1.Meaning of Operations Research

Operations research OR means to apply scientific and mathematical methods for decision making and problem solving.

OR does not provide decisions else it provides quantitative data to the managers. The managers use this data for making decisions.

OR tries to find better solutions to different problems. Hence, it is used to solve complex management problems.

OR helps to take decisions about operations and production.

OR was first used during the Second World War by England to solve their complex war problems. England made OR teams. These teams included expert mathematicians, statisticians, scientists, engineers, etc. These OR teams were very successful in solving England's war problems. Therefore, United States of America (USA) also started using OR to solve their war problems. After the war, soon industries and businesses also started using OR to solve their complex management problems.

Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

Analytical methods used in OR include mathematical logic, simulation, network analysis, queuing theory , and game theory . The process can be broadly broken down into three steps.

1. A set of potential solutions to a problem is developed. (This set may be large.)

2. The alternatives derived in the first step are analyzed and reduced to a small set of solutions most likely to prove

workable.

3. The alternatives derived in the second step are subjected to simulated implementation and, if possible, tested out in

real-world situations. In this final step, psychology and management science often play important roles.

QUESTION-1

The essential characteristics or features of Operation Research

1. Creating a Model : OR first makes a model. A model is a logical representation of a problem. It shows the relationships between the different variables in the problem.

2.[1.] Shows Important Variables : OR shows the variables which are important for solving the problem.

3.[2.] Symbolic representation of Model : its variables and goals are converted into mathematical symbols. These symbols can be easily identified, and they can be used for calculation.

4.[3.] Achieving the Goal : The main goal of OR is to select the best solution for solving the problem.

5.[4.] Quantifying the Model : All variables in the OR model are quantified. That is, they are converted into numbers. This is because only quantified data can be put into the model to get results.

6.[5.] Using Mathematical Devices : Data is supplemented with mathematical devices to narrow down the margin of error.

7.[6.] Use of Computer : The main focus is on decision-making and problem solving. It makes use of computer to solve large and complex problems.

8.[7.] Inter disciplinary : OR is interdisciplinary, because it uses techniques from economics, mathematics, chemistry, physics, etc.

9.[8.] Highest Efficiency : The main aim of OR is to make decisions and solve problems. This results in the highest possible efficiency. It gives Quantitative solution.

QUESTION-2 Limitations of Operations Research

1. Costly   : Operations Research (OR) is very costly. This is because OR makes mathematical models for taking decisions and solving problems. The company has to make various models for solving different problems. All this increments the cost.

2. Not Realistic   : OR experts make very complex models for solving problems. These models may not be realistic. Hence, they may not be useful for real-life situations.

3. Complex   : OR is very complex concept. It is very difficult for an average manager to understand it. Therefore, most managers do not use OR techniques.

QUESTION-3What is PERT?

or

What does Program Evaluation and Review Technique (PERT)mean?

Program evaluation and review technique (PERT) is a technique adopted by organizations to analyze and represent

the activity in a project, and to illustrate the flow of events in a project. PERT is a method to evaluate and estimate

the time required to complete a task within deadlines.

PERT serves as an management tool to analyze, define and integrate events. PERT also illustrates the activities

and interdependencies in a project. The main goal of PERT is to reduce the cost and time needed to complete a

project.

PERT was developed in 1950 by the U.S. Navy during the Cold War and is intended for large projects, which are:

Complex

Require a series of sequential tasks

Performed in parallel with other projects

PERT planning usually involves the following steps:

1. Identifying Tasks and Milestones: Every project involves a series of required tasks. These tasks are listed in a

table allowing additional information on sequence and timing to be added later.

2. Placing the Tasks in a Proper Sequence: The tasks are analyzed and placed in a sequence to get the desired

results.

3. Network Diagramming: A network diagram is drawn using the activity sequence data showing the sequence of

serial and parallel activities.

4. Time Estimating: This is the time required to carry out each activity, in three parts:

1. Optimistic timing: The shortest time to complete an activity

2. Most likely timing: The completion time having the highest probability

3. Pessimistic timing: The longest time to complete an activity

5. Critical Path Estimating: This determines the total time required to complete a project.

PERT not only determines the time to complete a specific software development activity, but also determines the

cost.

