What is Operations Research
Assist prof. Dr. Mushtaq Taleb
Chapter One
What Is Operations Research?
1.1 Introduction
The first formal activities of Operations Research (OR) were initiated in England during World War II, when a
team of British scientists set out to assess the best utilization of war materiel based on scientific principles rather
than rules. After the war, the ideas advanced in military operations were adapted to improve efficiency and
productivity in the civilian sector.
This chapter introduces the basic terminology of OR, including mathematical modelling, feasible solutions,
optimization, and iterative algorithmic computations. It stresses that defining the problem correctly is the most
important (and most difficult) phase of practicing OR.
1.2 Operations Research Models
Consider the following tickets purchasing problem. A businessperson has a 5-week commitment traveling
between Fayetteville (FYV) and Denver (DEN). Weekly departure from Fayetteville occurs on Mondays for
return on Wednesdays. A regular roundtrip ticket costs $400, but a 20% discount is granted if the roundtrip dates
span a weekend. A one-way ticket in either direction costs 75% of the regular price. How should the tickets be
bought for the 5-week period?
We can look at the situation as a decision-making problem whose solution requires answering three questions:
1. What are the decision alternatives?
2. Under what restrictions is the decision made?
3. What is an appropriate objective criterion for evaluating the alternatives?
Three plausible alternatives come to mind:
1. Buy five regular FYV-DEN-FYV for departure on Monday and return on Wednesday of the same week.
2. Buy one FYV-DEN, four DEN-FYV-DEN that span weekends, and one DEN-FYV.
3. Buy one FYV-DEN-FYV to cover Monday of the first week and Wednesday of the last week and four DEN-
FYV-DEN to cover the remaining legs. All tickets in this alternative span at least one weekend.
The restriction on these options is that the businessperson should be able to leave
FYV on Monday and return on Wednesday of the same week.
An obvious objective criterion for evaluating the proposed alternatives is the price of the tickets. The alternative
that yields the smallest cost is the best. Specifically, we have:
Alternative 1 cost = 5 * $400 = $2000
Alternative 2 cost = (.75 * $400) + (4 * 0.8 * $400) + (.75 * $400) = $1880
Alternative 3 cost = 5 * (0.8 * $400) = $1600
Alternative 3 is the cheapest.
Consider the following garden problem: A home owner is in the process of starting a backyard vegetable
garden. The garden must take on a rectangular shape to facilitate row irrigation. To keep critters out, the garden
1
Assist prof. Dr. Mushtaq Taleb
Chapter One
What Is Operations Research?
1.1 Introduction
The first formal activities of Operations Research (OR) were initiated in England during World War II, when a
team of British scientists set out to assess the best utilization of war materiel based on scientific principles rather
than rules. After the war, the ideas advanced in military operations were adapted to improve efficiency and
productivity in the civilian sector.
This chapter introduces the basic terminology of OR, including mathematical modelling, feasible solutions,
optimization, and iterative algorithmic computations. It stresses that defining the problem correctly is the most
important (and most difficult) phase of practicing OR.
1.2 Operations Research Models
Consider the following tickets purchasing problem. A businessperson has a 5-week commitment traveling
between Fayetteville (FYV) and Denver (DEN). Weekly departure from Fayetteville occurs on Mondays for
return on Wednesdays. A regular roundtrip ticket costs $400, but a 20% discount is granted if the roundtrip dates
span a weekend. A one-way ticket in either direction costs 75% of the regular price. How should the tickets be
bought for the 5-week period?
We can look at the situation as a decision-making problem whose solution requires answering three questions:
1. What are the decision alternatives?
2. Under what restrictions is the decision made?
3. What is an appropriate objective criterion for evaluating the alternatives?
Three plausible alternatives come to mind:
1. Buy five regular FYV-DEN-FYV for departure on Monday and return on Wednesday of the same week.
2. Buy one FYV-DEN, four DEN-FYV-DEN that span weekends, and one DEN-FYV.
3. Buy one FYV-DEN-FYV to cover Monday of the first week and Wednesday of the last week and four DEN-
FYV-DEN to cover the remaining legs. All tickets in this alternative span at least one weekend.
The restriction on these options is that the businessperson should be able to leave
FYV on Monday and return on Wednesday of the same week.
An obvious objective criterion for evaluating the proposed alternatives is the price of the tickets. The alternative
that yields the smallest cost is the best. Specifically, we have:
Alternative 1 cost = 5 * $400 = $2000
Alternative 2 cost = (.75 * $400) + (4 * 0.8 * $400) + (.75 * $400) = $1880
Alternative 3 cost = 5 * (0.8 * $400) = $1600
Alternative 3 is the cheapest.
Consider the following garden problem: A home owner is in the process of starting a backyard vegetable
garden. The garden must take on a rectangular shape to facilitate row irrigation. To keep critters out, the garden
1
