A shipping company wants to phase out a fleet of (homogeneous) general cargo ships over a period of p years. Its objective is to maximize its cash assets at the end of the p years by considering the possibility of prematurely selling ships and temporary replacing them by charter ships. The company faces a known nonincreasing demand for ships. Let d(i) denote the demand of ships in year i. Each ship earns a revenue of r_k units in period k. At the beginning of year k, the company can sell any ship that it owns, accruing a cash inflow of S_k dollars. If the company does not own sufficiently many ships to meet its demand, it must hire additional charter ships. Let h_k denote the cost of hiring a ship for the kth year. The shipping company wants to meet its commitments and at the same time maximize the cash assets at the end of the pth year. Formulate this problem as a minimum cost flow problem.

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