O.R. IS ALL AROUND YOU.

History of operations research

• Along the history, is frequent to find collaboration among scientists and armies officer with the same objective, ruling the optimal decision in battle. In fact that many experts consider the start of Operational Research in the III century B.C., during the II Punic War, with analysis and solution that Arquimedes named for the defence of the city of Syracuse, besieged for Romans. Enter his inventions would find the catapult, and a system of mirrors that was setting to fire the enemy boats by focusing them with the Sun's rays.

• Another antecedent of use of Operational Research obeys to F.W. Lanchester, who made a matematical study about the ballistic potency of opponents and he developed, from a system of equations differential, Lanchester's Square Law, with that can be available to determine the outcome of a military battle.

• Thomas Edison made use of Operational Research, contributing in the antisubmarine war, with his greats ideas, like shields against torpedo for the ships.

• In 1939, mathematical Russian L. Kantorovich, in association with the mathematical Dutchman T. Koopmans, developed the mathematical theory called "Linear programming", thanks to that went rewarded with the Nobel.

• During the years 1941 and 1942, Kantorovich and Koopmans studied in independent ways the Transport Problem for first time, knowing this type of problems like problem of Koopmans-Kantorovich. For his solution, they used geometric methods that are related to Minkowski's theory of convexity.

• But it is never considered that ;a new science called Operations Research until the II World War, during battle of England, where Deutsche Air Force, that is the Luftwaffe, was submitting the Britishers to a hard Air raid, since these had an little aerial capability, although experimented in the Combat. The British government, looking for some method to defend his country, convoked several scientists of various disciplines for try to resolve the problem to get the peak of benefit of radars that they had. Thanks to his work determining the optimal localization of antennas and they got the best distribution of signals to double the effectiveness of the system of aerial defense.

• To notice the range of this new discipline, England created another groups of the same nature in order to obtain optimal results in the dispute. Just like United States (USA), when joined the War in 1942, creating the project SCOOP (Scientific Computation Of Optimum Programs), where was working George Bernard Dantzig, who developed in 1947 the Simplex algorithm.

Some applications of OR knowledge

in army.

Case1- Reinventing U.S. Army Recruiting

• The Problem:

• In 1999, the U.S. Army Recruiting Command (USAREC) faced sustained, increasing challenges. By year's end, the organization was 6,300 personnel short of the annual required number of regular army enlisted soldier accessions. The fiscal year (FY) 2000 forecast projected a further shortfall of 17,500 — 22% of the requirement. Furthermore, those applicants USAREC managed to recruit and place in its traditional inventory-delivery system, known as the Delayed Entry Program (DEP), were dropping out in record numbers. The projected FY 2000 manpower shortfalls were quickly becoming a binding constraint on the army's ability to support the United States' national security strategy. Addressing these problems required operations research expertise in marketing science applications and inventory control.

• The O.R. Solution:

The multidisciplinary team combined production-forecasting expertise and resource allocation methodologies, augmented by marketing and market research techniques, to develop a new, comprehensive strategic recruiting plan that would reinvent Army recruiting for the next decade.

• The Value:

As a result of the strategic recruiting plan, the U.S. Army increased fiscal year 2000 military recruiting production by 17.5%. This achievement eliminated the forecasted 17,500 manpower deficit and provided an estimated efficiency savings of $204 million from a $1 billion program – a 20% savings. The new strategy continues to pave the way for successful Army recruiting.

Case2-Handling Nuclear Weapons for the U.S. Department of Energy

• The Problem:

The Pantex Plant, operated for the US Department of Energy (DOE) by the Mason and Hanger Corporation, is the sole assembly and disassembly facility for dismantling, evaluating, and maintaining the US nuclear stockpile. The end of the Cold War brought new challenges to DOE and the plant: new focus on reducing nuclear arsenals and reducing the threat of proliferation, meeting treaty provisions for verification, and ensuring the safety, security, and reliability of the enduring stockpile. Pantex management recognized that the changing mission of the plant called for agility in allocating resources to meet evolving needs. They turned to operations research expertise in decision support and production planning and scheduling.

