow for reduced food waste in the system and increase patient satisfaction.
Whereas the restaurant style delivery method presents many appealing attributes with
respect to improvement opportunities, the system also presents a few challenges. Of primary
concern is the time constraint placed on the delivery method. In the restaurant style delivery,
food leaves the kitchen hot and fresh and must be delivered to the patient within a tight time
constraint. Thirty to forty-five minutes was considered in one study to be the acceptable amount
of time between preparation and patient delivery [3]. This time limit presents a demanding
constraint on the system, as the size of the hospital layout and the number of inpatients to be
served grows. Along with time constraints, cost was presented as an additional issue with the
implementation of the restaurant style method. In a study surrounding best practices in hotel-
style inpatient meal service, one researcher found that an increased number of personnel were
required to effectively carry out the hotel-style system, adding to the cost of the food services
operation [3]. The study however does not mention any efforts taken to optimize the delivery
system, which could potentially reduce the cost of required resources.
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2.2 The Vehicle Routing Problem
The vehicle routing problem (VRP) can generally be represented in the form of a graph,
where vertices act as customer locations, and the arcs between them represent travel routes. One
vertex serves as a “depot”, where vehicles will originate from and return to after their route. The
goal is for each customer to be visited by one vehicle, one time, in such a way that associated
travel times, cost, and distance can be minimized. The problem is classified as NP-hard, and
therefore, heuristics are used to search for optimal solution strategies [8]. Furthermore, additional
constraints are commonly introduced into the general VRP, such as vehicle capacity constraints,
route duration constraints, or time window constraints [9]. Each of these additional constraints
has led to the creation of several classifications of the original VRP. Those related to the on-
demand food delivery problem are discussed in this section.
2.2.1 Capacitated vehicle routing problem
The capacitated vehicle routing problem (CVRP) extends the basic VRP by placing a
maximum allowable load on each vehicle [10]. The CVRP has been characterized by the
combination of two classic problems: the traveling salesman problem (TSP) and the Bin Packing
Problem [11] [12]. In the TSP, the objective is to find a route which can be executed in one tour
and reaches all customers in the shortest distance possible [13]. When applied to the CVRP, each
vehicle will use the TSP to find a route optimal to its assigned customers [14]. The Bin Packing
Problem seeks to find the minimum number of bins or carts required to handle a given capacity
[12]. Like the VRP, the Bin Packing Problem and TSP are considered NP-hard. By combining
techniques used to solve these two sub-problems, strategies have been developed to address the
challenges associated with the CVRP.
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Among the heuristics used to address the CVRP, global search heuristics have been
applied frequently. Specifically, evolutionary computation methods, such as particle swarm
optimization, genetic algorithms, and ant colony optimization, have been found to provide near
optimal solutions to the CVRP [15]. One challenge to consider when using such methods is
developing an effective framework to represent the solution space in the algorithm. One must
consider how to represent a route plan as a solution, how to handle infeasible solutions, as well as
how to represent the objective function to be solved by the algorithm [14].
2.2.3 Vehicle routing problem with time windows
A second well known version of the vehicle routing problem is the vehicle routing
problem with time windows (VRPTW). The problem constrains the time period during which a
delivery to a customer can be made. The earliest and latest times considered acceptable for
delivery to a customer make up the delivery time window [8]. In practice, this is an important
aspect to consider because not only do late deliveries cause problems, but deliveries made too
early can pose challenges as well. For example, a delivery may arrive to a store before the store
is open. This will then force the resources to wait until the store is open and able to accept the
goods. Therefore, an important aspect of this problem is the inclusion of the cost of waiting time
in an early delivery, along with the cost of service time for unloading the goods. In the problem
space, this temporal cost is included with the travel distance cost found in the traditional VRP
[16] [8].
There have been several algorithms proposed for addressing the VRPTW. Due to the
NP-hard nature of the problem, many of the proposed solutions are approximation heuristics. In
his paper, Solomon reflects on many of the well-known heuristics developed to solve the VRP.
Among these heuristics are “tour-building” algorithms, “insertion” algorithms, and also a
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“savings” heuristic. Solomon also describes a significant characteristic which distinguishes the
mechanism of these algorithms: whether they develop solutions sequentially or in parallel. A
sequential algorithm will build one route at a time, iteratively adding additional customers onto a
route, provided the addition results in a feasible routing. The feasibility is determined based on
constraints such as the capacity of the vehicle, the distance from the previous customer, and of
course, the time window requirement of the customers. A parallel algorithm will construct
multiple routes simultaneously and then adjust the structure to improve the overall performance
[8].
2.2.4 Vehicle routing problem with time windows and multiple trips
A further variation of VRPTW discussed in the literature is the incorporation of the
ability for a vehicle to perform multiple tours in one solution. This VRP extension is known as
the “minimum multiple trip VRP” or MMTVRP. The objective of the MMTVRP is to minimize
the number of multiple routes required by a fleet of vehicles. Solving this problem will also
result in minimizing the size of the fleet [17]. This is a very practical problem as delivery
vehicles will often make a delivery and return to the depot for a second round of deliveries in a
given planning period [16]. The problem is also useful in practical applications because of its
ability to address the need for a limited number of vehicles to deliver a large demand, or when
tight time window restrictions are placed on the demand. This is especially relevant in problems
involving the delivery of prepared food, where time restrictions will be of high concern, and
multiple short trips are taken in a given delivery period. The use of a vehicle for multiple routes
may reduce the investment for delivery resources, however, it may also further constrain the
solution space [17].
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The MMTVRP can be solved by decomposition. Battarra et al. (2009) describe the efforts
of multiple researchers who have decomposed the problem into two parts. The first part solves a
general VRP using techniques such as a savings-based algorithm or a global search heuristic. The
second part then assigns multiple routes to a vehicle by modeling the problem after a bin packing
problem. This approach is similar to the approach discussed above with regard to the capacitated
VRP.
