Design Commonality to Reduce Multi-Item Inventory: Optimal Depth of a Product Line

The problem of commonality is posed as a problem of economic balance. It involves the disutility of refusing to provide each segment of customers with an item fitting its exact requirements versus economies of scale achieved in producing and inventorying each item. The depth of the product line (the optimal number of items to produce) is determined by finding the minimum concave cost flow through a network. An efficient dynamic program (developed in production smoothing) is used to find this flow. Many products consist of interacting subassemblies; such multistage problems of finding the number of types of each subassembly can also be solved; a computational procedure is developed and an example presented. Along with modularity and cannibalization, multistage commonality is an essential component of a theory of efficient engineering design.