• The O.R. Solution:

Pantex decided to create a comprehensive planning and scheduling tool with enough scope and complexity to address all of its production activities. Systems integrator Sandia National Laboratories assembled a team composed of Sandia staff, Cornell University and Rensselaer Polytechnic Institute faculty, and Pantex production planning and scheduling department staff. The team developed the Pantex Process Model (PPM), a set of optimization modules coupled with a tightly integrated set of Pantex databases. PPM includes sophisticated user interfaces, a fully relational database, and analysis modules and optimization engines focused on planning short-term dismantlements, scheduling short-term evaluations, and planning long-term plant resources. Since its implementation, the PPM has become the primary tool for analyzing planning and scheduling issues at Pantex.

• The Value:

With PPM, Pantex can plan current and future production resources to meet mission requirements. It can provide timely, credible planning information to support decisions at the highest levels of the US government regarding treaty negotiations, dismantlement, and long-range planning for nuclear-weapon-stockpile stewardship. And treaty negotiators can commit to treaty language knowing the direct impact their decisions will have on Pantex operations and US national policy. Said Bill Richardson, former Secretary of Energy, "The Pantex Process Model is not only increasing the efficiency of the nuclear weapons complex, but it is also proving to be a valuable tool in the efforts of our government to significantly reduce the global nuclear danger."

• During the Cold War, the old Soviet Union (URRS), excluded of the Plan Marshall, wanted to control the terrestrial communications, including routes fluvial, from Berlin. In order to avoid the rendition of the city, and his submission to be a part of the deutsche communist zone, England and United States decided supplying the city, or else by means of escorted convoys (that would be able to give rise to new confrontations) or by means of airlift, breaking or avoiding in any event the blockage from Berlin. Second option was chosen, starting the Luftbrücke (airlift) at June 25, 1948

• This went another from the problems in wich worked the SCOOP group, in December of that same year, could carry 4500 daily tons, and after studies of Research Operations optimized the supplying to get to the 8000~9000 daily tons in March of 1949. This cipher was the same that would have been transported for terrestrial means, for that the Soviet decided to suspend the blockage at May 12, 1949.

OR On the Ball:Applications in sports scheduling and management

Sports management is a very attractive area for applications of operations research. Sports competitions involve many economic and logistic issues, including athlete evaluation, team evaluation, tournament planning, club management, economic estimation, marketing politics, security issues and designing fair rules. O.R. methods have been successfully applied in the evaluation of team performance. Team managers, players, fans and journalists are often eager to know a team's chances of making the playoffs in a given classification.

Timetabling is the major O.R. application in sports. Sports leagues and teams need schedules that satisfy different types of constraints and optimizing — for example, the fairness or the distance travelled. Timetable optimization in sports competitions is a difficult problem to which several O.R. techniques have been applied.

Deciding Playoff Elimination

• National Soccer Championship BRAZIL.• Fans love statistics as much as they love the

game itself.• Conservative method playing the spoilsport.• SOCCER – The Religion.

• The authors have developed two integer-programming models that can detect in advance when a team is already qualified for, or eliminated from, the playoffs. These models are based on the computation of the guaranteed qualification score (GQS), which is the minimum number of points a team has to obtain to be sure it will be qualified, regardless of any other results, and the possible qualification score (PQS), which consists of the minimum number of points a team has to win to have any chance to be qualified. A team is mathematically qualified for the playoffs if and only if its number of points won is greater than or equal to its GQS. Only at this point can its qualification for the playoffs be announced without any risk of contradiction. A team is mathematically eliminated from the playoffs if and only if its current number of points plus the number of points it is still able to win in the remaining games to be played is smaller than its PQS. An additional nice feature of these models is that they can be easily extended to accommodate some of the usual tie-breaking rules.

• Figure 1 illustrates that MNP got smaller than GQS for Fluminense at the 11th round, showing that at this time it was not on its own. Even if it obtained the maximum number of possible points by winning all its remaining games, there existed at least one set of results leading Fluminense outside of the qualification zone. At the 25th round, its number of points reached its PQS, meaning that it had a chance to qualify even if it lost all remaining games. Indeed, due to a sequence of favourable results, Fluminense did qualify at the eighth and last position only at the final round.

Sports Timetabling

• Professional sports leagues are a major economic activity around the world. Television costs in sports such as baseball, soccer, hockey and basketball amount to hundreds of millions of dollars in some competitions. Recent transfers of major soccer players such as Ronaldo to Real Madrid for record £80 million and David Villa to Barcelona for £35 million.

• The sponsorship of national teams by sporting goods makers such as Adidas, Nike and Reebok involve huge contracts. As an example, the contract of the Brazilian Soccer Confederation (CBF) with Nike amounts to almost $400 million.

