Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost
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Transcript of Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost
Integrated Production Scheduling and Vehicle Routing Problem to Minimum Total Cost
Student: Bing-Yu GaoStudent ID: M10021024Advisor: Chin-Yao Low, Ph.D.
Outline
• Introduction– Background– Motivation
• Literature review– HVRP– Integration problem (Type I & Type II)
• Research method– MILP/ and verification
• Conclusions
Background
• Pull based– How to response customer at once
• In the Past year:– Production scheduling .– Vehicle routing planning.
• But most of literatures of above are discussed individually.
‧Push based supply chainForecast accurately
Background
Individual IntegrationAdvantage 1. It can make the best of object
of production scheduling.
2. It can make the best of object of VRP problem.
1. The global optimal solution can be found.
2. Because the mutual cost will be considered Integrally.
Defect The mutual cost considerations will be ignored.
The algorithm will be more complexly.
– Comparison as following table:
Motivation
• Based on above description, 2 motivations are presented as follows:
– The plant needs more effect that pick goods and delivering plan.
– Most of problems are discussed individually by literatures.
Research process
Theme direction decided
conclusions
Similar literatures review
Theme decidedSingle machine scheduling
HVRP literature review
Integrated Scheduling and Delivering
Include type I and type II
Literature review
Research method
comparison results
Formula MILP model
Meta-algorithm
Literature review – VRP with heterogeneous fleet
Variety of the meta-algorithm Time windows year reference
Heuristic algorithm x 1984 Golden et al.
Tabu search x 1996 Osman and Salhi
Tabu search x 1999 Gendreau et al.
Tabu search x 2002 Wassan and Osman
B & B v 2007 Choi and tcha
Scatter search v 2007 Belfiore & Favero
Literature review – VRP with heterogeneous fleet
Variety of the meta-algorithm Time windows year reference
Heuristic algorithm v 2007 Dell’Amico et al.
EM-SA v 2008 Oili Bräysy et al.
Memetic algorithm X 2009 Christian Prins
-- V -- This research
Literature review – Integrated Scheduling and Delivering
• Type I: Single machine or parallel machine and deliver to single customer with multiple orders.
Plant
Customer
How many times of delivering?How to schedule?When to deliver?ANDFixed distance.
Literature review – Integrated Scheduling and Delivering
meta-algorithm M D Object year reference
Heuristic algorithm1 1
Min makespan 2004 Chang & Lee2 11 2
Heuristic algorithm 1 1 min delivery cost and mean of travel time 2005 Chen &
VairaktarakisHeuristic algorithm 2 1 Min makespan 2009 Su et al.
Heuristic algorithm 1 1Min weighted sum of
the last arrival timeWith independent setup time
2010 T.C.E. Cheng
Heuristic algorithm 1 1 Min makespan 2011 Liu & LuTabu search
Long-term memory 1 1 min Travel time, and lateness time 2012 Condotta et al.
M: number of Parallel Machines.(1 denotes no parallel machine)D: number of Demands.
Literature review – Integrated Scheduling and Delivering
• Type II: Single machine and deliver to multiple customers with multiple orders but release one time.
Plant
Customer
Customer
Customer
Customer
How to do the production schedule?
Literature review – Integrated Scheduling and Delivering
• Type II: Single machine and deliver to multiple customers with multiple orders but release one time.
Plant
Customer
Customer
Customer
Customer
When to deliver?How to solve the VRP problem?
Literature review – Integrated Scheduling and Delivering
meta-algorithm M V Object year referenceTabu search
short-term memory P 1 Max profit of supplier(time windows and travel time) 2005 Garcia &
LozanoDynamic
programming P 1 Min weighted sum of Delivery time and total distribution cost 2005 Chen &
Vairaktarakis
Heuristic algorithm 1 1 Max profit of supplier 2009 Huey-Kuo Chen
Dynamic programming 1 1
Min weighted sum of the last arrival time
With independent setup time2010 T.C.E. Cheng
-- 1 T Min total cost With fixed cost of vehicle -- This
Research
M: number of Parallel Machines.(1 denotes no parallel machine)V: Variety of the vehicle capacity.(1 denotes only one type)
Research method– Question description
Plant0
Customer4
Customer3
Customer2
Customer1
Ct01Ct10
d2
Ct23
Research method– Another Question restrict
• All of out of control aren’t considered whether conveyer or vehicle.
