MRP under uncertainty

In this chapter, issues of safety stock optimization in the domain of MRP-controlled planning (with dynamic discrete time demands) is discussed.

The preceding chapters have shown that there are a great number of approaches available to be applied in practice when it comes to the consideration of uncertainty under stationary conditions. These approaches, however, were primarily developed in support of replenishment decisions in demand-driven stochastic inventory systems. Replenishment lot sizes were assumed as given or determined with the help of a simple uncapacitated lotsizing model. The forecast-driven scheduling of production processes which is typical for industries using the Materials Requirements Planning approach and the associated dynamic lotsizing problems have not been dealt with.

However, usually a supply network does not just contain inventory nodes but in many cases it comprises also production nodes with resources which do not wait with the beginning of the value adding processes until a demand has occurred (pull principle) as we assumed in Section C.5. In fact, for a great number of
resources a detailed production schedule is developed on the basis of demand forecasts and is to a large extent carried out independently of the realization of the actual demand (push principle). In the planning phase of dynamic lotsizing and scheduling, for example, production orders are defined by quantity and time on the basis of the net end product demands forecasted for the upcoming planning horizon. In industrial practice, this forecast-driven planning of production is known as Material Requirements Planning (MRP). This widely used concept, at least as applied in practice, has the severe flaw in that the limited capacities of the resources are neglected during the construction of a production schedule. To a large extent this planning deficiency is caused by the application of uncapacitated lotsizing models within the frame of MRP. Several authors have made proposals to modify the MRP concept through the application of capacitated dynamic multi-item multi-level lotsizing models.

Both variations of planning and scheduling, with or without capacity consideration, are based on deterministic forecasts of the end product demands. However, the production processes are affected by numerous random influences in practice, whereby in a particular situation it may not even be clear what the deviation between the actual and the scheduled production process is caused by. This is because the occurring random influences are now no longer limited to a product or rather a production stage and therefore interdependencies between production processes on different stages often arise. Besides,
the decisions of operational production management and control, such as lotsizing, may increase the variance of the production processes. For example, in a given case it is often not detectable whether an observed unexpected increase in the derived demand for a component product is the result of an increase in the end product demand or whether it is caused by the change of a lotsizing decision for an intermediate parent product.

Under stochastic conditions, the situation often arises that the inventory on hand does not cover the period demand for a certain product. The result is a backorder which has to be delivered at the next opportunity. This is arranged by an appropriate increase in the net demand. If the production capacity is unlimited (which is assumed in the MRP concept), the backordered quantity is produced as part of the next production order, complying with the MRP logic. If the production capacity is limited, however, then the available capacity has to be allocated to the different competing products. This may involve complex changes of the actual production schedule and the resulting inventory development.

Just as in multi-level supply networks, also in a multi-stage production system under dynamic conditions, an answer has to be found as to where and with what means protection can be provided against the uncertainty which acts on the system from the outside (e. g. by demand) or from the inside (e. g. by machine breakdown). Research on this problem is quite limited as yet. Mainly the following approaches to the handling of uncertainty in multi-level production systems under dynamic conditions are discussed in the literature:

• Stochastic dynamic lotsizing models
• Buffers

• Safety stock
• Safety lead time
• Overestimation of the demand
• Underestimation of the output of a production stage
• Rationing
• Product substitution and cannibalization

• Freezing the schedule
• Rescheduling of production orders . . .

• with shortened planned lead time (express orders)
• with changed production quantity
• with changed due date

• Advance order information

These approaches are usually applied in a planning system in which rolling schedules are used. Accordingly, in regular intervals updated production schedules are defined which are associated to a planning window of T periods that is sliding over the time axis. Only those planning results which correspond to a few, imminent periods are fixed whereas the (partial) production schedules for the remaining periods are merely provisional and usually will be revised in further planning instants in reaction to the observed development of the inventory.