• Investments in marketing and advertisement are also enormous. Teams and leagues do not want to waste their investments in players and structure as a consequence of poor schedules of games, involving, for example, unattractive teams playing on prime dates or several important games played at the same time with losses in television rights. National and international competitions played in parallel require strong coordination of travel and game schedules. In this context, efficient schedules are of major interest for teams, leagues, sponsors, fans and the media .

• This problem is further complicated due to the travelling distances involved. In the case of the Brazilian soccer national championship, a single trip from Porto Alegre to Belém can take a full day and include many stops, due to the absence of direct flights to cover a distance of approximately 4,000 kilometres. The total distance travelled becomes an important variable to be minimized, so as to reduce travel costs and to give more time for the players to rest and train during a season that lasts approximately six months. In the case of the Brazilian national soccer championship, fairness rules stipulate that no team is supposed to play more than three home or away games consecutively. Other additional constraints vary from tournament to tournament.

Concluding Remarks

• O.R. methods have a large potential of applications in sports and are a useful strategy to motivate students in introductory courses on optimization and simulation. Better game schedules can significantly reduce travelling costs. There are many applications of optimization techniques to timetabling in different sports such as soccer, baseball, football, basketball, hockey and rugby, leading to reductions in travel costs and to more fairness.

• Models for deciding playoff elimination are very useful tools for team administrators, the press and the fans. They are quite effective in correcting common misleading statements made by the press and team managers.

Game theoryintroduction.Game theory is a branch of applied mathematics that is used in the

social sciences, most notably in economics, as well as in biology (particularly evolutionary biology and ecology), engineering, political science, international relations, computer science, and philosophy.

.Game theory attempts to mathematically capture behavior in strategic situations, or games, in which an individual's success in making choices depends on the choices of others (Myerson, 1991). While initially developed to analyze competitions in which one individual does better at another's expense (zero sum games), it has been expanded to treat a wide class of interactions, which are classified according to several criteria .Today, "game theory is a sort of umbrella or 'unified field' theory for the rational side of social science, where 'social' is interpreted broadly, to include human as well as non-human players.

Application of game theory• Game theory has been used to study a wide variety of human and l

behaviors. It was initially developed to understand a large collection of economic behaviors, including behaviors of firms, markets, and consumers. The use of game theory in the social sciences has expanded, and game theory has been applied to political, sociological, and psychological behaviors as well.

• Game theoretic analysis was initially used to study animal behavior by Ronald Fisher in the 1930s (although even Charles Darwin makes a few informal game theoretic statements). This work predates the name "game theory", but it shares many important features with this field. The developments in economics were later applied to biology largely by John Maynard Smith in his book

History of game theory• first known discussion of game theory occurred in a letter written by

James Waldegrave in 1713. In this letter, Waldegrave provides a minimax mixed strategy solution to a two-person version of the card game

• James Madison made what we now recognize as a game-theoretic analysis of the ways states can be expected to behave under different systems of taxation

• Although analysis is more general than Waldegrave's, game theory did not really exist as a unique field until John von Neumann published a series of papers in 1928. While the French mathematician Émile Borel did some earlier work on games, von Neumann can rightfully be credited as the inventor of game theory

• In 1950, the first discussion of the prisoner's dilemma appeared, and an experiment was undertaken on this game at the RAND corporation.

History of game theory• Around this same time, John Nash developed a criterion for mutual

consistency of players' strategies, known as Nash equilibrium, applicable to a wider variety of games than the criterion proposed by von Neumann and Morgenstern. This equilibrium is sufficiently general to allow for the analysis of non-cooperative games in addition to cooperative ones.

• 2005, game theorists Thomas Schelling and Robert Aumann followed Nash, Selten and evolutionary game theory. Aumann contributed more to the equilibrium school, introducing an equilibrium coarsening, correlated equilibrium, and developing an extensive formal analysis of the assumptio

• In 2007, Roger Myerson, together with Leonid Hurwicz and Eric Maskin, was awarded the Nobel Prize in Economics "for having laid the foundations of mechanism design theory." Myerson's contributions include the notion of proper equilibrium, and an important graduate n of common knowledge and of its consequences

Types of game theory

• Cooperative or non-cooperative• Symmetric and asymmetric• Zero-sum and non-zero-sum• Simultaneous and sequential. Perfect information and imperfect

information• Discrete and continuous games• One-player and many-player games

Challenges of game theory

• In addition to being used to predict and explain behavior, game theory has also been used to attempt to develop theories of ethical or normative behavior. In economics and philosophy, scholars have applied game theory to help in the understanding of good or proper behavior. Game theoretic arguments of this type can be found as far back Plato.

