Let us consider the oil rig example discussed in Section 6.4.

In that example, there are two stages, the onshore and oil rig facilities. Let us assume that an order placed by the material clerk on the oil rig at the beginning of a period nominally arrives at the beginning of the next period at the oil rig. We say nominally, because the quantity ordered can only be shipped if there is enough stock on hand at the onshore warehouse to satisfy the order. Orders placed by the onshore facility in the beginning of a period arrive there two periods later.

The cost to hold a unit at the end of a period at the onshore facility is $1. The installation holding cost for a unit held at the end of a period on the oil rig is $2. The backorder cost on the oil rig is $20 per unit per period.

The demand per period is either 0,1, or 2 units with probabilities .3, .5, .2 respectively. Demands are independent from period to period.

Determine the optimal stocking levels (echelon inventory position) for each facility.