Production Planning and Inventory Management

In the following we describe the relation of inventory management to the different planning steps which constitute a capacity-oriented system for production planning.

Production planning is strongly related to the layout type of a considered production system. An empirical analysis of production systems to be found in industrial practice reveals many differences which have a significant impact on the type of planning models that may be applicable in a certain planning environment. There are numerous different layout types, e.g. fixed position layout, process layout (job shop production), product layout (flow lines), just-in-time production systems, and cellular layout, among others. In each type of production system specific planning problems emerge for which the literature provides an appropriate modeling and solution approach.

For the solution of the production planning problems, the operations management literature provides a wide variety of planning approaches which are in part implemented in so-called Advanced Planning Software systems (APS). It is a common property of most of these approaches, such as aggregate production planning, master planning as well as lotsizing, that planning is based on forecasts of future demands which are treated as deterministic data in the planning process. That means, not only the external demand quantities but also the flow times (including waiting times caused by bottlenecks or machine breakdowns) as well as the scrap rates which in some industries are significant, are treated as deterministic factors.

However, since in reality random influences take effect, planning concepts are required which are able to take the unavoidable uncertainty on all levels of planning and control of the value-adding processes into account. From a theoretical point of view, this would mean to extend, say, a mixed-integer multi-level capacitated dynamic lotsizing model by including random variables in the model formulation. Unfortunately, such an approach is not very promising as for many production planning models not even the deterministic version of the problem can be solved satisfactorily.

Therefore, there are no concepts available that could be generally applied in practical planning environments, linking the above-mentioned deterministic and capacitated planning approaches to approaches that allow for the protection against stochastic influences. In contrast, depending on which characteristic dominates a given planning situation, basically two groups of planning approaches are discussed in the literature:

1. Deterministic approaches to production planning and scheduling which (sometimes) take the limited availability of resources into account. Uncertainty is often considered prior to optimization through the adjustment of the data (for instance, by using safety stock or safety time). The resulting production plans that are based on forecasts comply with the push principle. An example is the aggregate production planning based on deterministic linear programming models.
2. Stochastic approaches to inventory management which emphasize the uncertainty inherent in the planning problem and which neglect the capacity of the resources almost completely. Thus, there is no precise production schedule defined, but production rather reacts on the realization of the random variables, e.g. the demand quantity observed in a period. Many of these approaches follow the pull principle where activities are triggered by the arrival of a demand at the most downstream node of the supply network. An example is the $(s,q)$ inventory policy.