Optimal Installation of Several Related Equipment with Conversion Possibility

The problem in which a firm has to meet the c.emand for the services of several distinct but related equipment over a planning horizon is considered. An equipment of one type can be converted into an equipment of the other type at some costs. Hence demands may be met by direct capacity installation (expansion) or by converSiLQn from another type of eqUl.pment. Capacity installation and conversion costs are assumed to be concave reflecting possible economies of scale in these activities. The objective is to find a policy of capacity installations and conversions between the types of equipment such that the present value of th<~ total installation and conversion costs is minimized. The problem is formulated and given a network representation. A dynamic programming algorithm, an extension and refine· ment to that developed in [ 2] , is then developed which can be used to solve the problem efficiently when th€' number of distinct equipment is not too large.