QUESTION-4critical path method (CPM)Part of the Project management glossary:

The critical path method (CPM) is a step-by-step technique for process planning that defines critical and non-critical tasks with the goal of preventing time-frame problems and process bottlenecks. The CPM is ideally suited to projects consisting of numerous activities that interact in a complex manner.

In applying the CPM, there are several steps that can be summarized as follows:

Define the required tasks and put them down in an ordered (sequenced) list.

Create a flowchart or other diagram showing each task in relation to the others.

Identify the critical and non-critical relationships (paths) among tasks.

Determine the expected completion or execution time for each task.

Locate or devise alternatives (backups) for the most critical paths.The CPM was developed in the 1950s by DuPont, and was first used in missile-defense construction projects. Since that time, the CPM has been adapted to other fields including hardware and software product research and development. Various computer programs are available to help project managers use the CPM.

QUESTION-5

Differentiate between probabilistic and deterministic models?

A deterministic system is one in which the occurrence of all events is known with

certainty. If the description of the system state at a particular point of time of its

operation is given, the next state can be perfectly predicted.

 

A probabilistic system is one in which the occurrence of events cannot be perfectly

predicted. Though the behavior of such a system can be described in terms of

probability, a certain degree of error is always attached to the prediction of the

behavior of the system.

You have different mathematical models to suit various situations. Linear Programming is a deterministic model because here the data used for cost/ profit/ usage/ availability etc. are taken as certain. In reality these may not be certain but still these models are very useful in decision making because 

1. It provides an analytical base to the decision making2. The sensitivity of performance variables to system parameters is low near optimum.3. Assuming a situation to be deterministic makes the mathematical model simple and easy to handle.

But if the uncertainty level is high and assuming the situation to be deterministic will make the model invalid then it is better to use probabilistic models. Popular queuing models are probabilistic models as it is the uncertainty related to arrival and service that form a queue.

QUESTION-6 explain the assumption of proportionality additivity in lp models

1. The constraints and objective function are linear.o This requires that the value of the objective function and the response of each resource

expressed by the constraints is proportional to the level of each activity expressed in the variables.

o Linearity also requires that the effects of the value of each variable on the values of the objective function and the constraints are additive. In other words, there can be no interactions between the effects of different activities; i.e., the level of activity X1 should not affect the costs or benefits associated with the level of activity X2.

QUESTION-7 define key column and key row in simplex method

10. Key column: The column with the largest positive / negative index number. It indicates

the Entering variable in the Basis.

 11. Key row: The row with the smallest positive ratio found by dividing Quantity column values by

Key column values for each row. It indicates the Exiting variable from the Basis.

3 2 0 0 0

Base

Cb

P0

P1

P2P3

P4

P5

P3

0 2 0 1/3 1 0

-2/3

Key row

P4

026

0 7/3 0 1

-2/3

P1

3 8 1 1/3 0 01/3

Z24

0 -1 0 0 1

Key column

QUESTION-8 define dynamic programming

Dynamic Programming is an approach developed to solve sequential, or multi-stage, decision problems.it is a Method for problem solving used in math and computer science in which large problems are broken down into smaller problems. Through solving the individual smaller problems, the solution to the larger problem is discovered.

Dynamic programming (DP) models are represented in a different way than other mathematical programming models. Rather than an objective function and constraints, a DP model describes a

process in terms of states, decisions, transitions and returns. The process begins in some initial state where a decision is made. The decision causes a transition to a new state. Based on the starting state, ending state and decision a return is realized. The process continues through a sequence of states until finally a final state is reached. The problem is to find the sequence that maximizes the total return.

QUESTION-9

define the situation in which replacement is necessary operation research

FIRST Reasons for replacement1. Technological development2. Poor performance over years3. Unable to meet the required demandsSECOND Reasons for replacement1. Deterioration2. Obsolescence3. Technological development4. InadequacyModel1:“Replacement of items whose maintenance Cost increases with time and thevalue of the money remains constant during the period”Model 2: “replacement of items whose maintenance cost increases with timeand value of money also changes with time”.Model 3: “Group Replacement policy”

Question-10What is the purpose for maintaining an inventory system in organization?