When combined with the VRPTW, the problem becomes known as the “vehicle routing
problem with time windows and multiple routes” or MVRPTW [16]. Battarra et al. (2009)
applied this problem in the context of delivering goods from a central depot to several
supermarkets and hypermarkets within specified time window constraints. As with the general
VRPTW, they approached the problem through decomposition; first they used an insertion
heuristic to devise feasible routes for the vehicles and then they used a bin packing problem to
aggregate the routes among a limited number of vehicles. To further enhance the effectiveness of
this approach, they utilized a “guidance mechanism” aimed at improving the creation of the initial
set of routes to allow for more effective aggregation in terms of minimizing the number of trips
necessary and reducing the time required by a vehicle. Although other studies have developed
exact algorithms for the solution of a such a problem, the intractable nature of many realistically-
sized problems will likely favor the relatively efficient near-optimal approaches which use
heuristics [18] [16].
2.2.5 Stochastic vehicle routing problem
The traditional VRP considers the fulfillment of deterministic customer demands. An
extension of this problem, which is perhaps more realistic, incorporates stochasticity into the
demands of customers. This VRP is referred to as the Stochastic VRP (SVRP), or the
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Probabilistic VRP (PVRP). The extension is often incorporated with others, such as the
capacitated VRP or VRP with time constraints. The prominent challenge of handling stochastic
demands involves effective decision making surrounding the scheduling and adjustment of routes
to accommodate changes in demand on a periodic basis.
There are three factors that can be influenced by stochasticity in the SVRP. The first is
stochastic customers, the second is stochastic demands, and the third involves stochastic timing.
In the first, the presence or absence of a customer is a random variable, while the demand, in
terms of quantity is considered deterministic. In the second, the quantity of demand for each
customer is the random variable [9]. These two random variables can also occur together in a
SVRP. Both types of problems must consider the capacity of the vehicle used and often require
return trips to the depot to accommodate the demand uncertainty. The third factor influenced by
stochasticity reflects the variable nature of service and travel times throughout the route [19].
These times may have a significant effect on the service level and time constraints of a VRP.
There are three prominent strategies to address the presence of stochastic demands in this
VRP as described by Benton and Rossetti (1992). The first strategy uses a set of fixed routes
determined in an a priori fashion to minimize the total travel cost. These fixed routes may either
be designed using the maximum expected demand in a given period or the expected non-zero
demand in a period. The cost of this strategy is determined using the a priori routing cost, along
with the cost associated with the probability of exceeding capacity on the fixed route. The
objective when solving this problem is to minimize the cost of exceeding vehicle capacity. The
second strategy creates a fixed a priori route as in the first strategy, and then modifies the route by
removing any stops in which the customer demand is zero. The authors refer to this method as
the “modified-fixed routes alternative.” The third strategy is different from the first two in that it
creates no fixed routes prior to the realization of customer demand. Rather, this method requires
the development of an efficient route for each period of demand. The authors refer to this method
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as the “variable routes alternative.” Although the routing of this method will be capable of
accommodating large variances in demand and may address issues related to capacity constraints,
the technological requirements and advanced management oversight needed may outweigh the
benefits of such a system. The three strategies discussed above are suggested as useful in
different scenarios of stochastic vehicle routing. When there is low likelihood that customer
demand will be zero, an a priori method may be more efficient. On the contrary, when there is a
high probability of zero demand by customers, it may be more appropriate to employ the variable
routes alternative [20]. In addition, the best choice of method may depend on when in the process
the demand information becomes available for use [9].
Laporte, Louveaux, and Van Hamme (2002) developed a methodology to address the
capacitated SVRP using recourse, referred to as the “L-shaped method.” The recourse policy
implemented in this strategy allows the vehicle to return to the depot at the point when capacity is
exceeded. The vehicle then returns to the point of failure and continues on its original path. One
important constraint introduced in their model requires that the expected total demand allocated
to a vehicle does not exceed the vehicle’s capacity. The objective of the algorithm is to minimize
the cost of the original planned route along with the cost associated with recourse. The original
route can be developed similar to that of the development of a deterministic VRP. The challenge
is presented in determining the cost of recourse [21].
Gendreau et al. (1996) introduce the use of “preventative breaks” strategically placed
along an a priori route. This strategy was suggested to allow the vehicle to return to the depot at a
point where it is likely to run out of capacity. At the point when the vehicle returns to the depot,
a re-optimization process may take place to improve the solution of the remaining stops on the
route. A challenge often noted with this type of strategy is the time required to re-optimize in the
midst of the service process. Some researchers suggest that it may be less costly to use a type of
a priori modified-fixed route schedule, as discussed above, to limit the complexity of the
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problem. These heuristic strategies have been found to be competitive with those of the
stochastic programming strategies that are capable of finding an exact solution (for a reasonable
problem size), but require a more significant computing cost [22].
2.3 The Pickup and Delivery Problem
The pickup and delivery problem (PDP) is a special version of the vehicle routing
problem. The problem can be characterized by a set of items that require pickup from a certain
location, followed by delivery at another specific location, [23]. The problem can be further
classified based on the number of distinct pickup locations as well as unique customer locations.
For example, the many-to-many problem (M-M) describes situations in which items may be
picked up from multiple locations and then delivered to multiple locations. By contrast, the one-
to-many-to-one problem (1-M-1) requires delivery items to originate from one central depot. The
items may then be delivered to customers at various locations. Items may also be picked up from
the customers at various locations and then returned to a central depot [24]. Reverse logistics is
often incorporated into the return of items from customers to the central depot. Due to the nature
of this research, the following section on pickup and delivery problems will be focused to the
subset of 1-M-1 problems.
2.3.1 1-M-1 pickup and delivery problem
In the food delivery application, 1-M-1 PDP could apply to the delivery of food from the
central kitchen to each patient unit, combined with the reverse logistics problem of picking up
empty patient trays and returning them to the central kitchen. There are two types of 1-M-1
problems: combined and single demand problems. In combined demands, customers may request
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both delivery and pickup of items, much like in a food distribution model. In single demand
problems, customers may only request either pickup or delivery of items [24]. These two types of
PDPs are each addressed by different types of routing strategies.
