The Reject Allowance Problem for Multi-Stage Job Lot Production

摘要

The technical report is devoted to the study of the reject allowance problem for multi-stage job lot production. A lot of exactly L non-defective items is required. These items are produced by a sequence of N-stages (operations). Since every production process inevitably produces some defective items, a reject allowance must be used which provides for producing enough extra items to replace the defectives. Before each stage except the first, two decisions must be made. First, should we immediately process the items and pass on to the next stage, or should we process a supplementary run through the preceding stages before proceeding further. Second, if we process a supplementary run, what should be the number of items started. The objective is to minimize total expected cost. We begin by computing the smallest optimum starting run size and then investigate the structure of optimal order-processing policy for the sequential decision problem of supplementary runs. The problem also is studied in a broader and more general contest where shortage or disposal of non-defectives at intermediate stages is permitted. We demonstrate applicability of the Markovian decision framework to the problem and develop a linear programming formulation. Finally, we study the reject allowance problem for single-stage production processes which undergo stochastic deterioration. (Author)