An investigation of approximate reasoning as the decision process for the aggregate production and employment problem
Since the pioneering work of Holt, Modigliani, and Simon (1955), the subject of aggregate planning has been extensively researched. However, despite the existence of a multitude of aggregate planning models in the literature, documented cases of any of the proposed models having been actually implemented are extremely rare. Empirical evidence, on the other hand, seems to indicate that managers' judgmental models (heuristics) do remarkably well, considering the complex nature of the aggregate planning problem. Thus, it appears that a great deal can be learned from the decision processes that actual managers use to solve this important problem in capacity planning. The object of this study is to illustrate how managers using simple heuristic decision rules may be able to closely approximate the results of much more powerful optimizing techniques for the aggregate planning and scheduling problem. Cognitive simulation models for the aggregate production rate and work force size decisions have been developed. These models are distinguished from other heuristic approaches to aggregate planning in two important aspects. First, the models are based on the concepts of Zadeh's fuzzy sets and approximate reasoning. Of particular significance is the use of linguistic variables to transform a protocol into an operational model. Second, the protocol utilized is not of any individual (or group of individuals), but rather seeks to be a representation of reasonable rules of thumb. Since the cognitive simulation models (fuzzy algorithms) do not simulate the behavior of any particular subject, it is not possible to compare the decisions of the models with those of a subject. Therefore, in order to validate the models, the approach that has been taken is to make the comparison in a situation where there is a known optimal solution. Accordingly, the aggregate planning fuzzy algorithms are used to analyze the classic Holt, Modigliani, Muth, and Simon paint factory data, and the results are compared to those achieved by quadratic programming. The best of the models studied exhibited a 5-0 percent cost penalty over the optimal cost of linear decision rules. This is somewhat greater than that achieved by other heuristics such as Search Decision Rule and Parametric Production Planning (both reporting cost penalties of less than 1 percent) . However, the fuzzy algorithms do not even require an explicit cost function-an important feature that clearly differentiates these models from other mathematical models of aggregate planning. Furthermore, the simulation studies that were conducted suggest that the fuzzy algorithms are also quite robust with respect to forecast horizon, forecast weighting functions, demand patterns, and forecast errors. In short, it can be said that the fuzzy algorithm models are capable of emulating the performance of much more mathematically sophisticated techniques with only a small cost penalty. For situations where restrictive assumptions cannot be rationalized and sufficient data is not available to estimate the cost functions with reasonable precision, the results of the fuzzy algorithm simulations demonstrate that a manager's decision to use his judgmental model rather than a mathematical model may be fully warranted--indeed, the proper decision under the circumstances.