Dynamic Programming

The Rinky Dink Company makes machines that resurface ice rinks. The demand for such products varies from month to month, and so the company needs to de- velop a strategy to plan its manufacturing given the fluctuating, but predictable, demand. The company wishes to design a plan for the next n months. For each month i, the company knows the demand di, that is, the number of machines that it will sell. Let D = =i di be the total demand over the next n months. The company keeps a full-time staff who provide labor to manufacture up to m ma- chines per month. If the company needs to make more than m machines in a given month, it can hire additional, part-time labor, at a cost that works out to c dollars per machine. Furthermore, if, at the end of a month, the company is holding any unsold machines, it must pay inventory costs. The cost for holding j machines is given as a function h( j ) for j = 1, 2 h(j)