Formulation of the extended overtime x,T -rule

If K(i) xi for ailthen we do not produce at all during the period. Otherwise, we place the types with a sufficient amount of penalty points in a sequence with such that A (ji) (i2). . (i ). Types with an equal number of penalty points are placed according to an increasing average demand. In the uncapacitated situation we would produce all types in this sequence and the amount for type / would 

The first part of the extended overtime (x,7)-nile is now exactly the same as the first part of the extended (x,7)-rule. Following the sequence we allocate capacity to the various types. We do not allocate capacity to the next type if the remaining capacity is less than the minimum capacity level mcl and we can possibly produce some extra orders for some of the types if the remaining capacity level is less than the extra capacity level eel and if capacity has been allocated to all product types in the sequence. 

The difference with the extended (x,7 e happens in the situation in which there is no more capacity available after the first round. Usually this implies that for one of the types, type i say, we have not planned to use the uncapacitated amount Oi+S in the first round but a smaller amount, say Ct. If we have the situation in which only a subset of the orders for period h, with k Ti, are planned to be produced, we will at least produce all orders for type i with a residual lead time of k periods. In all other situations we produce all orders for type i with a residual lead time no longer than Ti, for which the sum of the holding costs and overtime costs is less than the penalty costs for one period  

We will not use extra capacity to produce orders with a residual lead time later than 

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