Reference no: EM131129149

Consider a cruise liner provisioning a certain consumable item for her next trip. In the first stage, the cruise liner procures from the home port region right before the start of the trip. The unit cost for the item at home port is c_1. 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 t_1 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 c_2, where c_2 > c_1. In the second leg, which takes t_2 days, the liner goes back to the home port to complete her voyage. Clearly, T = t_1 + t_2. The daily demand for this item during the cruise follows a normal distribution with a mean of mu and a standard deviation of sigma. The demand across days are 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 y_1 and y_2 denote the replenishment amounts at home port and port-of-call respectively. Compute the optimal replenishment policy that minimizes the cruise liner's expected cost.