PROSPECTS & OF OPERATIONS RESEARCH APPLICATlONS

IN AGRlCULTIlRE AND AGRICULTURAL POLICY

University of California, Berkeley.Department of Agricultural and Resource

Economics

I Over the years, the inherent dynamic and potential variability

of individual country and world agricultural food system has become increasingly obvious. For resource utilization at the agricultural production level all the way to final consumption of food, a variety of economic, political and technological forces has continued to evolve with pronounced structural implications. The qualititative implications of these forces are generally known and widely accepted, while the quantitative implications are far less certain.

Conventionally we can characterize the qualitative nature of food and agricultural systems by

• Highly inelastic aggregate demand• Low-income elasticity of aggregate demand• Rapid technological change• Asset fixity• Atomistic structure of the production sector• The physical limitations imposed by life cycles of plant and

animal growth• The growing nature of inventories• The climatic and weather uncertainties• Labor immobility, and

• The demand for and the propensity of governments to actively intervene in the private sector.

These qualitative features results in dynamic paths which are uncertain and contain the potential for much instability

To deal with the complexity of agricultural systems, their commodity components, and associated participant interactions, models have long been viewed as a potentially valuable aid to evaluating and forming policy strategies. Obviously, they provide the basis for generating quantitative forecasts and the means of evaluating the effects of alternative decisions or strategies under the direct control of policymakers. In essence, models of the system can offer a framework for conducting laboratory experiments without directly influencing the system. Since these experiments can be conducted with the model rather than the real system, potential mistakes that may result in costly consequences can often be avoided.

For agriculture and food systems or components thereof, many models have been constructed—some for descriptive purposes, some for explanatory or casual purposes, some for forecasting purposes, and others for the express purpose of decision analysis. The latter group of models is of direct interest to operation researchers. An examination of the anatomy of these models provides a basis for reaching the assessment that the potential for such efforts is largely unrealized.

As usually conceived, decision models involve controllable or decision & environmental variables, performance measures, objective functions, and structures that relate the controllable and environmental variables to the performance measures entering the objective function. Model constructs of these problems are usually advanced in an optimizing mode, and the results obtained from such frameworks provide the basis for system policy prescriptions. As a consequence, efforts in the construction of decision making models are concerned both with the implications of the optimizing solutions and the accuracy with which the model portrays the system.

In considering the design of decision making models in agricultural policy, the unfulfilled promise of modeling as an aid and support to policy analysis begins to assume shape to be sure, the design should begin with the specification of the relevant decision-makers can manipulate. The relevant decision points and procedures for revising policy actions in the light of new information should also be determined at this early stage of the analysis. Unfortunately, these aspects of policy modeling are often neglected. However, the more challenging aspects of decision-model construction are:

a) The specification, identification, estimation and verification of criterion functions

b) The specification, identification, estimation, and verification of constraint structures

c) The application of solution algorithms and the design of operational implementation.

APPLICATION OF OPERATION RESEARCH IN PLANNING AND BUDGETING

• Macro Economic Planning• Sectorial Planning• Micro Economic Planning• Operation research in public sector1. Federal, Provincial and Local Government 2. Health3. Defense

CAPITAL BUDGETING MODELFOR PEMEX EXPLORACIÓN Y PRODUCCIÓN

• PEMEX Exploración y Producción is in charge of oil and gas exploration and exploitation

• PEMEX Refinación produces, distributes and markets fuels and other oil products

• distributes and markets natural gas and L.P. gas; and produces and markets basic petrochemical products

THE MODEL

The complexity involved in the management and planning of the costly operations inherent in the exploration and exploitation of hydrocarbons, entailing thousands of variables, means that we need to have advanced tools to decide how to allocate capital, without losing sight of the interaction that exists between the operations and the goal of maximizing the economic value of the hydrocarbons. This situation was solved through the design , development and implementation of a mathematical model that made it possible to construct different scenarios in support of the planning budgeting of the company’s capital.

