# (Rosenthal, White, and Young, 1978). Consider the following version of the dynamic location model…

(Rosenthal, White, and Young, 1978). Consider the following version of the dynamic location model presented in Problem 3.17. There are Q = 4 work sites, with site 1 denoting the home office and 2, 3, and 4 denoting remote sites. The cost of relocating the equipment trailer is d(k, j) = 300 for k # j; the cost c(k, j) of using the equipment trailer is 100 if the work force is at site k > 1, and trailer is at site j # k with j > 1; 50 if j = k and j > 1 and 200 if the work force is at remote site j > 1, and the trailer is at the home office, site 1. If the work force is at site 1, no work is carried out, so the cost of using the trailer in this case can be regarded to be 0. Assume that the probability of moving between sites in one period p(jls) is given by the matrix

Assuming the discount rate A = 0.95, find a relocation policy which minimizes the expected discounted cost and describe the structure of the optimal policy.

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