The 1-M-1 problems with combined demands have been addressed with various solution
models. Of particular interest is one developed by Berbeglia et al. (2007) referred to as the
“double-path solution.” In this solution, the vehicle visits each customer location for pickup
(delivery) of items. Once all customers have been visited, the vehicle will visit each customer a
second time for delivery (pickup) of the items. The last customer to be visited for the initial
pickup (delivery) will experience simultaneous pick-up and delivery and therefore will only be
visited one time in the solution route. All other customers will be visited twice in the solution
route. This problem is also referred to as the “1-M-1 PDP with Single Demands and Backhauls,”
or the “Vehicle routing problem with Backhauls” (VRPB). The solution can be visualized as a
cluster of nodes with a path spanning from the central depot through the different customer
locations, and ending at the farthest location. A second path then exists traveling in the opposite
direction as the first path. An illustration of the solution is shown in Figure 1.
Figure 1. Illustration of Double Path Solution to VRPB, (Berbeglia et al. 2007)
A significant challenge to solving the VRPB exists in the development of efficient
clusters of customers for service by one vehicle. Berbeglia et al. (2007) describe a number of
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heuristics used to solve the VRPB, including “cluster-first-route-second” and tabu search. The
authors also describe exact algorithms capable of handling a maximum of 100 customers and 12
vehicles.
2.3.2 A tabu search algorithm for VRP with backhauls
In an effort to create an efficient algorithm to address the VRPB, Brandão (2006)
developed and tested three variations of a tabu search algorithm aimed at solving and optimizing
routes containing both linehaul and backhaul customers. These algorithms focused on a specific
category of VRPB problems that require that linehaul customers are always served before any
backhaul customers in a given vehicle route. Additionally, there can be no routes with only
backhaul customers. The algorithms differed in one of two ways: either they differed in the
development of initial solutions used in creating a population for the tabu search algorithm, or
they differed in parameter settings of the tabu search algorithm.
The first variation is referred to as the TSA-Open because the initial solution is created
using a so-called “open initial solution” approach. In this approach, the linehaul and backhaul
customers are separated and addressed independently. The solutions are then joined together
using an approach dictated by what is called the Open VRP (OVRP). In the OVRP, it can be
assumed that at the end of a route, the vehicle does not need to return to the depot. Using this
assumption, it is possible to allow the last customer of a linehaul path to be connected to the first
customer of a backhaul path. Additionally, the paths can be routed from first to last customer or
last to first customer depending on the best way to connect the linehaul and backhaul routes. This
provides four possible ways to complete the route. The routing for each set of customers is
determined using a “nearest neighbor heuristic,” and then each solution is improved upon using a
tabu search algorithm. Once the algorithm has been run for each set of customers, the linehaul
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and backhaul paths are linked together in each of the four possible ways to determine which
alternative results in the least cost solution. These solutions are then ready to be optimized using
the tabu search algorithm.
The second and third initial solutions are created using what is referred to as the “K-tree
initial solution.” The initial solutions are first defined using a minimum cost K-tree approach to
solving a VRP. First, the linehaul and backhaul customers must be addressed independently as
VRP problems. Next, a minimum cost K-tree is used to formulate the solution to the VRP.
Finally, the capacity and precedence constraints are relaxed to create the initial solutions.
The three initial solution sets can then be optimized using a tabu search algorithm with
three phases: an initial phase to create feasible solutions, and two subsequent phases, which
improve upon the solutions. The two K-tree solutions are differentiated by one of the tabu
parameters. Specifically, one of the solutions uses a modification to the tabu search algorithm.
In this case the tenure parameter of the tabu search algorithm is allowed to be random, and
therefore it is referred to as the TSA-K-tree_r.
The performance of the three algorithms was tested against a series of previously
published VRPB algorithms using a suite of 95 test problems. The experimental results
demonstrated that the TSA-K-tree_r algorithm performed the same or better and took less
computing time when compared to previously published approaches. The TSA-K-tree algorithm
performed slightly worse than the TSA-K-tree_r, but required less computation time. The open
initial solution method produced fewer optimal solutions than the K-tree methods, although it
took less time to run. The results, therefore, illustrate that the K-tree initial solution method
combined with the tabu search algorithm utilizing a random tabu tenure is the best known
approach to addressing the VRPB [25].
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2.4 Order Batching
When developing a delivery system, the incorporation of strategic product batching to
allow for efficient routing can significantly impact the system performance. Order batching, also
known as “lot-sizing,” involves efforts to strategically group items that can be transported or
processed together [26]. The most notable benefits of incorporating batching into processes are
the realized reduction in resource requirements and the reduction in mean travel time to retrieve
and order. These benefits can lead to increased throughput and efficiency. Furthermore, batching
can lead to a reduction in “order holding time,” which affects how long customers wait to receive
their orders [27] [26].
Although batching is recognized to increase efficiency in order processing scenarios,
there are several system parameters which must be properly set to achieve the benefits.
Specifically, the size of the batch will affect the efficiency of operations. According to Won and
Olafsson (1994), a trade-off exists between the use of large and small batch sizes. Large batch
sizes will result in longer processing time, which will increase the time to customer delivery. In
contrast, small batches are less efficient, mainly because they require the use of more resources
and additional trips or travel distance. The trade-off space must be explored through
experimentation or multi-criteria optimization to understand the proper batch size for the system
under consideration. In addition, the process of creating the batches requires time and effort [28].
Therefore, analysis must be performed to understand the trade-off between taking time to create
batches and the resulting time saved in transporting or processing the batched orders. Logically,
only when the time required to batch is less than the realized time savings in the delivery process
should batching be incorporated into operations.
There are several heuristics that can be used to create batches from a given set of orders.
The first, and arguably simplest approach is described by Gibson and Sharp (1992) as the “first-
18
come, first-served heuristic,” also known as “naïve batching.” In this heuristic, orders are
batched together based on the sequence in which they arrive. Given a batch capacity, c, orders
will be batched together upon arrival until the batch capacity is met, at which point another batch
of size c will be initiated. While this batching strategy does not consider delivery location, it can
be used as a baseline to compare other more advanced batching techniques [28].