• The state of road aren’t considered.• All orders are released on time zero.• All customer site can be visited only once, and
all vehicles back to plant are needed.
Research method– Question description
• Example:
2 4 1 3
0
Production scheduling
stage
VRPstage
02
Time
0 04
e2 l2e4 l4
Research method– Question description
• If the routing costs are considered, then it may give an integration solution as follow picture.
2 4 1 3
0
Production scheduling
stage
VRPstage
2
Time
04
e2 l2e4 l4
Research method– Question description
• How to scheduling involve HVRP problem is this research want to present mainly.
? … ? ?
0
Production scheduling
stage
VRPstage
?
Time
0
0 0? …
…
Research method– Formula the MILP model
Research method– Formula the MILP model
Research method– Formula the MILP model
Research method– Formula the MILP model
Min
Total cost = fixed cost + travel cost + delay penalty + early penalty
Flow constraints
Connection and subtour-breaking constraints
Vehicle capacity constraints
Research method– Formula the MILP model
• Production stage
Scheduling constraints, and the sequence only has one combination.
Production constraints
When customer i is processed before j then do the above constraint.
Research method– Formula the MILP model
• Transportation stage
Arrival time calculation constraints.
Soft time windows constraints.
Research method– Formula the MILP model
• Nonnegative constraints:
All decision variables are nonnegative.
But this model has some problems need to modified.In the next chapter will describe in detail.
Research method– MILP model verification
Customer Plant 1 2 3 4
Ei 0 189 198 150 168
Li 630 225 227 180 190
Type of vehicle 1 2 3
Fixed cost 10 15 18
Cij Plant 1 2 3 4
Plant 0 2 4 5 8
1 2 0 7 6 9
2 4 7 0 3 5
3 5 6 3 0 8
4 8 9 5 8 0
Customer Plant 1 2 3 4
EPTi 0 15 7 5 8
LPTi 20 14 9 8 6
Type of vehicle 1 2 3
Capacity 10 50 70
Customer 1 2 3 4
di 50 30 20 15
ti 2 8 2 4
Ctij plant 1 2 3 4
plant 0 17 15 13 15
1 17 0 19 18 21
2 15 19 0 15 8
3 13 18 15 0 6
4 15 21 8 6 0
Customer 1 2 3 4
si 3 2 8 9
Research method– MILP model verification
• The scheduling result as follows:– 4-3-1-2
• The VRP result as follows:– 0-2-0 use type 2– 0-3-4-1-0 use type 3
Research method– MILP model verification
• All completion of the production time as follows:•
• Hand calculations:– Demands of customer 4: d4*t4 = 60– And as follow is 3, 20*2 + 60 = 100– 1 is 20*2 + 100 = 140– And the customer 2 is 380.
Customer 4 3 1 2
Completion of the production time 60 100 140 380
Research method– MILP model verification
Customer 3 4 1 2
Arrival time 176 190 225 395
• All Arrival time as follows:
• Hand calculations:• Customer 3:140+13=153→176 (it can be accepted)
• At the same route, customer 4:176 + c34+ s3 =190• Customer 1: 190 + 8 + 18 = 216→225(Final maturity date)
• And the customer 2 is another route: Completion time is 380 + C02 = 395
Research method– MILP model verification
• Hand calculations the object as follows:• Penalty cost : – only customer 2 is delayed 395-227=168 units• 168*penalty cost = 168*9=1512
– Route cost is c03+ c34 + c41+ c10 + c02 + c20 =32– Fixed cost = 15+18=33– Total cost = 1512+32+33=1577
Conclusions
• The model still has shortage, and needs to be modified.
• Design of meta-heuristic algorithm:– Literature review– Design and application to solve in this problem