The impact of learning and forgetting on production batch sizes

Sunantha Teyarachakul, Purdue University

Abstract

We consider the batch-sizing problem with known demands under learning and forgetting in production time. It is assumed that learning occurs within a batch as more units are produced. Forgetting occurs between batches when there is an interruption in production. Our model differs from earlier models in that: (1) we allow forgetting to depend on the length of interruption between two successive batches; and (2) the amount forgotten is not allowed to be more than what the operator has learnt so far. The goal of this thesis is to investigate the effect of learning and forgetting on batch sizes. We investigate the short-term effect of learning and forgetting by assuming a finite horizon and time-varying demands. We develop an optimal dynamic programming algorithm that minimizes the total cost over the problem horizon. We use our algorithm to provide some interesting managerial insights on the effect of learning and forgetting on batch sizes. For example, we show that a consideration of forgetting could lead to smaller batch sizes. Thus, forgetting provides one more motivation for small-lot production, which is a well-known feature of just-in-time production. Since, the computational requirements for the optimal algorithm are exponential in the number of periods in the problem, we develop an effective heuristic to solve problems. Our computational results show that the heuristic is both fast and accurate. To investigate the long-term effect of learning and forgetting on batch sizes, we assume constant demand rate over an infinite horizon. We study the steady-state convergence in batch production-time. Similar work by Globerson & Levin (1987) found that the batch production-time converges to a unique value, based on numerical examples. We extend their study by providing a mathematical proof of convergence. We found that the batch production-time does not necessarily converge to a unique value; but, could alternate between two values. In the presence of learning and forgetting, “EOQ-type” policies that use a fixed batch size and produce only when inventory reaches zero are not necessarily optimal. Also, the first-order condition does not guarantee an optimal batch size because the average total cost per period in steady state production could be non-convex. We provide sufficient conditions for the uniqueness of optimum.

Degree

Ph.D.

Advisors

Ward, Purdue University.

Subject Area

Management|Business community

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