Capacity Expansion and Equipment Replacement: A Unified Approach

Businesses frequently have to decide which of their existing equipment to replace, taking into account future changes in capacity requirements. The significance of this decision becomes clear when one notes that expenditure on new plant and equipment is a significant proportion of the GDP in the United States. The equipment replacement literature has focused on the replacement issue, usually ignoring aspects such as future demand changes and economies of scale. On the other hand, the capacity expansion literature has focused on the expansion of equipment capacity to meet demand growth, considering economies of scale but ignoring the replacement aspect. This paper attempts to unify the two streams of research by developing a general model that considers replacement of capacity as well as expansion and disposal, together with scale economy effects. Even special cases of the problems discussed here, such as the parallel machine replacement problem, have been considered difficult so far. However, we show that the problem can be solved efficiently by formulating it in a novel, disaggregate manner and using a dual-based solution procedure that exploits the structure of the problem. We also provide computational results to affirm that optimal or near-optimal solutions to large, realistic problems can be determined efficiently. We demonstrate the robustness of this approach by showing how other realistic features such as quantity discounts in purchases, alternative technology types or suppliers, and multiple equipment types can be incorporated.