Inventory systems contain detailed records of the products, quantities and stock locations of the company's assets. The primary purpose of an inventory system is to keep an accurate record of stockroom supplies. The reasons to maintain accurate inventory records includes

1. Financial accounting,

2. Customer order fulfillment,

3. Stock replenishment

4. Maintaining the ability to locate specific an item.

1. Inventory on the Balance Sheet

The primary reason to maintain an inventory system is to keep accurate records of the company's assets. Companies are required to ensure that inventory balances reported on the balance sheet

reflect the true value of products in stock.

Inventory Accuracy for Stock Replenishment

By keeping an accurate record of stock on hand, the store's inventory replenishment system will maintain desired inventory levels.

Example: As shoes are purchased and scanned out of stock, the inventory replenishment system places re-stocking orders from the distribution center. When inventory is not accurate, the inventory system may errantly believe that stock is on hand. Such inventory inaccuracy causes the inventory control system to not re-order needed supplies and may result in stock-outs and lost sales.

Inventory to Support Sales

Companies invest in inventory to make product readily available to meet customer demand. Imagine shopping at a shoe store that did not have any shoes in stock. Customers would leave the store, sales would fall and the store would close.

Through proper maintenance of the inventory system, the store keeps accurate inventory records, which in turn keep the shelves stocked with the latest styles and sizes customers need. To ensure the inventory system is accurate, the staff must properly transact all inventory receipts, returns and sales in the inventory system.

Locating Inventory

Maintaining accurate inventory locations within the inventory system allows employees to quickly go to a specified storage . to find the product needed. Organizing and maintaining accurate records of the product, quantity on hand and storage location allows employees to quickly access inventory.

Inventory cost types: In managing inventories, To determine cost, the firm should determine the optimum level

of inventory. Excessive stock of inventories increases the cost of maintaining inventory imbalanced for the company. There are mainly two types of costs are associated with holding inventory when a company is willing to maintain its optimum level of inventory. These costs are:

Ordering Cost: The term ordering cost is used in case of raw materials and supplies and includes the entire costs of acquiring raw materials. These costs incurred in the following activities for example, requisitioning, purchase ordering, transporting, receiving and inspecting. Ordering costs increase in proportion to the number of orders placed. Ordering costs increase with the number of orders and thus the more frequently the inventory is acquired, the higher the firm’s ordering costs. Therefore, firms should be considering the ordering cost when they placed orders and obviously they try to minimize ordering cost as low as possible.

Carrying Costs: Costs incurred for maintaining a given level of inventory are called carrying costs. They include storage, insurance, taxes, deterioration and also obsolescence. The storage costs comprise of storage space alternatively it is called warehousing costs, store handling costs and administrative costs incurred in recording and providing special facilities such as safeguarding for warehousing. Carrying costs vary based on the inventory volume. This cost is totally reverse from the ordering costs. Carrying cost declines as volume of inventory increases. The economic size of inventory would thus depend on trade-off between carrying costs and ordering costs.

define travelling salesman problem

QUESTION-11define simulation.why it is necessary for solving operational research problems

Simulation is a modeling and analysis tool widely used for the purpose of designing, planning, and control of manufacturing systems. Simulation in general is to pretend that one deals with a real thing while really working with an imitation. In operations research, the imitation is a computer model of the simulated reality. The task of executing simulations provides insight and a deep understanding of physical processes that are being modeled. 1.The phenomenal growth of simulation throughout industry and particularly within the Department of Defense (DOD) has led to a growing demand for simulation professionals to develop models and modeling tools, and to manage large and complex simulation-based projects.

2 In the case of manufacturing and service fields where discrete-event simulation is the predominant Approach , many of these skills could be obtained as part of a degree program in operations research , Management science or industrial engineering.

3 In a similar manner, expertise in communications or radar simulation might be developed by recruiting and retraining generalists from physics or electrical engineering.

4. To determine how different the modelling process followed by DES and SD modellers is.

5. To establish the differences and similarities in the modelling approach taken by DES and SD modellers in each stage of simulation modelling.

6. To assess how different DES and SD models of an equivalent problem are from the users’ point of view.  

Write steps in monte carlo simulation:

The Monte-Carlo method also known as monte carlo simulation

The basis of Monte-Carlo technique is random sampling of variables values from a distribution of that variable. Monte-

Carlo takes the use of sampling methods to approximate the value of non-stochastic variables.