A second strategy described by Gibson and Sharp (1992) is referred to as the “sequential
minimum distance batching heuristic,” or SMD. This heuristic is considered a “greedy” heuristic,
because it batches orders based on their proximity to one another. To create the batches, a seed
order is chosen from the group of available orders. The next order to be added to the batch will
be the one with the closest delivery location to that of the seed order. The third order will be the
one that has the closest delivery location to that of the second order. This will continue until the
capacity of the batch is met, at which point, a new seed order will be chosen from the remaining
orders, and the process will be repeated.
2.4.1 A GA-based order batching method
One strategy, which was extensively tested against the first-come first-served and SMD
heuristic, is referred to as the “GA-based order batching method,” or GABM. This heuristic
claims to create efficient batches for both 2-D and 3-D facility systems. Given a set of orders to
be picked, the GABM utilizes a genetic algorithm (GA) to determine the best combination of
batches that minimizes total travel distance. Furthermore, the authors claim that their approach
can successfully accommodate any batch structure or facility layout [29].
The GA in this heuristic is encoded as follows. Each chromosome contains a gene for
every order required to be picked. In the place holder of a given order in the chromosome is a
number corresponding to the batch where the order will be placed. For example, the chromosome
19
(1, 3, 2, 1, 2) prescribes the first and fourth order to be in batch one, the third and fifth order to be
in batch two, and the second order to be in batch three. The GA tests many different
combinations of batches and evaluates each using a fitness measure. In GABM, the fitness is
calculated by taking the difference between the travel distance in the worst performing feasible
solution in the current population of solutions and the travel distance of the solution under
evaluation. The goal is to maximize this fitness value. To ensure that the tested solutions satisfy
capacity constraints, thus remaining feasible, a correction mechanism was devised to transfer
orders from over-capacitated batches to those which have available capacity.
The GA utilizes two techniques to promote diversity in the set of solutions: crossover and
mutation. The crossover mechanism allows for two chromosomes to swap parts of their encoded
solution, whereas the mutation mechanism allows for each gene in a solution to be swapped with
another gene with some low probability. Feasible solutions are chosen to join the mating pool
using a roulette wheel selection technique that provides a probability of being selected based on
their fitness value. A solution is able to survive into the next generation based on a second
probability-based approach that relies on the rank of the solution as compared to others in the
pool.
Hsu et al. (2005) conduct a study to compare the effectiveness of their GABM against
Gibson and Sharp’s SMD (1992) and the baseline first-come, first-served heuristic, using test
order sets and a rectangular facility layout with parallel aisles. The results of the experimentation
on the 2-D problems show that GABM performs in a superior manner to the SMD in terms of
number of batches, as well as total travel distance. Specifically, in seven experiments, the
GABM traveled between 0.85 to 0.91 times the distance traveled by the SMD, and between 0.69
and 0.81 times the distance of the first-come, first-served heuristic.
There are several factors that must be noted when considering the result of the
experiments by Hsu et al. As mentioned by the authors, the CPU time of the GABM to solve the
20
2-D problem was 0.7 hours, and 5.5 hours to solve the 3-D problem. These times were taken on
an IBM PC with a Pentium IV processor [29]. One important note to make regarding the
experiments is that they are tested only on scenarios in which all order data are known in advance
and batches can be planned hours before picking begins. Such a situation may allow for hours of
computation time; however, in a real-time, on-demand scenario, this may not be possible.
Additionally, on-demand scenarios may realize different test results because the heuristics may
handle the random arrival of batches in a different manner. It would likely be necessary to test
these three heuristics on real-time on-demand order batching problems to critically evaluate
which would perform best. Such an experiment, however, was not found in the literature search.
21
Chapter 3
Model Development
3.1 Introduction
This work undertakes the development of a model to allow for the analysis of a food
delivery system to be implemented within Geisinger Medical Center’s inpatient units. A discrete
event simulation model will be used to examine the impact of different batching and routing
strategies to deliver food to inpatients throughout the hospital. From the analysis, a
recommendation will be made to allow for routing of food in an on-demand fashion, that achieves
a sufficient level of service to the patient. Specifically, the model analysis will provide for insight
into the following operational strategies:
1. Food delivery cart size
2. Delivery resource requirements
3. Food cart dispatching rules
4. Routing strategies in the form of physical zoning of the facilities
The model will be developed to allow evaluation of different strategies on the basis of their effect
on patient service levels and the utilization of delivery resources.
3.2 System Description
The inpatient food delivery system to be modeled encompasses 345 licensed patient beds.
The beds are located across 19 units throughout the GMC hospital facility and will be occupied
22
by patients who require up to three meals per day. In the on-demand system, patients will be able
to order their meals between the hours of 6:30 am and 9:30 pm. Meals are ordered via telephone,
which allows the order to be sent to the kitchen staff. Each meal is prepared on an individual
basis (i.e., meals are prepared as the order arrives).
The facility layout of GMC lends itself to three natural spatial zones. Referenced by the
names of the elevators in the zones, the zones will be referred to as Zone A, Zone B, and Zone
JK. The zones contain six, seven, and five units, respectively. Meal orders will be segregated
into three batches, one for each zone. The batches of meals will be handled independently of
each other. This will allow for carts to be specifically allocated to one of the three zones.
3.2.1 Meal order arrival process
As food orders arrive to the kitchen, they will be identified by the zone and unit from
which the orders originated. A member of the food services team will then prepare the meal for
the patient. Once prepared, the meal will be placed on a cart designated for delivery to the zone.
If there is currently a cart designated for the zone with meals already on it, the meal will be added
to that cart. Otherwise, a new cart will be designated to that zone. The meals will continue to
accumulate on the cart until a time limit has been reached, or the capacity has been met,
whichever occurs first. Figure 2 demonstrates the logic of this portion of the food delivery
process.
23
Figure 2. Food Order Arrival Logic
To accurately model the order arrival process as it pertains to GMC, an estimate of
ordered meals in half hour increments is provided by Geisinger Health System. This estimate,
accompanied by data outlining how many beds are in each inpatient unit are used to develop
arrival distributions of meals in a given unit for every half hour between the operating times of
6:30 AM and 9:30 PM.
