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**preview**shows page 1. to view the full**5 pages of the document.**The Q.M. in Action, Tea Production and Distribution at Duncan Industries

Limited, illustrates the diversity of problem situations in which linear

programming can be applied and the importance of sensitivity analysis. In the

next chapter we will see many more applications of linear programming.

Chapter 9 Linear Programming Applications in Marketing, Finance, and

Operations Management

a broad range of applications that demonstrate how to use linear programming

to assist in the decision-making process. We formulated and solved problems

from marketing, finance, and operations management, and interpreted the

computer output.

Many of the illustrations presented in this chapter are scaled-down versions of

actual situations in which linear programming has been applied. In real-world

applications, the problem may not be so concisely stated, the data for the

problem may not be as readily avail- able, and the problem most likely will

involve numerous decision variables and/or constraints. However, a thorough

study of the applications in this chapter is a good place to begin in applying linear

programming to real problems.

Chapter 10 Distribution and Network Models

models related to supply chain problems—specifically, transportation and

transshipment problems—as well as assignment, shortest-route, and maximal

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flow problems. All of these types of problems belong to the special category of

linear pro- grams called network flow problems. In general, the network model

for these problems consists of nodes representing origins, destinations, and, if

necessary, transshipment points in the network system. Arcs are used to

represent the routes for shipment, travel, or flow be- tween the various nodes.

Transportation problems and transshipment problems are commonly

encountered when dealing with supply chains. The general transportation

problem has m origins and n destinations. Given the supply at each origin, the

demand at each destination, and unit shipping cost between each origin and each

destination, the transportation model determines the optimal amounts to ship

from each origin to each destination. The transshipment problem is

an extension of the transportation problem involving transfer points referred to

as transshipment nodes. In this more general model, we allow arcs between any

pair of nodes in the network.

The assignment problem is a special case of the transportation problem in which

all sup- ply and all demand values are 1. We represent each agent as an origin

node and each task as a destination node. The assignment model determines the

minimum cost or maximum profit assignment of agents to tasks.

The shortest-route problem finds the shortest route or path between two nodes

of a net- work. Distance, time, and cost are often the criteria used for this model.

The shortest-route problem can be expressed as a transshipment problem with

one origin and one destination. By shipping one unit from the origin to the

destination, the solution will determine the shortest route through the network.

The maximal flow problem can be used to allocate flow to the arcs of the network

so that flow through the network system is maximized. Arc capacities determine

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