The main steps of this method are listed below

Step 1 - To get a general idea of the system, firstly draw a flow diagram of the system

Step 2 - Then, take accurate sample observations to choose some suitable model for the system. In this step, calculate

the probability distributions for the variables of our interest.

Step 3 - Then, change the probability distribution to cumulative distribution function

Step 4 - A series of random numbers is now chosen with the help of random number tables

Step 5 - Establish the sequence of values of variables of interest with the sequence of random numbers getting in step 4.

Step 6 - Lastly create standard mathematical function to the values obtained in step 5

QUESTION-12 three main reasons for using a simulation rather than actually doing something. They are

Cost : Using a simulation can be much cheaper than actually doing something. Crashing cars to see how the passengers (replaced by dummies) are affected by an impact would be very expensive. Many cars would be destroyed. Simulating this on a computer is far cheaper.

Safety : Some things are very dangerous. Finding out what would happen if a cooling system failed in a nuclear reactor by actually turning the system off would be highly dangerous. Using physical laws the effect could be predicted by a computer simulation.

Feasibility : There are some things that humans simply can not do. It would be interesting to be able to travel through a human body to see how the organs in the body worked. Unfortunately a human simply can't do this. But a human can use a simulation which shows what it would be like to travel around a body.

QUESTION-13Group Replacement TheoryThere are certain items which do not deteriorate but fail completely after certain amount of

use. These kinds of failures are analysed by the method called as ” group replacement theory”. Here, large numbers of items are failing at their average life expectancy. This kind of items may not have maintenance costs as such but they fail suddenly without any prior warning. Also, in case of sudden breakdowns immediate replacement may not be available. Few examples are fluorescent tubes, light bulbs, electronic chips, fuse etc.

Let’s consider the example of street lights. We often see street-lights being repaired by the corporation staff using extendable ladders. If a particular light is beyond repairs, then it is replaced. This kind of policy of replacement is called as ‘replacement of items as-and-when they fail’ or ‘Individual Replacement’. On the other hand, if all the street lights in a particular cluster are replaced as and when they fail and also simultaneously in groups, then the policy is called as ‘Group Replacement’. It should be noted that, group replacement does involve periodic simultaneous replacements along with individual replacements in between.

QUESTION-14 Unbounded Solution in simplex method or linear programming

In some LP models, the values of the variables may be increased indefinitely without violating any of the constraints, meaning that the solution space is unbounded in at least one direction. As a result, the objective value may increase (maximization case) or decrease (minimization case) indefinitely. In this case, both the solution space and the optimum objective value are unbounded. Unboundedness points to the possibility that the model is poorly constructed. The most likely irregularities in such models are that one or more nonredundant constraints have not been accounted for, and the parameters (constants) of some constraints may not have been estimated correctly. The rule for recognizing unboundedness is that if at any iteration all the constraint coefficients of any non basic variable are zero or negative, then the solution space is unbounded in that direction. If, in addition, the. Objective coefficient of that variable is negative in the case of maximization or positive in the case of minimization, then the objective value is unbounded as well.

QUESTION-15define degeneracy and infesibility in simplex method in operation research

A definition of the term "degeneracy" is presented. It refers to the situation in which a linear-programming problem has a basic feasible solution with at least one basic variable equal to zero. If the given problem is degenerate, then an extreme point of the convex set of solutions may correspond to several feasible bases.

Infeasible Solution

Infeasibility is a condition when constraints are inconsistent (mutually exclusive) i.e., no value of the variable satisfy all of the constraints simultaneously. There is not unique (single) feasible region. It should be noted that infeasibility depends solely on constraints and has nothing to do with the objective function.

If in the final table, an artificial variable appears in the final solution with a positive value, that means that the

problem does not have any feasible solution.

QUESTION-16 what are the characteristics of a good model

A good model has to be as close to the real system as possible; at the same time, it should not be too difficult or

complicated to use for analyzing the behavior of the system. 

That means, a good model should be realistic enough so that the results of the model can give a fairly realistic

description of how the system would behave under certain changes. At the same time, a good model should also

be easy to use. 

Models must be both tractable, capable of being solved, and valid, representative of the original situation. These dual goals are often contradictory and are not always attainable. It is generally true that the most powerful solution methods can be applied to the simplest, or most abstract, model.

