The two-step overtime rule

We do not consider any variability, but we just consider the costs for working overtime we would have if the number of orders would equal F,- and if, from the second period on, we would take the maximum action The penalty costs is this model are given by  

We only have to consider the first N periods, since we assume that C e N. 

We also consider the first N periods, because we cannot produce extra orders for later periods. 

The two-step overtime rule is not much different from the two-step rule. In the first part we calculate the base cost for every type and for those actions that consist of producing all orders for a type for an integer number of periods (including 0) or the action in which the normal available completely. This set of possible actions is denoted by A,-, where i is the type of product we consider. 

We define Co(i,j)=°° if a,- Ai, that is for those actions we expect to be non-optimal or actions which are simply impossible, because there are not enough orders for the type we consider. As in the two-step rule we now determine the base cost reduction Ko(i,j)y defined as the difference in the base costs between the use of j units and 0 units of capacity for type i. Using J units of capacity implies that action a,- =j-Sis taken. The 

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