3.2.2 Meal delivery process
Once the food cart is ready for delivery, a member of the food services team will
transport the cart throughout the designated zone to deliver meals to the patients. For each zone,
24
there is a recommended routing to be used by the delivery host. Essentially, the routing follows a
nearest neighbor heuristic throughout the zone, starting at the units on the lowest floor served and
moving to the units on the highest floor served. In a zone, there may be more than one unit on a
given floor. These units are scheduled next to each other so that only one stop is made at a given
floor during the delivery route.
When on the delivery route, the delivery host will consider the next unit on the zone route
and determine whether there is a meal to be delivered in that unit. If so, the delivery host will
travel to that unit; otherwise, the host will consider the next unit on the zone route. Once the last
meal has been delivered, the delivery host will return the cart back to the food service kitchen to
allow the cart to be refilled. The logic for this delivery process is shown in Figure 3.
25
Figure 3. Food Cart Routing Logic
Once the delivery cart has arrived at a unit, all meals destined for patients in that unit will
be delivered. To enhance the quality of service, the delivery host will bring the meal to the
patient and take the necessary time to ensure that the patient has what they need to eat their meal.
If the patient has special dietary needs, the delivery host will also be required to inform the nurse
that the meal has been delivered so that the patient may be monitored. Additionally, if the patient
is an isolation patient, the delivery host will be required to put on a gown while they serve the
patient. This process will add to the service time spent with each isolation patient.
26
3.3 Modeling Approach
The discrete event simulation model representing the proposed food delivery system will
be built as an extension to an already existing simulation model representing all material routing
within Geisinger Medical Center. The model, which captures all units within the Danville
facility, was created in the simulation modeling program, Simul8.
By including all aspects of material handling flow within the hospital, the model captures
the essence of traffic throughout the GMC facility. This traffic is likely to have a significant
effect on service times of the food delivery system. In particular, system travelers often
experience a longer wait time for elevators during periods of increased traffic. The food delivery
carts rely on the elevators as well as on many of the heavily traveled hallways of the facility.
Therefore, including the general traffic as well as other material handling routing will better
reflect the performance of the system.
Figure 4 provides a partial snapshot of the Simul8 modeling environment. The GMC
model is unique in that it represents the physical structure of the GMC facility. Logic pertaining
to a particular department is contained in a box, such as the Food Service logic shown in Figure 5.
Departmental logic is placed in the model in a location representative of its real-life facility
location. Elevator nodes exist in the model as well and contain logic to allow transportation
objects to traverse floors. In addition, the model contains a node that represents the physical
location of each patient care unit. Finally, there exists a set of logic that represents any actions
taken once a material transport object reaches a location of interest. In total, the model includes
eight support services departments which perform pickup and delivery activities within GMC.
There are 19 inpatient units, 33 outpatient clinics, and 51 ancillary service departments across
eleven floors all of which are included in the model and accessed through a network of hallways
and elevators.
27
Figure 4. Simul8 Modeling Environment
Figure 5. Food Service Logic Modules
28
3.3.1 Modeling assumptions
Several assumptions were made in the development of the food delivery portion of the
model to facilitate model building while allowing for reliable results. The following list provides
the significant assumptions made:
1. The delivery host will mirror the cart usage; therefore, it will be assumed that if there
is a cart to be delivered to patients there will also be a host available to deliver it.
2. There are an unlimited number of delivery resources available; the model will profile
usage of these resources over time.
3. Only the process of delivering meals to patients will be modeled; the process of
collecting the empty trays from patients after they have finished their meal will not
be considered.
4. The scope of the food delivery model will be limited to the delivery process from the
time the food is prepared by the kitchen staff and placed on a cart to the time the
meal is delivered to the patient.
5. Only inpatient units that regularly receive meals delivered from the food service
kitchen will be included in the routing schedule.
The first assumption allows the model to track a single delivery resource representing
both the meal cart and delivery host. This assumption is considered valid because these two
resources must be available together to deliver meals. Therefore, the model will assume that the
number of carts is adequately matched to the number of delivery hosts staffed to deliver meals.
The second assumption allows the model to have access to a cart/delivery host at all
times. This eliminates the situation when a tray must wait for a cart/host before it can be sent for
delivery. By this assumption, the model allows for the analysis to demonstrate the number of
delivery resources required to prevent delays due to a lack of food carts or available delivery
29
hosts. In other words, it will allow for insight on the maximum required number of resources to
ensure that there are always sufficient delivery resources available.
The third and fourth assumptions pertain to the scope of this study. While this model will
only capture the meal delivery processes, a return process, which involves the patient’s empty
trays does take place in the real-world system. These two processes are currently considered
independently of one another and therefore will remain independent in this study, resulting in a
focus on the delivery of meals. In addition, because the process of preparing individual patient
meals is new to GMC, no current data exists to estimate the amount of preparation time required
for each meal. Therefore, the modeling process will not consider this aspect of the process, and
will focus on the routing and delivering of meals to patients.
Finally, the fifth assumption simply eliminates from the scope the delivery of any
meals/food to patients not regularly serviced by the food services department. Although there are
instances where the food service department prepares meals for patients outside its traditional
domain, the occurrence is considered sporadic, and therefore difficult to estimate.
30
Chapter 4
Analysis of Results
4.1 Introduction
This chapter describes the approach taken to analyze the on-demand food delivery system
at GMC. Eight scenarios were tested in the simulation model, each with a different combination
of system parameters. The results of the experiments allowed for confidence in the decision
making regarding operational system parameters based on how stakeholders value the affected
system performance measures.
4.2 Experimental Plan
This section outlines the experimental parameters and performance measures selected to
provide key insights into the food delivery system.
4.2.1 Performance Measures
Several performance measures were used to analyze the on-demand food delivery system,
as outlined in Table 4-1. The performance measures were determined based on stakeholder input.
The main objectives of the research were to understand resource needs to attain acceptable
service levels; therefore, the performance measures reflect these aspects of the food delivery
system model. The GMC Guest Services management team identified a goal delivery time of 45
minutes or less. This goal time specified by GMC includes the meal preparation time and
31
therefore the dispatch, routing, and delivery time should occur in less than 45 minutes to allow
time for the preparation.