QUESTION-17 describe the cost relevant for crashing of networks

One important extension to the basic network analysis technique relates to project cost/ project time tradeoff.

In this extension to the basic method we assume that, for each activity, the completion time can be reduced (within limits) by spending more money on the activity. Essentially each activity now has more than one possible completion time (depending upon how much money we are willing to spend on it).

This use of cost information is the CPM technique.

A common assumption is to say that for each activity the completion time can lie in a range with a linear relationship holding between cost and activity completion time within this range (as illustrated below).

Reducing an activity completion time is known as "crashing" .

QUESTION-18 transportation problem 

A programming problem that is concerned with the optimal pattern of the distribution of goods from several points of origin to several different destinations, with the specified requirements at each destination.

Transportation Problem 

a problem concerned with the optimal pattern of the distribution of units of a product from several points of origin to several destinations.

Suppose there are m points of origin A1, . . .,Ai, . . ., Am and n destinations B1, . . .,Bj, . . .,Bn. The point Ai(i = 1, . . .,m) can supply ai units, and the destination Bj(j = 1, . . ., n) requires bj units. It is assumed that

The cost of shipping a unit of the product from A¡ to B, is c¡¡. The problem consists in determining the optimal distribution pattern, that is, the pattern for which shipping costs are at a minimum.

Moreover, the requirements of the destinations Bj, j = 1, . . ., n, must be satisfied by the supply of units available at the points of origin Aj, i = 1, . . .,m.

If xij is the number of units shipped from Ai to Bj, then the problem consists in determining the values of the variables xij, i = 1, . . ., m and j = 1, . . ., n, that minimize the total shipping costs

under the conditions

(3) xij ≥ 0 i = 1,..., m and j = 1,..., n

Transportation problems are solved by means of special linear programming techniques.

QUESTION-19mathematical model Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively.Eykhoff (1974) defined a mathematical model as 'a representation of the essential aspects of an existing system (or a system to be constructed) which presents knowledge of that system in usable form'.Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models.Types of mathematical modelAccording to how much a priori information is available of the system.

1. black box models:A black-box model is a system of which there is no a priori information available.

2. white box modelsA white-box model (also called glass box or clear box) is a system where all necessary information is available.

3.Linear model:In a mathematical programming model, if the objective functions and constraints are represented entirely by linear equations, or all the operators in a mathematical model exhibit linearity, the resulting mathematical model is defined as model.

4.Nonlinear model: If one or more of the objective functions or constraints are represented with a nonlinear equation, then the model is known as a nonlinear model.

5.Static vs. dynamic model : A dynamic model accounts for time-dependent changes in the state of the system, while

a static (or steady-state) model calculates the system in equilibrium, and thus is time-invariant. Dynamic models typically are

represented by differential equations.

6.Explicit vs. implicit: If all of the input parameters of the overall model are known, and the output parameters can be

calculated by a finite series of computations (known as linear programming, not to be confused with linearity as described

above), the model is said to be explicit. But sometimes it is the output parameters which are known, and the corresponding

inputs must be solved for by an iterative procedure, such as Newton's method (if the model is linear) or Broyden's method (if

non-linear) is called explicit model.

7.Discrete vs. continuous: A discrete model treats objects as discrete, such as the particles in a molecular model or the states

in a statistical model; while a continuous model represents the objects in a continuous manner, such as the velocity field of fluid

in pipe flows, temperatures and stresses in a solid, and electric field that applies continuously over the entire model due to a

point charge.

8.Deterministic vs. probabilistic (stochastic): A deterministic model is one in which every set of variable states is uniquely

determined by parameters in the model and by sets of previous states of these variables. Therefore, deterministic models

perform the same way for a given set of initial conditions. Conversely, in a stochastic model, randomness is present, and

variable states are not described by unique values, but rather by probability distributions.

