The multi x,T -rule

One production rule that allows an almost exact calculation of the performance is the rule in which we produce every product type according to a separate (x THule, independent of the production of other types. If the capacity restrictions are tight ot if the costs for working overtime are not very small, this production rule will not yield cry satisfying results. Therefore we will add some of the ideas from Chapter S to this rule, in order to make it more sensible. We will call the resulting production rule the multi (x,T)-rule. 

As we have already indicated in the introduction of this chapter, this decision rule is based on a separate (x,7)-rule for ev type. Some characteristic elements from other rules will be added. For every type the urgency is measured by the number of penalty points. A minimum number of penalty points is necessary before the production of a type is considered. Of course, the order states for the different types will be dependent. We will consido a special form of dependence. Therefore, from the semifixed cycle production rule the so-called multi-type level will be added, introduced in 5.2.4. If the number of types with a sufficient number of penalty points is less than the multi-type level, then we produce the orders for all of these types. If the number of 

From the extended overtime (x.7)-rule, introduced in 5.3.2., we will use the element of producing the type(s) with the highest number of penalty points and the element that we will not produce one more type if the remaining capacity is too small. If two types have the same number of penalty points, we will prefer the one with the smallest average demand. One element that remains from the original uncapacitated (x,7 -rule is that we will always produce all known orders of the type that we produce. This element is essential for the simplicity of the analysis. 

The analysis of this rule will be done by using a decomposition approach, which may give a lot of information without too much effort, at least when the multi-type level is very small. The choice of the multi-type level can be done in the same way as we have described in Section 5.2. If the level is too high, we can shorten the length of the periods and thus decrease the level. The analysis of the production rale will be described in the next subsection, where we will use a multi-type level of one and a multi-type level of two. 

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We can determine the multi-type level in a simple way by calculating T,-, the average time between set-ups for type i, using for instance the cyclic production rule Jt,- or the uncapacitated (x,7>-njle. From these T-values we can determine the average number of set-ups. Then we set the multi-type level equal to the rounded value of the average number of set-ups. Of course we have to verify that the available capacity C is large enough to allow the multi-type level we have chosen. 

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