To understand how long it takes for a meal to reach the patient from the time it has been
prepared in the kitchen, six performance measures were developed, namely, the service time
performance measure, wait time on cart before routing performance measure, and the percent
delivered beyond 25, 30, 35, and 40 minutes performance measures. A range of times was used
for the “percent delivered beyond” performance measures to allow for an understanding of
service levels depending on the realized food preparation time. By examining the performance
for the entire range, it will be possible to make a more informed decision once there is a better
understanding of how long it will take to prepare the food.
When considering resources, the delivery carts are a key aspect of the delivery model
and, therefore, three performance measures were created to estimate their utilization and the
efficiency with which they were used. Specifically, the cart utilization measure tracks the ratio of
average number of meals on a cart to the capacity of the cart when it leaves for delivery; a high
utilization will signify efficient use of the cart resource, while a low utilization will suggest that
the system is not getting the best use out of the resources available. Furthermore, the maximum
number of carts used over a day and the number of delivery trips made in a day represent how
efficiently the cart and host resources are used. Additional carts required, or a greater number of
delivery trips made, will require more host resources to accompany the extra carts needed. If
scenarios present an opportunity to make fewer trips with fewer carts, that will allow for savings
in resource expenditures.
32
Table 4-1. List of System Performance Measures (bold measures represent key performance measures)
Two performance measures were identified as key: Maximum number of carts used over
a day and Percent of meals delivered after 30 minutes. The maximum number of carts used over
a day was considered a key measure because it allows for an understanding of how many carts are
necessary to keep the system running at high performance. The percent of meals delivered
beyond 30 minutes was considered a key performance measure because it will provide insight
into the possibility of meeting the 45 minute service levels, provided a meal preparation time of
fifteen minutes of less. From this measure, the additional “percent delivered after” performance
measures can be used to understand how service will be affected if the preparation process
requires more or less time. This key performance measure simply gives a middle ground from
which to interpret the patient service level analysis. The pairing of these two key performance
measures is effective for decision making because it considers the balance between resource
usage and patient service levels.
System Performance Measures
Max Number of Carts Used Over a Day
Number of Delivery Trips Made in a Day
Cart Utilization
Service Time
Wait Time on Cart Before Routing
Percent Delivered after 25 minutes
Percent Delivered after 30 minutes
Percent Delivered after 35 minutes
Percent Delivered after 40 minutes
33
4.2.2 Experimental design
The simulation was run using eight different combinations of cart capacities and dispatch
timer settings. Table 4-2 contains each of the combinations tested and analyzed using the
simulation model.
Table 4-2. Experimental Scenarios
The cart capacity settings were chosen based on the available options of food carts for
purchase. The dispatch timer settings were chosen based on operational insight. Specifically,
consideration for the times to travel to and within the various zones was balanced against the need
to wait long enough for the cart to fill with a sufficient amount of meal trays for a given zone.
Given that some units can take more than four minutes to walk to and that hosts spend between
one and two minutes serving a meal to each patient, it was imperative that food not wait on the
cart so long as to compromise the ability to reach the patient in under 45 minutes from the time an
order is placed.
Data were collected on each scenario for a period of 30 days. This provided 30
independent replications to use for statistical analysis and comparison of the different scenarios.
95% confidence intervals were computed on each resulting performance measure using Student’s
t-distribution along with the assumption that the data are normally distributed.
ScenarioDispatch Time
(Minutes)
Cart Capacity
(Trays)
1 8 12
2 8 14
3 8 18
4 10 12
5 10 14
6 10 18
7 12 12
8 12 14
34
4.3 Results
Table 4-3 displays the resulting performance of the system under each combination of
parameters tested. The table contains averages and 95% confidence intervals for each
performance measure.
Table 4-3. Experimental Results
Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI
8 12 17.22 (17.15, 17.29) 16.00 (15.83, 16.17) 242.60 (241.40, 243.80)
8 14 17.20 (17.13, 17.27) 15.93 (15.66, 16.21) 242.70 (241.39, 244.01)
8 18 17.23 (17.17, 17.29) 15.90 (15.72, 16.08) 243.23 (241.64, 244.82)
10 12 19.23 (19.16, 19.30) 14.63 (14.45, 14.82) 206.53 (205.36, 207.70)
10 14 19.31 (19.23, 19.38) 14.64 (14.46, 14.83) 205.00 (203.77, 206.23)
10 18 19.31 (19.23, 19.39) 14.37 (14.18, 14.55) 205.43 (204.39, 206.47)
12 12 20.97 (20.89, 21.04) 13.70 (13.53, 13.87) 179.60 (178.82, 180.38)
12 14 21.20 (21.11, 21.30) 13.27 (13.10, 13.43) 177.77 (176.79, 178.75)
Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI
8 12 0.3613 (0.3597, 0.3629) 4.78 (4.77, 4.80) 10.24 (9.79, 10.69)
8 14 0.3086 (0.3068, 0.3105) 4.80 (4.78, 4.83) 10.13 (9.71, 10.55)
8 18 0.2399 (0.2387, 0.2412) 4.80 (4.78, 4.81) 10.14 (9.69, 10.59)
10 12 0.4235 (0.4210, 0.4259) 5.80 (5.82, 5.77) 19.11 (18.61, 19.61)
10 14 0.3660 (0.3640, 0.3681) 5.83 (5.81, 5.85) 19.61 (19.15, 20.07)
10 18 0.2850 (0.2835, 0.2864) 5.85 (5.83, 5.87) 19.06 (18.44, 19.68)
12 12 0.4878 (0.4856, 0.4899) 6.72 (6.69, 6.76) 27.22 (26.74, 27.70)
12 14 0.4238 (0.4217, 0.4260) 6.81 (6.78, 6.84) 29.1324 (28.67, 29.60)
Minutes Cart Capacity Average 95% CI Average 95% CI Average 95% CI
8 12 2.06 (1.83, 2.29) 0.1645 (0.104, 0.225) 0 (0, 0)
