Production planning and control for the stochastic economic lot scheduling problem.

We address the stochastic economic lot scheduling problem (SELSP) and use it as the context for studying planned idle time as a buffer against demand uncertainty and related issues. In the SELSP several different parts are produced, one at a time, on a single machine, and changing from one part to another consumes capacity. Demands are random but must be satisfied on time whenever possible, using overtime if necessary. Long changeover times make frequent changeover in response to uncertainty impractical, and planning for uncertainty desirable. We develop a two-level hierarchical approach--a planning problem and a control problem. Modeling the major tradeoffs in the SELSP planning problem requires a better understanding of the deterministic-demand version of the problem. We present a formulation that illustrates the relationships among existing solution approaches. We show computationally that one approach gives superior results and gives an improved lower bound on the optimal schedule for a fixed sequence. In the SELSP, we need a tractable and realistic approach to modeling first-passage-time (or runout-time) distributions in a production setting. We present our method in the context of a continuous-review inventory system where demands are random, and where the lead time can be reduced at a cost. We optimally set the production quantity, reorder point, and lead time. With this practical approach to modeling first-passage-time distributions, in the SELSP planning problem we simultaneously set the safety stock levels, set the total planned idle time, and allocate it within the schedule. In addition to providing a practical procedure for fixing production targets, we analyze the relative benefit of safety stocks and idle time. We demonstrate (analytically and computationally) that idle time can be a costly alternative to safety stock and discuss the reasons. We use the results of our planning problem as a production plan, and examine different strategic approaches to the use of planned idle time in the SELSP. We develop and test three control algorithms that also use different elements of the plan to guide decisions about how much to produce and whether to produce on overtime. We show computationally that matching planned inventory levels through time is preferable to the other methods.PhDIndustrial and Operations EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/105346/1/9123981.pdfDescription of 9123981.pdf : Restricted to UM users only