Process quality improvement and setup reduction in dynamic lot-sizing

Previous work on setup reduction to dynamic lot-sizing with process improvement is extended. In this dynamic lot-sizing model, a new calculation of lot size is made at every setup, but the decision to invest jointly in setup reduction and process improvement is made at the initial setup. In the analysis, it is assumed that setup reduction and process quality are functions of capital expenditure. Such setup cost reductions and process quality improvements can arise from investing in new technology. A procedure is developed to find the optimal lot size, total cost, and required investments, and the solution is illustrated using declining exponential functions and power functions to model both setup cost reduction and process quality improvement. The implications of the analysis and the tradeoffs involved are discussed and illustrated numerically and graphically.