Backorders case with Poisson demands and constant procurement lead time

Here we would like to state the assumptions and the variables used thereof where the Poisson process generates the times between demands and they are:

1.  = Mean rate of demand in units per year
2.  = Procurement lead time which is constant
3.  = Order quantity which is discrete
4.  = Reorder point, which is also considered as discrete

Few simple calculations will result in the following which are :

1. Expected number of backorders is  and it is given by , where .
2. Expected number of backlogs is  and it is given by , where .
3. Expected on hand inventory is  and it is given by .
   
4. Average annual variable cost is  and it is given by .

Few other examples where one can have different concepts of , , , , etc are shown in Figures 9.3, 9.4 and 9.5

Figure 9.3: Ordering time periods are different, quantum of ordering is same, lead time is deterministic, base stock level is defined