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Artificial neural network models have been used successfully to solve demand forecasting and production scheduling problems; the two steps that typically precede and succeed Material Requirements Planning (MRP). In this paper, a neural network model is applied to the MRP problem of lot-sizing. The model’s performance is evaluated under different scenarios and is compared to common heuristics that address the same problem. Results show that the developed artificial neural network model is capable of solving the lot-sizing problem with notable consistency and reasonable accuracy.

This paper investigates the applicability of artificial neural networks (ANNs) to the problem of lot-sizing in Materials Requirement Planning (MRP) for the case of a deterministic time-varying demand pattern over a fixed planning horizon. Specifically, we are interested in the ANN’s ability to generate the optimum order pattern as compared to other commonly used heuristics. Although an algorithm to obtain the optimum solution to this problem has been developed by Wagner and Whitin [1], our motivation in developing a neural-network-based solution is due to the fact that ANNs are successfully being used in demand forecasting and production scheduling; the two steps that usually precede and succeed MRP, respectively [2], [3], [4], [5], [6], [7], [8] and [9]. Thus, extending the use of ANNs to the MRP lot-sizing problem will permit the integration of the production information system, a key requirement for its success. With ANNs supporting all major functions in production planning, historical data and other inputs may be directly converted into planned order releases or production schedules in a transparent way. Some benefits of such integration have been documented in the literature [10]. The ANN solution developed in this paper is compared to the optimum solution, as well as to solutions developed using other heuristics including Periodic Order Quantity (POQ), Silver-Meal (SM), and MINS [11]. POQ and SM are based on the EOQ approach, which minimizes the total inventory cost per unit, in different ways. The POQ determines the average number of periods covered by the EOQ and then orders the exact quantity to cover the demand for those periods. The SM finds the number of periods for which the total inventory costs per period is minimized and then orders the exact quantity to cover the demand for those periods. Details of these two heuristics may be obtained from standard production planning textbooks (e.g., [12] and [13]). On the other hand, MINS is a mnemonic that indicates the method’s repetitive selection of the period with minimum demand to explore the benefit of accelerating the delivery of its requirements. The chosen heuristics are simple, and on average, provide close to optimal solutions [11]. Therefore, comparing an ANN-based approach to these heuristics provides a good indication of its performance. For comparison purposes, POQ was chosen to provide a bottom line of acceptable performance as it is known to be the least accurate of the three methods, but the most simple at the same time. SM was chosen because it is one of the most commonly used methods with reasonable accuracy. Finally, MINS was chosen as one of the most recently developed methods with reasonable simplicity and notable accuracy. These choices were made to evaluate the ANN model against common algorithms to assure acceptable performance in support of the main objective of extending the use of ANNs to the lot-sizing problem for production planning integration. Zhiwei et al. [11] provide a simplicity/accuracy scale comparing various approaches to the lot-sizing problem that justifies our choices.

In this paper, a fully developed neural network model for solving the lot-sizing problem for the case of a deterministic time-varying demand pattern was presented. The NNM was trained using optimum order patterns obtained from the Wagner–Whitin algorithm. A special output coding scheme was used to filter out noise and to assure that the order quantity matched the forecasted demand over the planning horizon. The NNM displayed a robust performance in all test cases with an average percentage of optimum order patterns exceeding that of the POQ, MINS, and SM. We have, thus, demonstrated that a properly developed neural network model provides a valid alternative for solving the lot-sizing problem. The paper also provided an investigation of the POQ, MINS, and SM lot-sizing algorithms, with respect to changes in demand patterns and planning horizons. For the cases investigated, the performance of the three algorithms was affected by the two selected factors, with both the MINS and the SM algorithms outperforming the POQ. The superiority of the MINS and the SM algorithms over the POQ, however, may be practically insignificant, and thus, allowing the simplest approach to be used. When combining results presented in this paper with other results reported in the literature, it is clear that a general accuracy scale for all methods may be misleading. Although the research results demonstrate the success of the NNM in generating the optimum order pattern, they also indicate that a better cost performance may be obtained by training a NNM using optimum cost information. This may be achieved by adding a computational layer (with no learning taking place) after the output layer where the cost is computed as a function of the lot sizing decision described in the output layer. Then, the cost error (the difference between the optimum cost and the estimated cost from the NNM output) is computed and back propagated. Future research will focus on developing such a NNM. Another extension of this research is to develop an integrated NNM that supports the three major functions of a production planning system: forecasting, MRP, and scheduling.