Quality and production control with opportunities and exogenous random shocks

Abstract

In a production process, opportunities arise due to exogenous or indigenous factors, for cost reduction. In this dissertation, we consider such opportunities in quality control chart design and production planning for the lot sizing problem. In the first part of the dissertation, we study the economic design of X control charts for a single machine facing exogenous random shocks, which create opportunities for inspection and repair at reduced cost. We develop the expected cycle cost and expected operating time functions, and invoking the renewal reward theorem, we derive the objective function to obtain the optimum values for the control chart design parameters. In the second part, we consider the quality control chart design for the multiple machine environment operating under jidoka (autonomation) policy, in which the opportunities are due to individual machine stoppages. We provide the exact model derivation and an approximate model employing the single machine model developed in the first part. For both models, we conduct extensive numerical studies and observe that modeling the inspection and repair opportunities provide considerable cost savings. We also show that partitioning of the machines as opportunity takers and opportunity non-takers yields further cost savings. In the third part, we consider the dynamic lot sizing problem with finite capacity and where there are opportunities to keep the process warm at a unit variable cost for the next period if more than a threshold value has been produced. For this warm/cold process, we develop a dynamic programming formulation of the problem and establish theoretical results on the optimal policy structure. For a special case, we show that forward solution algorithms are available, and provide rules for identifying planning horizons. Our numerical study indicates that utilizing the undertime option results in significant cost savings, and it has managerial implications for capacity planning and selection.