Results for the normal extended service

If we have a normal extended service discipline, then we can simplify the formulae obtained in the previous subsection. In this service discipline we cannot wait for fiirther orders of a type if we have produced all the orders for this type. This implies that we cannot go from the state 1 to the state 0 if the last order is finished a set-up will be necessary before we can continue the production. Usually we will produce one or more other types of products before we start a set-up for the type that is just finished. The effect of this on the formulae is very simple by substituting c,- = 0 for every type i, we can find the formulae for the normal extended service discipline. By choosing this value for c,-, we will also find that the elements containing d,- disappear completely from the formulae. This is of course not a surprise, because the state 0 simply disappears. 

The probability that there are no orders for a type with a given p and x is now given by  

From this probability and from the average number of orders in the queue, we can calculate the average delivery time and the set-up rate. Again the choice of 6,- is iitqrortant, but we have found that we can use the same approximation as in (6.3.12) and determine bi by means of iteration. 

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Determining the optimal value of X exactly by means of analysis will be impossible in complex situations. Simulation studies on the other hand may be very time consuming. Therefore we will describe a decomposition approach, which may give much of the required information without too much effort. We start with the extra extended service discipline. The results for the normal extended service discipline are then easily found by substitution in the formulae that will be obtained for the extra extended service discipline. 

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