(Rosenthal, White, and Young, 1978) Consider the following modification of Problem 6.48. 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 utilizing the equipment trailer is 100 if the repairman is at site k > 1 and trailer is at site j # k with j > 1 and 200 if the repairman is at remote site j > 1 and the trailer is at the home office, site 1. If the repairman is at site 1, no work is carried out, so the cost of using the trailer if it is there equals 0. Assume that the probability of the repairman moves from site s to site j in one period, p(j(s) is given by the matrix

instead of that in Problem 6.48. Note that, in this formulation, state 1 is absorbing, so that once the repairman reaches the home office, no future decisions are made.

a. Formulate this as a negative Markov decision problem. Note that a finite horizon formulation will not apply.

b. Find a relocation policy that minimizes the expected total cost in one cycle.