The semi-fixed cycle rule

The semi-fixed cycle rule does not change very much if there becomes a possibility for woridng overtime. As well as in the situation with a strict capacity we choose the relative firequency for all types in a production cycle and we will produce the different types according to their sequence in this production cycle. The difference between the mle in the strictly capacitated situation and the rule in this situation is found in the orders that we produce for a type if there is a production opportunity for this type. 

Now we always produce at least all known orders that have to be delivered before the next production opportunity. Possibly some extra capacity is necessary for this production. However, if there is still available capacity and if the next production opportunity for the type we produce, type i say, is less than T periods later, then it may be profitable to produce some extra orders and thus avoid future capacity problems. This extra production will only be done for those orders that have to be delivered within T/ periods. In the situation in which the available capacity has to be divided over more than one type, this will be done according to the so-called South-East strategy, that has been described in S.2.4.2. 

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In order to find out whether the extended (x,7>-rule performs well, its performance will be compared with the two-step rule and the semi-fixed cycle rule. In the simulation we will consider three examples, in which we compare the CPU-time as well as the average costs per period. One example has a multi-type level of one, once with tight capacity restrictions and once with a lot of capacity available and a third example in which usually two types of products will be produced in a period and in which the capacity restrictions are rather tight again. In all examples, the orders arrive according to independent Poisson processes. 

Table 5.1 The performance of the production rules the semi-fixed cycle rule are very high and this mle does not seem very useful for practical situations. Quite surprising in this example are of course the average costs of the extended (x,7>-rule. We expected that the average costs would be the same as for instance the average costs of P, but the average costs are lower than for any other rule. Moreover, the CPU-time is only a little more than the CPU-time for the semifixed cycle. The CPU-time for the semi-fixed cycle rule is only based on the generation of the random demand and the administration.

Comparing the results from Table 5.4. with the results from Table 5.1. we find that the effect of the possibility of working overtime only has a very small effect upon the average costs for the different rules, except for the semi-fixed cycle rule. For both Qi and Qi it would even be better not to use the possibility of working overtime. For Q2 and for the extended overtime (x,7>-rule the average costs have decreased a little. Obviously the costs of one unit of extra time are too high to make the use of extra time voy profitable and we see that in all production mles except in the semi-fixed cycle rule the average use of extra capacity is only about 3 percent of the normal available capacity. 

From Table S.S. we learn that working overtime indeed can be profitable. The average costs are now much smaller for most of the production rules and the choice of the parameter for Q2 and becomes relatively unimportant. In the two-step rule the use of extra capacity has increased to about IS percent. Due to our definition of the extended overtime (x,7>-nde and of the semi-fixed cycle rule, the use of extra capacity in these rules is still less than 10 percent. In the following example we will study the effect of flexible capacity on the situation described in Example 5.2. 

In Table 5.7. the lowest average costs are about the same as in Example 5.2. From this we can learn that for the more complicated rules such as Q2 and 03, the possibility of working overtime does not have much advantages unless the extra capacity is very cheap. For the simple production rules such as the (x,7>-rule and especially the semi-fixed cycle rule, the use of extra capacity is much more interesting. 

The semi-fixed cycle we will use in this example is the same cycle as the one in Example 5.2 with 107 periods. The penalty points for the extended overtime (x,T)-nile and the pairs (xiTi) and the level of mcl and eel are also the same as in Example 5.2, not because this would be the best choice, but to illustrate the robusmess of this rule. The results for this example are given in Table 5.6. 

Consider once again the situation of Example 5.6, but with costs for working overtime that are less than the penalty costs z =5. Again the semi-fixed cycle is not affected by this change, but the extended overtime (x,7>-rule is. For this rule we have found the following set of penalty points ... 

In the Examples 5.1 and 5.2 the capacity restrictions were very tight. In order to see whether the differences in average costs also appear in the situation in which the capacity is rather loose, we will consider a third example. Therefore we take again Example 5.1, but now with an available capacity of 15 instead of 12. With one set-up every period, about 72 percent (10.75 out of 15) of the available capacity will be used. The cyclic rules w,- are not affected by the change in capacity, therefore (5.2.18) still holds and we can also use the same semi-fixed cycle. For the extended (x,7>-mle we used the same set of values for the pairs iXi,Ti) as in (5.2.20). Because it will not be very profitable to produce orders with a longer residual lead time, the penalty points for these orders have been decreased and after some trials we have found the following set of values for the penalty points ... 

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