9.Deductive, inductive, or floating: A deductive model is a logical structure based on a theory. An inductive model arises from

empirical findings and generalization from them. The floating model rests on neither theory nor observation, but is merely the

invocation of expected structure. Application of mathematics in social sciences outside of economics has been criticized for

unfounded models.[2] Application of catastrophe theory in science has been characterized as a floating model.[3]

Advantages of mathematical model:

• The students are more intrested in an activity such as mathematical modeling than learning the context, solving some problems, and learn how to solve an equation, without knowing how the problem can be applied in real world, since in general, the mathematics problems have no meaning for students, not even for teachers;

• The students learn how to make a connections to other situations, especially to the physical situations; in fact, the student will feel more prepared to the use of mathematics in other areas;

• The learning will have a real meaning; in other words, it becomes easy to make connections to other situations and problems;

• It is much easier for most students to remember a modeling problem that spent much time on than a mathematical equation;

• It can happen in any level of education, primary and secondary education;

• In addition, the mathematical modeling process is more felexible and controlable for a professor that the traditional mathematics learning methods, and etc.

Disadvantages of mathematical model:

• The choosing of good problem to discuss in the classroom is not very simple, in general, and in fact is the art of the professor!

• The mathematical modeling process (or any active learning approach) take more time than the traditional approaches;

• The students do not like to test a new approach, in general. So, the chose of a good problem or situation is very essential.

QUESTION-20 explain the four types of float ?FLOAT :

Float or spare time can only be associated with activities which are non-critical. By definition,

activities on the critical path cannot have float. There are four types of floats. Total Float, Free Float,

Interfering Float and Independent Float.

(i)      Total Float :

The total float of an activity represents the amount of time by which an activity can be delayed without

delaying the project completion date. In order words, it refers to the amount of free time associated

with an activity which can be used before, during or after the performance of this activity. Total float is

the positive difference between the earliest finish time and the latest finish time or the positive

difference between the earliest start time and the latest start time of an activity depending upon which

way it is defined.

 

(ii)     Free Float :

Free float is that portion of the total float within an activity which can be manipulated without affecting

the float of subsequent activities. It is computed for an activity by subtracting the head event slack

from its total float. The head event slack is the difference between the latest and earliest event

timings of head event of an activity that is its (L-E)

 

(iii)    Interfering Float :

Utilisation of the float of an activity may affect the float times of the other activities in the network.

Interfering float is that part of the total which causes a reduction in the float of the successor activities.

It is the difference between the latest finish time of the activity in question and the earliest start time of

the following activity or zero, whichever is larger. It indicates that portion of the float of an activity

which cannot be consumed without affecting adversely the float of the subsequent activities.

 

(iv)    Independent Float :

This is the amount of time an activity can be delayed when all preceding activities are completed as

late as possible and all succeeding activities started as early as possible. Independent float therefore

does not affect float of either preceding or subsequent activities. It is computed by subtracting the tail

event slack from the free float of the activity. If the result is negative it is taken as zero.

For examination purposes the most important type of float is total float because it is involved with the

overall project duration. On occasions the term ‘Float’ is used without qualification. In such cases

assume that Total Float is required.

QUESTION-21 rule for network construction

RULES FOR NETWORK CONSTRUCTION

The following are the primary rules for constructing AOA diagram.

1. The starting event and ending event of an activity are called tail event and head event, respectively.

2. The network should have a unique starting node (tail event).

3. The network should have a unique completion node (head event).

4. No activity should be represented by more than one arc in the network.

5. No two activities should have the same starting node and the same ending node.

6. Dummy activity is an imaginary activity indicating precedence relationship only. Duration of a dummy activity is zero.

1.3

QUESTION-22 MAINTENANCE

1.3.1 GENERAL

Facilities maintenance is the normally funded ongoing program for the upkeep and preservation of buildings,

equipment, roads, grounds, and utilities required to maintain a Facility in a condition adequate to support the

University's mission.

Maintenance in this normal program includes the planned, preventive, emergency, as well as the unplanned or

reactive maintenance required to provide a safe, healthful, and secure environment. Each type of maintenance (see

1.4 below) is utilized by the different OMP functions (see 1lete their tasks. The University defers certain

maintenance work due to budget constraints. This maintenance work constitutes a deferred maintenance backlog.

1.3.2 DEFINITIONS

Maintenance: Maintenance is the upkeep of property, machinery, systems, and facilities, including buildings, utility

infrastructure, roads, and grounds. Maintenance consists of those activities necessary to keep facilities and systems

operational and in good working order. It consists of the preservation, but not the improvement, of buildings and

grounds, other real property improvements and their components. Maintenance may include replacement of

components of equipment or building systems (roof, flooring, HVAC, etc.) if replacement is performed:

1. on a routine or recurring basis,

2. to bring the equipment or building system back to its fully functional state,

3. to ensure the equipment or building system retains its functionality for its anticipated useful life.

