In some situations, the available resources are adequate to carry out the alternative operating plan selected. In others, however, this is not true. For example, a machine has only a certain amount of capacity. If that capacity is entirely used by one product, it cannot be used for another. Similarly, a factory building has room for only so many machines. In these situations, there are constraints on the uses of resources. Linear programming is a model for solving problems that involve several constraints. In it, a series of linear mathematical relationships is developed. The first, called the objective function, is the quantity to be optimized. This is usually a formula for differential costs, which the model will minimize, or one for differential income, which is to be maximized. The other statements express the constraints of the situation.
Note on Linear Programming: A Brief Overview
Core Disciplines: Operations Management/Supply Chain
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After reading and discussing the material, students should:
- Use linear programming to determine constraints.
- Identify areas of highest contribution.
- Calculate a shadow price for each constrained resource.