Introduction to Operation Research

The course " Computer Oriented Optimization Technique" is associated with the term Operation Research.

What is Operation Research?

• Operations research, operational research, or simply O.R., is the use of mathematical models, statistics and algorithms to aid in decision-making. It is the discipline of applying appropriate analytical methods to help make better decisions.
• It is most often used to analyze complex real-world systems, typically with the goal of improving or optimizing performance.
• OR is an interdisciplinary branch of applied mathematics and formal science that uses methods such as:

                     Mathematical modeling

                     Statistics

                     Algorithms

Origin

• The modern field of operations research arose during World War II.

• Scientists in the United Kingdom including Patrick Blackett, Cecil Gordon, C. H. Waddington, Owen Wansbrough-Jones and Frank Yates, and in the United States with George Dantzig looked for ways to make better decisions in such areas as logistics and training schedules. After the war it began to be applied to similar problems in industry.

• It is known as "operational research" in the United Kingdom (and "operational analysis" within the UK military and UK Ministry of Defence, where OR stands for "Operational Requirement") and as "operations research" in most other English-speaking countries, but "OR" is the common abbreviation everywhere. With expanded techniques and growing awareness, OR is no longer limited to only operations, and the introduction of computer data collection and processing has relieved analysts of much of the more mundane labor.

Tools

• Statistics

• Optimization

• Probability theory

• Queing theory

• Game theory

• Graph theory

• Decision analysis and

• Simulation

Because of the computational nature of these fields, OR also has ties to computer science.

Scope of OR


Operations research plays an increasingly important role in both the public and private sectors. Operations research addresses a wide variety of issues in transportation, inventory planning, production planning, crew planning, communication network design and operation, computer operations, financial assets and risk management, revenue management, market clearing and many other topics that aim to improve business productivity. In the public domain it deals with such topics as energy policy, defense, health care, water resource planning, forestry management, design and operation of urban emergency systems and criminal justice.



Operation Research and Decision Making

Operation research or management science as the name suggests, is the science of managing. As is known, management is most of the time making decisions. It is thus decision science which helps management to make better decision. Decision is , in fact, a pivotal world in managing. It is not only the headache of management , rather all of us make decision. We daily decide about minor to major issues. We choose to be engineers , doctors, lawyers , managers etc.

Decision making can be improved and , in fact , there is a scope of large scale improvement. The essential characteristics of all decision are

1. Objectives 2. Alternatives 3. Influencing factors

Scope of OR in Management

Operations research is problem solving and decision making science. It is a kit of scientific programmable rules providing the management a ‘quantitative basis’ for decisions regarding the operation under its control. Some of the areas of management where OR techniques have been successfully applied are:

Allocation and distribution

Optimal allocation of limited resources such as men, machine, materials, time and money. Location and size of whearhouse, distribution centres, retail depots etc.

Production and facility planning

• Selection ,location and design of production plants.

• Project scheduling and allocation of resources.

• Maintenance policy.

• Determination of the number and size of the items to be produced.

Procurment

• What , how and when to purchase at the minimum procurement cost?

• Bidding and replacement policies.

Marketing

• Product selection, trimming and competitive actions.

• Selection of advertising media.

• Demand forecasts and stock levels.

• Customer preference for size, color and packing of various products.

Finance


Operation Research has wide scope and has been successfully applied in the following areas of Financial Management: Cash Management, Inventory control , Simulation Technique, Capital Budgeting.

Cash Management :

A financial manager of responsible for adequate supply of funds to all the sections, departments and units of the organization as adequate funds are essential for their proper function throughout the year. Linear programming techniques are helpful to determine the allocation of funds to each section. Linear programming techniques have also been applied to identify sections having excess funds; these funds may be diverted to section that need them.

Inventory control:

In big organizations the amount invested in inventories can run into millions of rupees. Inventory control techniques of OR can help management to develop better inventory policies and bring down the investment in inventories. These techniques help to achieve optimum balance between inventory carrying costs , ordering costs and shortage costs. They help to determine which items to hold , how much to hold when order and how much to order.

Simulation Technique :

Simulation consider various factors that affect present and projected cost of borrowing money from commercial banks, and tax rates etc. and provides an optimum combination of financing for the desired amount of capital. Simulation replaces subjective estimates , judgment and hunches of the management by providing reliable information.

Capital Budgeting :

It involves of various investment proposals (market introduction of a new product or replacement of an equipment by a new one)

Personnel:

• Selection of personal, determination of retirement age and skills.

• Recruitment policies and assignment of jobs.

Research and development:

1. Determination of areas for research and development.

2. Reliability and control of development projects.

3. Selection of projects and preparation of their budgets.

From all the above areas of application, it can be concluded that OR can be widely used in taking timely management decision and can be also used as a corrective measure.

 OR Models


The operations research analyst has a wide variety of methods available for problem solving. For mathematical programming models there are optimization techniques appropriate for almost every type of problem, although some problems may be difficult to solve. For models that incorporate statistical variability there are methods such as probability analysis and simulation that estimate statistics for output parameters. In most cases the methods are implemented in computer programs.

