A cruise company provisioning a certain consumable items its next trip. In the first stage, the cruise company procures from the home port region right before the start of the trip.
The unit cost for the item at home port is c1.
The trip duration is T days.
From the provisioning stand point, the trip is completed in two legs:
At the end of the first leg, which takes t1 days, the cruise liner arrives at her port-of-call (midpoint). This is when she has a chance to replenish her inventory for this item. The unit cost at this location is c2, where c2 > c1.
In the second leg, which takes t2 days, the liner goes back to the home port to complete her voyage. Clearly, T = t1 + t2. The daily demand for this item during the cruise follows a normal distribution with a mean of? and a standard deviation of ?.
The demand across days is assumed to be independent. Stock-out cost for the liner is p per unit. Any excess inventory at the end of the trip costs h per unit for landing and salvaging. Let y1 and y2 denote the replenishment amounts at home port and port-of-call respectively. Compute the optimal replenishment policy that minimizes the cruise liners expected cost.