Q1 Mischief Company had been experimenting with various sales and operations plans. As the firm started to lay out plans for next year, management decided to use a four-month planning horizonto reduce computation cost. The firm’s basic data were: Employment level for this December 20 people. Demand forecast for January of next year 200. Demand forecast for February of next year 220. Demand forecast for March of next year 200. Demand forecast for April of next year 220. Inventory level planned for the end of this December 0. Back orders aren’t allowed in the plan. Desired April ending inventory 0. Regular time per month $2,000 per worker-month. Production 10 units/person/month. Overtime premium 50 percent of regular time. Overtime limit 25 percent of regular time per person per month. Inventory carrying cost $150/month/unit (on the average per month). Hiring (or firing) cost $2,000 per person. Use a spreadsheet model to compare the cost of a fixed employment production plan (i.e., 20 peo-ple) that uses overtime to meet demand to a level production plan that uses no overtime to meet production. Q 2 Consider the following information for the Fairmount Company: Production change cost $20/unit of change (from a base of 4,000 units). Most efficient production rate 4,000 units per period. Maximum amount of production capacity 4,600 units per period. Inventory costs $4/unit per period on the ending inventory. Shortage costs $15/unit per period. Subcontracting costs $18/unit (maximum of 1,000 units per period). Beginning inventory 1,200 units. Period Demand (Units) 1 6,000 2 4,500 3 6,000 4 5,100 a. As production manager of Fairmount, you’re in charge of meeting the preceding demand schedule for periods 1 through 4. President Shea specifies that you keep your production plan level for all four months. In addition, Shea limits the total amount of production per month to 4,600 units. Also, since the market Fairmount competes in is very competitive, planned stockouts are not allowed. Therefore, you must decide if and when to subcontract. Maximum amount of subcontracting available in any one period is 1,000 units. Ending inventory at the end of period 4 should be zero. Use a spreadsheet to determine your plan’s cost. b. Assuming the same facts as in part a, except that no subcontracting is allowed, could you follow a pure chase strategy and still meet demand? Why or why not? Q3 On December 31, the ABC Company forecast its next year’s sales to be: Quarter Sales Forecast 1 9,000 units 2 12,000 3 16,000 4 12,000 49,000 Currently, the firm has 12 employees, each producing up to 1,000 units per quarter and earning $2,000 per quarter. The firm estimates its inventory carrying cost to be $2 per unit of ending inventory per quarter and its hiring or layoff costs to be $1,600 per employee. The firm could increase production by working overtime, but overtime work is limited to 25 percent of the regular production rate (or 250 units per employee per quarter). Overtime work is paid at the rate of 1.5 times the regular pay rate. Unused regular time costs the firm $4.16 per hour. (Assume there are 60 eight-hour days per quarter.) The company currently has an inventory of 1,000 units and wishes to have an ending inventory of 1,000 units at the end of the year. The company does not plan to incur inventory shortages. a. Develop the total incremental cost expression of this problem. b. Formulate this problem for solution, using linear programming. c. What’s the total incremental cost of a production plan that assumes a constant production rate(include both regular and overtime production) and level workforce (assume 12 workers)each quarter? d. Compare the cost of the production plan in c to one based on a production rate equal to salesin each quarter. Which has the lowest cost? Q 4 The production manager at the Boston Paint Company is preparing production and inventory plans for next year. The production manager has the following data concerning the firm: Quarter Sales Forecast 1 3,000 units 2 1,800 3 2,400 4 3,500 Current inventory level 300 units. Current employment level 600 people. Production rate last quarter 2,400 units (4 units/employee/quarter). Inventory carrying cost $20/unit/quarter (on ending inventory). Hiring cost $200/employee hired. Layoff cost $200/employee laid off. Regular time production cost per unit $320/unit. Cost of overtime $60/unit. Desired closing inventory level 100 units (minimum). The production manager sees no equipment capacity limitations during the next two years. Employees are hired or laid off only at the beginning of each quarter. Formulate a linear programming production planning model for this company, in sufficient detail so the production manager can solve it to determine the production plan.