An integer programming model with special forms for the optimum provision of needed manufactures with an application example

TL;DRAbstract

Many practical problems are concerned with the provision of manufactured components; the provision can be done using three different methods, production in normal and over times, importing/storing, and subcontracting. The decision maker can evaluate the market demand, and the total cost elements. The problem is to determine how many components should be provided using different methods in order to accomplish the required demand and to minimize the total provision cost. A mathematical model for such a problem is formulated. The decision variables represent the number of components to be provided using different methods. The objective function is to minimize the total fixed and variable costs. A special (If-Then) form for the objective function is generated due to the fixed costs associated with some of the provision methods. Another combined (If-Then/Or) form for the objective function is generated due to the fixed cost associated with the subcontracting method. A third special form

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