8 14 2.00 (1.78, 2.21) 0.1811 (0.131, 0.232) 0.003 (-0.003, 0.010)
8 18 2.10 (1.92, 2.29) 0.2471 (0.195, 0.299) 0.003 (-0.003, 0.010)
10 12 5.67 (6.02, 5.32) 0.9099 (0.792, 1.028) 0.061 (0.026, 0.095)
10 14 6.08 (5.78, 6.38) 1.2301 (1.080, 1.380) 0.117 (0.073, 0.161)
10 18 5.97 (5.59, 6.35) 1.2742 (1.098, 1.450) 0.199 (0.129, 0.270)
12 12 10.79 (10.41, 11.16) 2.4365 (2.258, 2.615) 0.231 (0.175, 0.288)
12 14 12.04 (11.58, 12.49) 3.1487 (2.845, 3.448) 0.434 (0.310, 0.558)
Parameters
Parameters
Parameters
Percent delivered after
35 min
Percent delivered after
30 min
Service Time Max Number of Carts Number of Delivery Trips
Cart UtilizationWait Time on Cart
Before Routing
Percent delivered after
25 min
Percent delivered after
40 min
35
Several trends are present in the data. First, as the dispatch timer increases, it is apparent
that the cart utilization and service time increase, while the maximum number of carts used over a
day, the number of delivery trips made, and the service level decrease. Additionally, the results
show that as the cart capacity increases, the cart utilization decreases. These trends reveal a broad
theme within the food delivery system: a trade-off exists between patient service and efficient use
of resources. The results also show that for any given scenario, dispatch to delivery time can take
between 17.15 and 21.3 minutes on average, leaving between 23.7 and 27.85 minutes to prepare
the meal for delivery. When focusing solely on patient service, the eight minute dispatch timer
provides the best performance in terms of percent of meals delivered beyond each of the time
intervals of interest. Finally, it is important to note that there were few instances where meals
were delivered beyond 40 minutes. These results suggest that given a reasonably efficient meal
preparation process, the 45 minute service time goal set by management is achievable and can be
further improved upon depending on which parameter settings are chosen and how much time the
meal preparation process requires.
A closer examination of the resulting cart utilization for each of the scenarios reveals that
a cart capacity of twelve meal trays provides the highest utilization for each of the three dispatch
timer settings. Table 4-4 shows the average number of carts filled to capacity for each of the
eight scenarios. The table demonstrates that when using a cart capacity of twelve trays, the cart
fills to capacity more often than when using a larger cart capacity, allowing for better use of the
resource. Furthermore, the results in Table 4-3 suggest that the cart utilization is the only
measure significantly affected by a change in cart capacity. For this reason, the three options
with a cart capacity of twelve trays and each of the three dispatch timer settings were given the
most consideration for recommendation. Visuals of the resource performance measures and
service performance measures for the twelve tray cart scenarios can be found in Figure 6 and
Figure 7, respectively. The trends in the two plots further emphasize the service-resource trade-
36
off discussed above. As the dispatch timer increases, the results show an improvement in the
efficient use of resources; however, the factors measuring patient service perform worse as the
timer length grows.
Table 4-4. Average Number of Carts Filled to Capacity for Each Scenario
Figure 6. Resource Performance Measures Plot for Twelve Tray Cart Scenarios
Dispatch Timer Cart Capacity
Average Number
of Carts Filled to
Capacity
8 12 1.13333
8 14 0
8 18 0
10 12 5.6667
10 14 0.93333
10 18 0
12 12 12.5667
12 14 4.367
16.00
242.60
36.1306 14.63
206.53
42.3489 13.70
179.60
48.7761
0.00
50.00
100.00
150.00
200.00
250.00
300.00
Max Number of Carts Number of Delivery Trips Cart Utilization (as apercentage)
Resource Performance Measures 12 Tray Carts
8 Minutes 10 Minutes 12 Minutes
37
Figure 7. Service Performance Measures Plot for Twelve Tray Cart Scenarios
Figure 7 can also provide assistance in planning for food preparation times. Logically, as
preparation time increases, the time to available to dispatch, route, and deliver meals decreases.
From Figure 7, it becomes clear that the service level quickly decreases as more preparation time
is required. For example, if meals only require five minutes to prepare, the percent of meals
delivered after 40 minutes is between 0 and 0.231% depending on the dispatch timer setting. This
means that greater than 99% of meals will achieve the order-to-delivery time goal of 45 minutes.
By contrast, if food preparation takes twenty minutes, the percent of meals delivered after 25
minutes suggests that between 10.24 and 27.22% of meals may be delivered beyond the 45
minute goal because it becomes much more unlikely that meals can be dispatched, routed, and
delivered in less than 25 minutes.
Whereas the previous results provided insight into the maximum number of carts used
over a given day, it does not provide insight into how often those maximum numbers of carts are
in use throughout the day. Figure 8 provides a visual representation of this information. For each
17.22
4.78
10.24
2.06 0.1645 0
19.23
5.80
19.11
5.67
0.9099 0.061
20.97
6.72
27.22
10.79
2.4365 0.231
0.00
5.00
10.00
15.00
20.00
25.00
30.00
Service Time Wait Time onCart Before
Routing
Percentdelivered after
25 min
Percentdelivered after
30 min
Percentdelivered after
35 min
Percentdelivered after
40 min
Service Performance Measures 12 Tray Carts
8 Minutes 10 Minutes 12 Minutes
38
dispatch timer setting, the chart provides a profile of the percent of time a given number of carts
is in use throughout a day. While, for example, the eight minute dispatch timer experiences a
count of seventeen carts in use for a period of time in a day, it is for less than 0.01% of the time
that food services is delivering meals to patients. This again emphasizes the trade-off between
resources and service: a balance must be struck between the need to have a cart available to
deliver food, and the acceptable limit of time that a meal may take longer to be delivered because
it is waiting for a cart.
