Modelling and Operations Research Course

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Suppose that you are the production manager of a firm that manufactures webcams. You wish to decide how many webcams to produce in each of next 3 weeks in order to meet known demand for webcams at minimum cost. You have no webcams in your inventory at the beginning of the first week and wish to end-up with no inventory at the end of 3 weeks. Certainly, the number of webcams to be produced has to be integer. The production capacity of your manufacturing plant is 3 webcams per week. You can hold at most 2 webcams in your warehouse in a week. Inventory holding cost is 3 dollars per webcam per week. The demand for webcams over the next 3 weeks and the cost of producing each webcam in each of these weeks is given in the below table. . . Week n Demand (D) Production cost per webcam (Cn) 1 1 14 2 4 16 3 3 17 Find an optimal weekly production plan that minimizes total cost using dynamic programming (also clearly define stages, states, and decision variables). That is, find the optimal number of webcams to be produced for each week