Linear Programming

• Linear programming is a widely used model type that can solve decision problems with many thousands of variables.

• Generally, the feasible values of the decisions are delimited by a set of constraints that are described by mathematical functions of the decision variables.

• The feasible decisions are compared using an objective function that depends on the decision variables.

• For a linear program the objective function and constraints are required to be linearly related to the variables of the problem.

Network Flow Programming

• The term network flow program describes a type of model that is a special case of the more general linear program. The class of network flow programs includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, the pure minimum cost flow problem, and the generalized minimum cost flow problem.

• It is an important class because many aspects of actual situations are readily recognized as networks and the representation of the model is much more compact than the general linear program.

• When a situation can be entirely modeled as a network, very efficient algorithms exist for the solution of the optimization problem, many times more efficient than linear programming in the utilization of computer time and space resources.

Network models are constructed by the Math Programming add-in and may be solved by either the Excel Solver, Jensen LP/IP Solver or the Jensen Network Solver.

Integer Programming

Integer programming is concerned with optimization problems in which some of the variables are required to take on discrete values. Rather than allow a variable to assume all real values in a given range, only predetermined discrete values within the range are permitted. In most cases, these values are the integers, giving rise to the name of this class of models.

Nonlinear Programming

When expressions defining the objective function or constraints of an optimization model are not linear, one has a nonlinear programming model. Again, the class of situations appropriate for nonlinear programming is much larger than the class for linear programming. Indeed it can be argued that all linear expressions are really approximations for nonlinear ones.

Dynamic Programming

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.

Stochastic Programming

The mathematical programming models, such as linear programming, network flow programming and integer programming generally neglect the effects of uncertainty and assume that the results of decisions are predictable and deterministic. This abstraction of reality allows large and complex decision problems to be modeled and solved using powerful computational methods.

Combinatorial Optimization

The most general type of optimization problem and one that is applicable to most spreadsheet models is the combinatorial optimization problem. Many spreadsheet models contain variables and compute measures of effectiveness. The spreadsheet user often changes the variables in an unstructured way to look for the solution that obtains the greatest or least of the measure. In the words of OR, the analyst is searching for the solution that optimizes an objective function, the measure of effectiveness. Combinatorial optimization provides tools for automating the search for good solutions and can be of great value for spreadsheet applications.

Stochastic Processes

In many practical situations the attributes of a system randomly change over time. When aspects of the process are governed by probability theory, we have a stochastic process.

The model is described in part by enumerating the states in which the system can be found. The state is like a snapshot of the system at a point in time that describes the attributes of the system.

Discrete Time Markov Chains

Say a system is observed at regular intervals such as every day or every week. Then the stochastic process can be described by a matrix which gives the probabilities of moving to each state from every other state in one time interval. Assuming this matrix is unchanging with time, the process is called a Discrete Time Markov Chain (DTMC). Computational techniques are available to compute a variety of system measures that can be used to analyze and evaluate a DTMC model. This section illustrates how to construct a model of this type and the measures that are available.

Continuous Time Markov Chains

Here we consider a continuous time stochastic process in which the duration of all state changing activities are exponentially distributed. Time is a continuous parameter. The process satisfies the Monrovian property and is called a Continuous Time Markov Chain (CTMC). The process is entirely described by a matrix showing the rate of transition from each state to every other state. The rates are the parameters of the associated exponential distributions. The analytical results are very similar to those of a DTMC. The ATM example is continued with illustrations of the elements of the model and the statistical measures that can be obtained from it.

Simulation

When a situation is affected by random variables it is often difficult to obtain closed form equations that can be used for evaluation. Simulation is a very general technique for estimating statistical measures of complex systems. A system is modeled as if the random variables were known. Then values for the variables are drawn randomly from their known probability distributions. Each replication gives one observation of the system response. By simulating a system in this fashion for many replications and recording the responses, one can compute statistics concerning the results. The statistics are used for evaluation and design.

Applications

• Applications in which operations research is currently used include:

• Critical path analysis or project planning: identifying those processes in a complex project which affect the overall duration of the project

• Designing the layout of a factory for efficient flow of materials

• Constructing a telecommunications network at low cost while still guaranteeing QOS (quality of service) or QOE (Quality of Experience) if particular connections become very busy or get damaged.

• Road traffic management and 'one way' street allocations i.e. allocation problems.

• Determining the routes of school buses (or city buses) so that as few buses are needed as possible

• Designing the layout of a computer chip to reduce manufacturing time (therefore reducing cost)

• Managing the flow of raw materials and products in a supply chain based on uncertain demand for the finished products.

• Efficient messaging and customer response tactics

• Robotic zing or automating human-driven operations processes

• Globalizing operations processes in order to take advantage of cheaper materials, labor, land or other productivity inputs

• Managing freight transportation and delivery systems (Examples: LTL Shipping, inter-modal freight transport)

• Scheduling:

• personnel staffing

• manufacturing steps

• project tasks

• network data traffic: these are known as queuing models or queuing systems.

• sports events and their television coverage

• Blending of raw materials in oil refineries

• Operations research is also used extensively in government where evidence-based policy is used.