Abstract
In a previous paper written by the same authors, the provision of manufactured components of only one type was presented, the provision can be done using, three different methods, production, importing/storing, and subcontracting. The problem is to determine how many components should be provided using different method in order to accomplish the required demand and to minimize the total cost of provision. A mathematical model for such a problem was formulated and used to obtain the optimal solution.
In another paper for the same authors, a more generalized problem with multiple manufactured components was considered. The objective function is to minimize the total fixed and variable costs of provision of all needed types of components. A special (If-Then) form for the objective function is generated due to the addition of the fixed cost elements. Another special form for the objective function is generated due to the stepped unit prices. The main problem constraints are: The provision of the total demand, maximum available time for production, the limited area for storing, and the constraints corresponding to the subcontracting stepping prices conditions. The if-then conditions were transformed into conditional relations with the addition of auxiliary 0-1 variables.
In the previous papers, the interior design of the provision systems was determined, and it was taken as structure constraints. In this paper a comprehensive model is designed in order to take care of the optimal interior design of the provision systems in addition to all the previously mentioned system constraints. The design includes the determination of the optimal number of different machines for the production facilities, and the optimal area for the import/storing facilities.