A Dynamic Model for Requirements Planning with Application to Supply Chain Optimization

Abstract

This paper develops a new model for studying requirements planning in multistage production-inventory systems. We first characterize how most industrial planning systems work, and we then develop a mathematical model to capture some of the key dynamics in the planning process. Our approach is to use a model for a single production stage as a building block for modeling a network of stages. We show how to analyze the single-stage model to determine the production smoothness and stability for a production stage and the inventory requirements. We also show how to optimize the tradeoff between production capacity and inventory for a single stage. We then can model the multistage supply chain using the single stage as a building block. We illustrate the multistage model with an industrial application, and we conclude with some thoughts on a research agenda.M ost discrete parts manufacturing firms plan their production with MRP (materials requirements planning) systems, or at least, with logic based on the underlying assumptions of MRP. A typical planning system starts with a multiperiod forecast of demand for each finished good or end item. The planning system then develops a production plan (or master schedule) for each end item to meet the demand forecast. These production plans for the end items, after offsetting for lead times, then act as the requirement forecasts for the components needed to produce the end items. The requirements forecast for each component gets translated into production plans for the component, similar to how the production plan for the end items was created. The planning system continues in this way, developing requirement forecasts and production plans for each level of the bill of materials.Implicit in this planning process are assumptions about the production and demand process. The production plan is developed assuming that the forecast is accurate and will not change. Within the production process, requirements are generated assuming that there are deterministic production lead times and deterministic yields. Needless to say, these assumptions of a benevolent world do not match reality. Inevitably, the forecast changes, and uncertainties in the production process arise that result in deviations from the plan. To respond to these changes, most planning systems will completely revise their plan after some time period, say a week or a month. Again, the planning process starts with the (new) forecast and repeats the steps necessary to regenerate a plan for each level in the products' bills of materials.The intent of this paper is to present a model that captures the basic flavor of this planning process, and does so in such a way that it can be used to look at various tradeoffs within the production and planning systems. In particular, we model the forecasts for the planning system as a stochastic process. In this way, we try to represent a dynamic input to the planning system, namely, how forecasts change and evolve over time. The forecast process is a key input for the model. Another key...

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