This model makes it possible to guarantee maximum economic value in the allocation of the investments and obtain, among other things, the multiannual

production forecasts, attending to the multi-periodic demand for hydrocarbons to meet

the requirements for national consumption and the export platform, under limited budget

conditions . It is worth mentioning that every one of the estimated declines in production are derived from the optimizations done for those years.

This model makes it possible to build as many scenarios of maximum economic value and minimum cost

Advantages:• It provides the multiannual project portfolio that complies with the budget

constraints and the demand for production constraints and the demand for production.

• It estimates production forecasts for the short, medium and long term.• It presents the multiannual investment requirements per project type.• It makes it possible to calculate the cost of the constraints.• It facilitates the programming of the dependence between projects:• economic, technology, etc.• It gives the elements needed to be able to successfully enter into negotiations about the budget with the Federal Government

Operations Research in Aviation

Case:British Airways uses O.R. to

Improve Punctuality and Save £Millions

The Problem

• British Airways operating from Heathrow is responsible for 2,600 flights per week, to 42 UK destinations, using a fleet of 85 aircraft.

• Airline industry surveys identify punctuality as the biggest factor in providing customer satisfaction. Being late costs money too, and it was clear that any punctuality improvement for British Airways could provide both financial and customer relationship benefits.

The O.R. Solution

• A problem structuring and analysis exercise was undertaken using tried and tested O.R. methodologies. Comparison was also made between Heathrow punctuality for the whole day and second wave departure performance. The study then focused on the chain of events leading to Heathrow second wave departures – a chain of events was drawn up, and each event in the chain was decomposed and measured

Chain of events leading to departure

• This resulted in the creation of new metrics – Ontime Achievables (OTA), and OTA conversion rate.

• On-time achievable (OTA). This measures those occasions where there is sufficient aircraft ground-time available between its arrival and subsequent Scheduled Time of Departure (STD) to execute all activities required to make it ready for departure. OTA is basically a measure of the effectiveness of strategic and tactical schedule planning processes.

• OTA conversion rate (OCR). This measures how well the airport delivery teams actually convert these OTA opportunities into on-time RtG(Ready to Go) departures. OCR is basically a measure of delivery conformance.

The O.R solution (cont.)

• So a simplified graphical approach was devised - the creation of ‘waterfall’ diagrams. The diagrams were used to show the effect of circumstances on departure situations which could theoretically achieve 100% efficiency. However, correlation with the OTA metric indicated it was more a realistic goal to achieve 83% efficiency - a considerable improvement on past performance.

The Value

• The benefits of these endeavours soon became apparent; a 3% improvement in ‘ready to go’ performance was reported almost immediately, and on time performance increased by 6%. The improved scheduling process showed an OTA improvement of 5% (the financial benefit from this was £5 million).

Operations Research Applications in the field of

Information and Communication Technologies

INTRODUCTION

• Traditionally, Operations Research is the scientific study of logistic networks to provide for decision support at all levels in order to optimize production and distribution of the commodity flows. Nowadays, these logistic networks have become very large and may range over several countries, while the demands for quality of service have grown similarly to ever higher standards. Generally one agrees that to maintain such large networks successfully, one needs the control of all the information flows through the network, that is, continuous information on the status of the resources. In this sense one could say that Operations Research and Information Technology has joined together..

• Management science, or operations research, is a specialized discipline for business decision-making. The term Operations Research (OR) describes the discipline that is focused on the application of information technology for informed decision-making. In other words, OR represents the study of optimal resource allocation. The goal of OR is to provide rational bases for decision making by seeking to understand and structure complex situations, and to utilize this understanding to predict system behavior and improve system performance

OPERATIONS RESEARCH IN INFORMATION TECHNOLOGY

• The operations research modeling has been a very difficult task. But by the arrival of information technology and the usage of computers in modeling the job has become much easier. The practice of OR involves a major activity in problem formalization and model construction and validation; other activities include a computational part, analysis of solutions, arriving at conclusions, and implementation of the decision. The increased computing power has stimulated large-scale use of mathematical programming models for planning and on line control. Databases and computer networks make reliable up-to-date data available for more effective decision making. TORA and SIMNET II are examples of software packages in OR.

Some of the possible solution techniques include:

• 1 Simulation• 2 Network Flow Programming• 3 Data Mining• 4 Network routing

APPLICATION OF OPERATION RESEARCH IN CONSTRUCTION

MANAGEMENT

INTRODUCTION

Similar to other sectors , a company which is active in the construction sector has to use management tools in order to achieve an effective allocation of various resources in order to remain competitive in today’s dynamic markets. The efficiency of a construction firm’s numerous activities such as bidding, project management, project risk assessment equipment management, can be increased by introducing analytical management technique from the Operations Research (OR) discipline.

