A company knows that the demand for its product during each of the next four months will be as follows: Mar Apl Jan 1 Feb 3 2 4 At the beginning of each month, the company must determine how many units should be produced during the current month. During a month in which any units are produced, a setup cost of $3 is incurred. In addition, there is a variable cost of $1 for every unit produced. At the end of each month, a costing cost of 50 cents per unit on hand is incurred. Capacity limitations allow a maximum of 5 units to be produced during each month. The company wants to determine a production schedule that will meet all demand on time and will minimize the sum of production and holding costs during the four months. Assume that 0 units are on hand at the beginning of the first month. Use dynamic programming to model is problem by answering the following questions. (a) How many stages are involved in this decision problem. (b) Identify an appropriate definition of the system state. (c) Identify the actions (decisions) to undertake at each stage. (d) What is the stage cost associated as a function of state and action variables. (e) For the state and action defined, determine the state transition equation (f) Complete dynamic programming backward recursion steps for the months of April and March, only. A company knows that the demand for its product during each of the next four months will be as follows: Mar Apl Jan 1 Feb 3 2 4 At the beginning of each month, the company must determine how many units should be produced during the current month. During a month in which any units are produced, a setup cost of $3 is incurred. In addition, there is a variable cost of $1 for every unit produced. At the end of each month, a costing cost of 50 cents per unit on hand is incurred. Capacity limitations allow a maximum of 5 units to be produced during each month. The company wants to determine a production schedule that will meet all demand on time and will minimize the sum of production and holding costs during the four months. Assume that 0 units are on hand at the beginning of the first month. Use dynamic programming to model is problem by answering the following questions. (a) How many stages are involved in this decision problem. (b) Identify an appropriate definition of the system state. (c) Identify the actions (decisions) to undertake at each stage. (d) What is the stage cost associated as a function of state and action variables. (e) For the state and action defined, determine the state transition equation (f) Complete dynamic programming backward recursion steps for the months of April and March, only
