(1) Provide a linear programming formulation to find the best production plan. (2) Provide an intermediate production plan other than the three plans given in the case.

Case Study:

BACKGROUND MRL had sales of about $28.5 million. The company began in Stratford almost 30 years ago, specializing in commercial refrigeration. Ten years ago the company opened a new 300,000 square foot plant in Stratford and diversified into consumer refrigeration. Subsequently, MRL added air conditioners to its freezer and refrigerator lines. The company sold its Hercules brand appliances through independent furniture and appliance stores in southern Ontario. THE STRATFORD PLANT In the past 20 years, manufacturing efficiency at the plant had increased dramatically through changes in both process design and assembly technology. During this time, annual output per worker had increased from about 240 to 450 appliances, it was expected to be about 480 appliances next year. Although the Canadian market was too small to allow the productivity levels of American appliance manufacturers, MRL was considered to be relatively efficient by Canadian standards. THE PLANNING PROCESS Each year in September the marketing and sales department produced a forecast of appliances by month for the next year. The production planning department used these forecasts to plan production for the next year. The first step in the planning process was to construct an aggregate production plan. This plan consisted of planned gross production by month for the year and did not indicate numbers of specific appliance types, sizes, or models to be made each month but, as the name indicates, was an aggregate. Linda Metzler's task in October was to construct this aggregate plan. As the production periods approached later in the year, master production plans would be formulated which would be specific regarding appliance type, model number, etc. Exhibits 1-4 present the September forecast showing the expected seasonal fluctuations and the aggregate number of appliances to be shipped each month. Linda knew that, although there would be significant variation of specific appliance types within each month, each type of appliance required roughly similar materials and labour resources. Thus, for aggregate planning purposes, the number of appliances to be shipped would be sufficient THE AGGREGATE PLAN In preparation for her decision, Linda gathered the following information: 1. The Stratford plant had the physical capacity to make only 13,000 appliances per month 2. On October 1, MRL employed 160 hourly paid unionized production workers. Their two year contract, signed in February of last year, called for an increase of $0.75 per hour effective next January 1, bringing the average hourly rate to $10.50. With fringe benefits, the monthly cost to MRL would be about $2,400 per worker. Under the agreement, overtime was 1.5 times the regular hourly rate but, because not all fringes were affected, a worker-month of overtime cost about $3,300. The standard work week was 40 hours. The aggregate plan in effect until December 31 called for a total production workforce of 160 at that time. 3. The personnel department estimated that hiring, training, and related expenses would amount to $1,800 per worker. It also estimated that severance and other layoff expenses would cost a total of $1,200 per worker. 4. The accounting department predicted that it would cost about $8 to hold an appliance in inventory for a month during the next year. Raw materials were readily available from regional sources on short notice. The current aggregate plan, supported by marketing's most recent revised forecasts and the master production schedule, predicted an inventory of 240 finished units on December 31. 5. Although MRL manufactured some parts and subassemblies, the plant was primarily a final assembly operation with a throughput time of about three days. The company used an MRP-based planning system. For aggregate planning purposes, management had found that it was adequate to assume that all worker hours scheduled in a particular month would contribute directly to output in the same month. Similarly, they had learned from experience that they would not have to consider any special allowances for learning. 6. There appeared to be three basic tools available to meet demand fluctuations, each of which involved both quantitative and qualitative trade-offs: building inventory to meet peaks using overtime hiring and laying off workers THE ALTERNATIVES Linda identified three alternatives the company could follow to meet forecasted demand: 1. The production level and the workforce could be held constant throughout the year at a level sufficient to meet the peak demand period. In periods of low demand inventory would be accumulated and would be drawn down during peak demand periods. Linda was attracted by the protection this plan offered against unforeseen demand changes. This plan is one example of a level strategy and is shown in Exhibit 1. 