Subject to the above limitations, replacement of a component of a building system (for preservation, not

improvement) is a form of maintenance when the replacement component is a duplicate, i.e., replacement-in-kind,

or, if not, the replacement item is an upgrade because a duplicate component is obsolete or is no longer reasonably

available. When the replacement is undertaken for the purpose of upgrading a system, it is not maintenance.

QUESTION-23 ECONOMIC ORDER QUANTITY (EOQ) MODEL

The economic order quantity (EOQ) is the order quantity that minimizes total holding and ordering costs for the year. Even

if all the assumptions don’t hold exactly, the EOQ gives us a good indication of whether or not current order quantities are

reasonable.

An inventory-related equation that determines the optimum order quantity that a company should hold in its inventory given a set cost of production, demand rate and other variables. This is done to minimize variable inventory costs. The full equation is as follows:

where : S = Setup costs D = Demand rate P = Production cost I = Interest rate (considered an opportunity cost, so the risk-free rate can be used) 

The EOQ formula can be modified to determine production levels or order interval lengths, and is used by large corporations around the world, especially those with large supply chains and high variable costs per unit of production. 

Despite the equation's relative simplicity by today's standards, it is still a core algorithm in the software packages that are sold to the largest companies in the world. 

the EOQ Model? Cost Minimizing “Q”

Assumptions:

Relatively uniform & known demand rate

Fixed item cost

Fixed ordering and holding cost

Constant lead time

(Of course, these assumptions don’t always hold, but the model is pretty robust in practice.)

What Would Holding and Ordering Costs Look Like for the Years?

A = Demand for the year

Cp = Cost to place a single order

Ch = Cost to hold one unit inventory for a year

Total Relevant* Cost (TRC)

Yearly Holding Cost + Yearly Ordering Cost

* “Relevant” because they are affected by the order quantity Q

Economic Order Quantity (EOQ)

EOQ Formula

Same Problem

Pam runs a mail-order business for gym equipment. Annual demand for the TricoFlexers is 16,000. The annual holding

cost per unit is $2.50 and the cost to place an order is $50. What is the economic order quantity?

QUESTION-24 Deterministic and Probabilistic Models

To understand it better, let us visualize deterministic and probabilistic situations. 

A deterministic situation is one in which the system parameters can be determined exactly. This is also called a situation of certainty because it is understood that whatever are determined, things are certain to happen the same way. It also means that the knowledge about the system under consideration is complete then only the parameters can be determined with certainty. At the same time you also know that in reality such system rarely exists. There is always some uncertainty associated. 

Probabilistic situation is also called a situation of uncertainty. Though this exists everywhere, the uncertainty always makes us uncomfortable. So people keep trying to minimize uncertainty. Automation, mechanization, computerization etc. are all steps towards reducing the uncertainty. We want to reach to a situation of certainty. 

Deterministic optimization models assume the situation to be deterministic and accordingly

provide the mathematical model to optimize on system parameters. Since it considers the system to be deterministic, it automatically means that one has complete knowledge about the system. Relate it with your experience of describing various situations. You might have noticed that as you move towards certainty and clarity you are able to explain the situation with lesser words. Similarly, in mathematical models too you will find that volume of data in deterministic models appears to be lesser compared to probabilistic models. We now try to understand this using few examples.

Take an example of inventory control. Here there are few items that are consumed/ used and so they are replenished too either by purchasing or by manufacturing. Give a thought on what do you want to achieve by doing inventory control. You may want that whenever an item is needed that should be available in required quantity so that there is no shortage. You can achieve it in an unintelligent way by keeping a huge inventory. An intelligent way will be to achieve it by keeping minimum inventory. And hence, this situation requires optimization. You do this by making decisions about how much to order and when to order for different items. These decisions are mainly influenced by system parameters like the demand/ consumption pattern of different items, the time taken by supplier in supplying these items, quantity or off-season discount if any etc. Let us take only two parameters -- demand and time taken by supplier to supply, and assume that rest of the parameters can be ignored.

