The J. Mehta Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows: Month 1 2 3 4 Demand for Stainless Steel Sinks 100 160 240 120 The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices: (1) He/she can produce up to 30 more sinks per month in overtime but at a cost of $130 per sink; (2) He/she can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period combined is 200 sinks, at a cost of $150 each); (3) Or, he/she can fill the demand from his/her on-hand inventory (ie beginning inventory). The inventory carrying cost is $10 per sink per month (ie the cost of holding a sink in inventory at the end of the month is $10 per sink). A constant workforce level is expected. Back orders are NOT permitted (eg. orders taken in period 3 to satisfy the demand for period 2 is not permitted). Inventory on hand at the beginning of month 1 is 30 sinks (i.e. beginning inventory in month I is 30 sinks) 2. b. Set up and formulate algebraically the above "production scheduling problem as a TRANSPORTATION Model to minimize cost. (18 points) Solve using Excel's solver (Provide the corresponding "Excel Spreadsheet" and the **Answer Report"). Also include a managerial statement that describes verbally the results. (10 points) Does this problem have an alternate optimal solution? Justify your answer. (2 points) Note: This problem can be formulated as a multi-period production scheduling LP problem. However, if you try to formulate it this way then you will get ZERO as the problem requirement is to formulate it as a transportation problem. c. The J. Mehta Company's production manager is planning a series of one-month production periods for stainless steel sinks. The forecasted demand for the next four months is as follows: Month 1 2 3 4 Demand for Stainless Steel Sinks 100 160 240 120 The Mehta firm can normally produce 100 stainless steel sinks in a month. This is done during regular production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular production, the production manager has three other choices: (1) He/she can produce up to 30 more sinks per month in overtime but at a cost of $130 per sink; (2) He/she can purchase a limited number of sinks from a friendly competitor for resale (the maximum number of outside purchases over the four-month period combined is 200 sinks, at a cost of $150 each); (3) Or, he/she can fill the demand from his/her on-hand inventory (ie beginning inventory). The inventory carrying cost is $10 per sink per month (ie the cost of holding a sink in inventory at the end of the month is $10 per sink). A constant workforce level is expected. Back orders are NOT permitted (eg. orders taken in period 3 to satisfy the demand for period 2 is not permitted). Inventory on hand at the beginning of month 1 is 30 sinks (i.e. beginning inventory in month I is 30 sinks) 2. b. Set up and formulate algebraically the above "production scheduling problem as a TRANSPORTATION Model to minimize cost. (18 points) Solve using Excel's solver (Provide the corresponding "Excel Spreadsheet" and the **Answer Report"). Also include a managerial statement that describes verbally the results. (10 points) Does this problem have an alternate optimal solution? Justify your answer. (2 points) Note: This problem can be formulated as a multi-period production scheduling LP problem. However, if you try to formulate it this way then you will get ZERO as the problem requirement is to formulate it as a transportation problem. c
