Joint inventory and technology selection decisions

In some manufacturing systems, the type of production technology selected dictates the lot size, or sets an upper limit on it. In this paper, we formulate a model in which the lot sizing decision has to be made at the technology selection stage. Furthermore, the cost of the technology depends on the lot size it can produce. The problem is addressed under two different assumptions about demand. First demand is assumed to be constant. A closed-form expression for the optimal lot size is derived for this case. Second, demand is assumed to be linearly decreasing. Using an accurate approximation to the total cost function, a closed-form expression for the optimal lot size is derived. We illustrate the models with numerical examples.