A company's production process depends on a supply of a special component. Demand for the component...

Transcribed Image Text:

A company's production process depends on a supply of a special component. Demand for the component is shown in the table below: MONTH 1 1 unit MONTH 2 2 units MONTH 3 1 unit MONTH 4 4 units The company can order units at the beginning of each month. Orders are delivered immediately. It costs 60 to place an order, no matter how many units are ordered. However, it costs 30 to store a unit for one month in a warehouse. Assume the company has no unit in store at the very beginning. (a) Use dynamic programming (DP) to define an ordering policy with the minimal total cost. Solve the DP and provide all the details. How many stages are there in the DP formulation? What are the state variables at each stage? What is the total cost? What is the optimal ordering policy? [60%] (b) Now consider a general case. Suppose that the company knows the demands for T months, which are d1, d2,..., dr. It costs a to place an order regardless of order quantity and b to keep one unit in store for a month. Formulate dynamic programming recursions to find an optimal ordering strategy for this general case. [40%] A company's production process depends on a supply of a special component. Demand for the component is shown in the table below: MONTH 1 1 unit MONTH 2 2 units MONTH 3 1 unit MONTH 4 4 units The company can order units at the beginning of each month. Orders are delivered immediately. It costs 60 to place an order, no matter how many units are ordered. However, it costs 30 to store a unit for one month in a warehouse. Assume the company has no unit in store at the very beginning. (a) Use dynamic programming (DP) to define an ordering policy with the minimal total cost. Solve the DP and provide all the details. How many stages are there in the DP formulation? What are the state variables at each stage? What is the total cost? What is the optimal ordering policy? [60%] (b) Now consider a general case. Suppose that the company knows the demands for T months, which are d1, d2,..., dr. It costs a to place an order regardless of order quantity and b to keep one unit in store for a month. Formulate dynamic programming recursions to find an optimal ordering strategy for this general case. [40%]