If the demand is deterministic, it means that it is well known and there is no possibility of any variation in that. If you know that demand will be 50 units, 70 units and 30 units in 1st, 2nd and 3rd months respectively it has to be that only. But in a probabilistic situation you only know various possibilities and their associated probabilities. May be that in the first month the probability of demand being 50 units is 0.7 and that of it being 40 units is 0.3. The demand will be following some probability distribution. And you can see that the visible volume of data will be higher in case of probabilistic situation.

You have different mathematical models to suit various situations. Linear Programming is a deterministic model because here the data used for cost/ profit/ usage/ availability etc. are taken as certain. In reality these may not be certain but still these models are very useful in decision making because 

1. It provides an analytical base to the decision making2. The sensitivity of performance variables to system parameters is low near optimum.3. Assuming a situation to be deterministic makes the mathematical model simple and easy to handle.

But if the uncertainty level is high and assuming the situation to be deterministic will make the model invalid then it is better to use probabilistic models. Popular queuing models are probabilistic models as it is the uncertainty related to arrival and service that form a queue.

QUESTION-25 Queueing Disciplines

queueing disciplines, also known as scheduling policies, and describes their effect on theperformance of computer systems, call centers, and other systems where queueing is involved.

1. FCFS or FIFO First-Come-First-Served also known as First-in-First-Out. Jobs are served in the order thatthey arrive, with each job being run to completion before the next job receives service. This policy istypically used in manufacturing systems, call centers, and supercomputing centers. In such settings it isoften difcult to preempt a running job, and it seems fair to serve customers in the order that they arrive.

2. RANDOM Random-Order-Service. Whenever the server is free, it chooses a random job in the queue to runnext and runs that job to completion. This policy is mostly of theoretical interest.

3. LCFS Last-Come-First-Served (non-preemptive). Whenever the server is free, it chooses the last job to arriveand runs that job to completion. This policy is used for applications where jobs are piled onto a stack.

4.

QUESTION-26 explain the role of operation research in solving industrial problemApplicationsApplications of management science are abundant in industry such as airlines, manufacturing companies, service organizations, military branches, and in government. The range of problems and issues to which management science has contributed insights and solutions is vast. It includes:

scheduling airlines, both planes and crew, deciding the appropriate place to place new facilities such as a warehouse or factory, managing the flow of water from reservoirs, identifying possible future development paths for parts of the telecommunications industry, establishing the information needs and appropriate systems to supply them within the health service, and identifying and understanding the strategies adopted by companies for their information systems.

Marks 5

QUESTION-27 Bellman's principle of optimality

The principle that an optimal sequence of decisions in a multistage decision process problem has the property that whatever the initial state and decisions are, the remaining decisions must constitute an optimal policy with regard to the state resulting from the first decisions.

This principle was formulated by one of the originators of dynamic optimization - the American mathematician Richard Bellman. It states:

“Regardless of the decisions taken to enter a particular state in a particular stage, the remaining decisions made for leaving that stage must constitute an optimal policy.” Consequence: If we have entered the final state of an optimal policy we can trace it back. .

Example 6. With the help of Bellman’s optimality principle find the policy for minimal profit shown in fig. 3. Here the numbers of the nodes have been placed in rectangles and the length of the arcs (the prices) are the numbers in bold. The decisions taken are to be entered in the circles.

Solution: It has been shown in fig. 4. According to Bellman's Optimality Principle we start from the end node 15. In the circle we write a price of 0. We can reach this state only from nodes 13 or 14. If we are at node 13 the only transition to 15 has a price of 8, likewise the price of transition from 14 to 15 is 5 The transitions chosen are marked with a stylized marker . The next stage is filling in the decisions for states, 11 and 12. From 10 there is a single transition to 13 with a price of 10 + 8 = 18. From state 11 there are to possibilities - through 13, which costs 7 + 8 = 15 and 14, which costs 6 + 5 = 11. Because we are looking for the maximal profit we choose the transition to 13. From state 12 we choose the only transition to 14 with a total price of 14. From node 9 there are to possible transitions which have identical prices, so both are acceptable. At node 8 we choose a transition to 11 the price of which is 27 > 24 and so on. We continue with this procedure back to state 1 with a price of 57, which is the sought maximal price. The optimal policy which results in this maximal profit is achieved following stylized arrow: <1, 2, 5, 8, 11, 13, 15>. Profit check: 10 + 9 + 11 + 12 + 7 + 8 =57.