Technical Supplement 1
Linear Programming with Transportation in Operations Management

LEARNING OBJECTIVES
After studying this technical supplement, you should be able to: 1. Explain the importance of optimization to operations management 2. Demonstrate how to develop linear programming models 3. Show how linear programming models can be solved using EXCEL 4. Demonstrate 0-1, transportation, and assignment models

LINEAR PROGRAMMING MODELS IN OPERATIONS MANAGEMENT

Linear programming (LP) is one of the most powerful analytic tools available to improve operations management. LP provides the optimal, or best possible, solution to problems that can be formulated by a linear function subject to a set of linear constraints. This has proven extremely useful in many operations management applications, some of which are described in Table 1.

TABLE 1
Linear Programming
Models
|Type of Model |Variables |Function to Optimize |Typical Constraints |
|Product Mix |Number of products to produce |Maximize contribution to |Resource limits, such as time, |
| | |profit |labor, material; Maximum or |
| | | |minimum quantities |
|Blending |Amount of materials to combine |Minimize cost |Resource limits; Demand |
| |to produce one unit of product | |requirements |
|Production Line |Sequence of production |Minimize cost |Resource limits; Time requirements|
|Scheduling | | | |
|Inventory