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 theory
introduction
.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 sector
1. Federal, Provincial and Local Government
2. Health
3. Defense
CAPITAL BUDGETING MODEL
FOR 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 decisionmaking. 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-todate 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
CONCLUSION
Application 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
Definition of 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.
Inventory control is concerned with two
questions:
• when to replenish the store and
• by how much.
There are two main control systems. The twobin system (sometimes called the min-max
system) involves the use of two bins, either
physically or on paper.
INVENTORY COSTS
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 MODELS (E.O.Q.
MODELS)
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.
Purchasing model with no shortages
EOQ
Purchasing model with shortages
Shortage
period
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
Japanese approaches
• 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.
Other areas where OR techniques have been proven to
be useful includes
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–
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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.