A semi-fixed cycle rule

A production rule that is even more simple than the extended (x,7 -rule is the fixed cycle production rale. As described in Chapter 3, a fixed production cycle is a cycle in which both the sequence in which the types will be produced as well as the available capacity for the production of a type is fixed. The fixed cycle rale follows this production cycle, which is repeated over and over again. In the situation with a normal gating service discipline without possibilities for working overtime, which we are considering now, the fixed cycle rale assumes that during a period only one type of product can be produced. Sometimes this is not a problem, for instance if we find that the best value for the time between set-ups, r,- in the cyclic production rale it, which can be found by formula (4.2.10), is for all types equal to M periods, where M is the number of different types. In that situation it is very logical that in a fixed cycle we produce exactly one type every period. 

If we find however, that for even M the best value for the time between set-ups, 7), is equal to V4W for every type i, then it is not logical to produce exactly one type every period. In that situation, we have two options we split up the original period in two equal parts, which become the new periods, or we decide to produce two different types in one period, dividing the available capacity according to the (varying ) capacity requirements for both types. A rale in which the production takes place according to the second option, that is with a cycle in which we can produce a number 

If we want to determine the production cycle in this multi-type capacitated situation, two elements are important the (maximum) number of types we can produce during a period, the so-called multi-type level, and the relative frequency of a type. If we denote the multi-type level by L and the relative frequency for type i by rfi, then the absolute frequency of type i, denoted by q/i, is given by  

The absolute frequency of a type represents the average number of production opportunities for a type during one period. The two important elements, the multi-type level and the relative frequency, can both be chosen freely. 

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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