Figure 8. Cart Usage Profile Plot for each Twelve Tray Cart Scenario
Figure 9 displays yet another view of the delivery resource data analyzed for each of the
three twelve tray cart scenarios. This plot shows the average maximum number of carts in use
throughout the meal delivery operation hours for each dispatch timer setting. In any given hour,
more carts are in use throughout the system with the eight minute dispatch timer, and the least
number of carts are in use with the twelve minute dispatch timer. Additionally, three peaks are
visible in the plot around traditional meal times (8am, 12pm, and 6pm). Although the number of
39
carts available for use throughout the day will likely remain constant, the number of delivery
hosts staffed throughout the day will depend on meal order demand. This plot suggests that host
staffing levels should be increased around traditional meal times and can be cut back during the
off-peak hours. The use of part-time hosts may be useful to accommodate these peaks in demand.
Figure 9. Average Number of Carts in Use throughout a Day for all Twelve Tray Cart Options
4.4 System Limitations
The logic and simulation modeling undertaken for this research has proven valuable in
providing insight into the operational abilities and trade-offs of the on-demand food delivery
system; however, it is important to outline the limitations of the system to allow for appropriate
use of the data. Specifically, resource assumptions and the scope of the model must be taken into
consideration when using the results for operational decision making.
0
2
4
6
8
10
12
14
16
18
Av
era
ge
Nu
mb
er
of
Ca
rts
In U
se
Hour
Average Number of Carts in Use Throughout a Day
12 Tray Carts
8 Minutes 10 Minutes 12 Minutes
40
As mentioned in Section 3.3.1, the model represents delivery hosts in the same way it
represents delivery carts: if there is a cart ready for delivery, it is assumed there will be a host
available to route it. While this assumption will still allow for insight into the needs of both
delivery cart resources as well as host resources, it does not account for the human factors
associated with delivery hosts. There are no shifts or break schedules incorporated into the
model, and, therefore, additional hosts may be required to account for employee downtime during
breaks and shift changes.
4.5 Recommendations
Based on the results of the eight scenarios tested and analyzed in the simulation model, it
is recommended that GMC purchase carts with a capacity of twelve trays for use in the food
delivery system. This will allow for the best cart utilization as compared with the fourteen and
eighteen tray carts. Choosing the twelve tray carts will also not greatly affect the patient service
levels when compared with the other options, as seen in Table 4-4. The timer on the carts with
larger capacity expires more often before the cart is full and therefore service time is not affected
because the carts leave for delivery regardless of how full they are.
When choosing the dispatch timer, it is imperative to consider whether any sacrifice can
be made in patient service to save in resource expenditures. Furthermore, it is important to
consider how service will be affected with the realization of longer or shorter meal preparation
times. If meal delivery beyond 45 minutes cannot be tolerated, it is recommended that an eight-
minute dispatch timer be used. This will help ensure that even with food preparation time
incorporated into the system, meals will more likely be delivered under the 45 minute time
constraint. If some sacrifice in service is acceptable, a ten-minute dispatch timer will provide a
better balance between efficient use of resources and patient service levels, provided meals take
41
fifteen minutes or less to prepare. This is shown through the lower number of delivery trips and
lower number of carts (and hosts) needed throughout the day while serving only 5.67% of meals
beyond 45 minutes (given a 15-minute meal preparation time). If meals take longer than fifteen
minutes to prepare, it is recommended that an eight-minute dispatch timer be used to keep the
patient order-to-delivery time under 45 minutes; however, as shown in the results, as much as
10.24% of meals will be delivered late in this scenario.
42
Chapter 5
Conclusions and Future Research
This research has demonstrated the use of simulation modeling to make informed
operational decisions for a new on-demand delivery system at Geisinger Medical Center in
Danville, PA. The simulation model has captured the dispatch, routing, and delivery process of
hot meals to inpatients, reflecting the system performance that can be expected given eight
different operational strategies. The operational strategy that allowed for the best balance
between resource utilization and patient service levels utilized delivery carts with a capacity for
twelve trays, and a dispatch timer setting of ten minutes, provided a meal preparation time of less
than fifteen minutes. The results suggest that this policy will allow for approximately 94.3% of
patients to receive their meals within 45 minutes of placing an order. If meals are expected to
take more than fifteen minutes to prepare, a policy using delivery carts with a capacity for twelve
trays and a dispatch timer setting of eight minutes will provide the best patient service levels of
89.67% percent of meals delivered within 45 minutes of placing an order, at the cost of less
efficient use of resources. The results also provide an expectation for the number of carts
needed, as well as information to assist planning for host staffing levels depending on the
operational policy chosen. Finally, the results confirm that segregating the hospital facility into
three spatial zones allows for efficient delivery service to patients.
There are several opportunities for future research involving the on-demand food delivery
model. The simulation model, in particular, presents many opportunities for expansion. For
example, host resources can be modeled independently from delivery carts. This would allow for
the inclusion of employee breaks and shift changes to better represent the staffing needs of host
resources to meet desired service levels. Additionally, estimates regarding meal preparation time
could lead to the ability to incorporate this process into the model. This would provide a better
43
estimate around patient service time from order to delivery of meals because it could incorporate
the variability inherent in the meal preparation process.
GMC has initially decided to operate the on-demand delivery process between the hours
of 6:30am and 9:30pm. It is common, however, for patients to be admitted later in the evening
and need to eat a meal. Further analysis of admissions data could help validate that the current
operating hours are best-suited to accommodate the majority of patients requiring meals
throughout the day, or may suggest that an adjustment in operation hours would better serve the
needs of patients. In addition, once the on-demand delivery system has been implemented,
additional data can be collected on the patient meal order distribution to ensure that the model
still accurately reflects the actual events of the system.
Finally, this research has shown the operational insight provided by simulation modeling
for the food delivery process. This work can be expanded to help design an efficient process for
the return of dirty trays to the kitchen. Currently, GMC’s food service operational policies dictate
that the return of dirty trays be a separate process using separate resources and separate routing
schedules. Vehicle routing research suggests that these two processes may be combined to create
efficiencies. By incorporating the return process into the model, alternative return strategies can
be tested, including those that take advantage of the food carts and delivery hosts who are
currently returning empty handed to the kitchen after delivering meals. Exploring these
alternative strategies may result in opportunities to make both the delivery and return processes
more efficient.
44
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