MODELLING ASPECTS IN CONSTRUCTION MANAGEMENT

Models without uncertainty considerations

Models for resources management.Models for risk management

MODERN MANAGEMENT CONCEPTS IN CONSTRUCTION INDUSTRIES

Total quality management application

CONTIBUTION TO CONSTRUCTION ENGINEERING AND MANAGEMENT

FROM COMPUTER SCIENCE

CONCLUSIONApplication area in construction management were multidisciplinary approaches involving operation research techniques are deemed suitable as solution methods. Modern management concepts (e.g., TQM) probabilistic OR tools used in risk analysis (e.g., AHP) Combinatorial optimization solution techniques in resources and cash flow management, basic project monitoring techniques (CPM, LOB), and AI techniques and soft computing methods (SA,TS,GA,NN) integrated with conventional OR tolls (simulation and combinatorial optimization techniques) proposed for different practical problems in construction engineering.

APPLICATION OF OPERATION RESEARCH IN INVENTORY

CONTROL

• Inventory is the physical stock of items held in any

business for the purpose of future production or sales. In a production shop the inventory may be in the form of raw materials. When the items are in production process, we have the inventory as in-process inventory and at the end of the production cycle inventory is in the form of finished goods.The problem of determining inventory policies is not a new concept beginning. It is only in he last two decades that it has been tackled with quantitative techniques and mathematical models, a method amenable to optimization.

Definition of inventory control

Inventory control is concerned with two questions:

• when to replenish the store and • by how much. There are two main control systems. The two-

bin system (sometimes called the min-max system) involves the use of two bins, either physically or on paper.

There are four major elements of inventory costs that should be taken for analysis, such as Item Cost (C1) This is the cost of the item whether it is manufactured or purchased. it is denoted by Rs.C1 per

item. Purchasing or Setup or Acquisition or Ordering Cost (C2) Administrative and clerical costs are involved in processing a purchase order, expediting, follow up

etc., It includes transportation costs also. This is denoted by Rs.C2 per set up or per order. Inventory holding cost (C3) If the item is held in stock, the cost involved is the item carrying or holding cost. This cost is denoted by Rs.C3/item/unit time.Shortage Cost (C4) The shortage cost is due to the delay in satisfying demand (due to wrong planning); but the

demand is eventually satisfied after a period of time. This cost is denoted by Rs.C4 per item per unit time of shortage.

INVENTORY COSTS

The inventory control model can be broadly classified into two categories:

(1) Deterministic inventory problems. (2) Probabilistic or stochastic inventory problems. In the deterministic type of inventory control, the

parameters like demand, ordering quantity cost, etc are already known or have been ascertained and there is no uncertainty. In the stochastic inventory control, the uncertain aspects are taken into account.

INVENTORY MODELS (E.O.Q. MODELS)

Purchasing model with no shortages

EOQ

Purchasing model with shortages

It shows that the back ordering is possible (i.e.) once an order is received, any shortages can be made up as the items are received. Consequently shortage costs are due to being short of stock for a period of time

Shortage period

• In the 1970s several Japanese firms, led by the Toyota Motor Corporation, developed radically different approaches to the management of inventories. Coined the “just-in-time” approach, the basic element of the new systems was the dramatic reduction of inventories throughout the total production system. By relying on careful scheduling and the coordination of supplies, the Japanese ensured that parts and supplies were available in the right quantity, with proper quality, at the exact time they were needed in the manufacturing or assembly process.

• A second Japanese technique, called kanban (“card”), also permits Japanese firms to schedule production and manage inventories more effectively. In the kanban system, cards or tickets are attached to batches, racks, or pallet loads of parts in the manufacturing process. When a batch is depleted in the assembly process, its kanban is returned to the manufacturing department and another batch is shipped immediately. Since the total number of parts or batches in the system is held constant, the coordination, scheduling, and control of the inventory is greatly simplified.

Japanese approaches

– Warehouse design, storage and retrieval, order picking– Vehicle routing– Delivery transport mode selection– Capacity and manpower planning– Production scheduling

…and other resource usage and allocation decisions.

Other areas where OR techniques have been proven to be useful includes