2. The production level could vary to meet demand with a constant workforce by the use of overtime in peak months and restricted output in slow months; it is an example of a chase strategy and is shown in Exhibit 2. The workforce would be held at just the number to meet average monthly requirements. MRL would incur no inventory carrying costs with such a scheme. However, Linda wondered if excessive overtime might lead to lower efficiency, or if restricted production might promote poor work habits and low morale. 3. Some of these potential problems could be overcome by a strategy that met demand by varying workforce levels. Linda's calculations showed this to be the cheapest of the three alternatives (see Exhibit 3). However, she was well aware that union relations and employee morale could be adversely affected by frequent layoffs. As well, hiring and training new employees brought their own headaches, especially in a limited labour market such as existed in Stratford. THE DECISION Linda knew that these three very different plans were by no means the only feasible ones available. She realized that her decision on an aggregate plan would involve both quantitative and qualitative trade-offs. One thought nagged in the back of her mind: no matter which plan she chose, how would she know if a better one existed? She decided to start by filling out her blank form (Exhibit 4) one more time. Exhibit 1 LEVEL PRODUCTION TO MEET PEAK DEMAND Month Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Totals Production Plan 4400 8440 4400 4400 8440 4400 6000 8440 6000 8000 8440 8000 6600 8440 6600 11800 8440 11800 13000 8440 13000 11200 8440 11200 10800 8440 10800 7600 8440 7600 6000 8440 6000 5600 8440 5600 95400 101280 95400 240 4280 8320 10760 11200 13040 9680 5120 2360 0 840 3280 6120 75000 160 211 0 Shipment Forecast Production Plan Shipments Inventory Extraordinary Labour Costs Number of Workers Hirings Layoffs Worker Months Overtime Cost of Alternative 1 Hiring Costs Layoff Costs Inventory Holding Costs Labour Costs Regular Overtime TOTAL COSTS 211 51 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 211 0 0 0 OOC 2532 51 0 0 51 x 1800 = 0 75000 x 8 91,800 0 600,000 2532 x 2400 = 0 6,076,800 56,768,600 On December 31 finished goods inventory was predicted to be 240 units. On December 31 the workforce was predicted to be 160 workers. 2 Exhibit 2 CHASE PRODUCTION PLAN WITH CONSTANT WORKFORCE AND OVERTIME Month Dee Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Totals Production Plan Shipment Forecast Production Plan Shipments Inventory 4400 4160 4400 4400 4400 6000 6000 6000 8000 8000 8000 6600 6600 6600 11800 11800 11800 13000 13000 13000 11200 11200 11200 10800 10800 10800 7600 7600 7600 6000 6000 6000 5600 5600 5600 95400 95160 95400 4400 240 0 0 0 0 0 0 0 0 0 0 0 0 0 160 Extraordinary Labour Costs Number of Workers Hirings Layoff's Worker Months Overtime 199 39 0 0 199 0 0 0 199 0 0 0 199 0 0 1 199 0 0 0 199 0 0 96 199 0 0 126 199 0 0 81 199 0 0 71 199 0 0 0 199 0 0 0 199 0 0 0 2388 39 0 375 39 x 1800 0 Cost of Alternative 2 Hiring Costs Layoff Costs Inventory Holding Costs Labour Costs Regular Overtime 70,200 0 0 2388 x 2400 375 x 3300 5,731,200 1.237.500 TOTAL COSTS $7,038,900 On December 31 finished goods inventory was predicted to be 240 units. On December 31 the workforce was predicted to be 160 workers. Exhibit 3 CHASE PRODUCTION PLAN WITH VARYING WORKFORCE Month Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Totals 4400 4160 4400 4400 4400 4400 6000 6000 6000 8000 8000 8000 6600 6600 6600 11800 11800 11800 13000 13000 13000 11200 11200 11200 10800 10800 10800 7600 7600 7600 6000 6000 6000 5600 5600 5600 95400 95160 95400 240 0 0 0 0 0 0 0 0 0 0 0 0 0 160 Production Plan Shipment Forecast Production Plan Shipments Inventory' Extraordinary Labour Costs Number of Workers Hirings Layoffs Worker Months Overtime Cost of Alternative 3 Hiring Costs Layoff Costs Inventory Holding Costs Labour Costs Regular Overtime TOTAL COSTS 104 0 56 0 110 6 0 0 150 40 0 0 200 50 0 0 165 0 35 0 295 130 0 0 325 30 0 0 280 0 45 0 270 0 10 0 190 0 80 0 150 0 40 0 140 0 10 0 2379 256 276 0 256 x 1800 276 x 1200 0 460,800 331,200 0 2379 x 2400 0 5,709,600 $6,501,600 On December 31 finished goods inventory was predicted to be 240 units. On December 31 the workforce was predicted to be 160 workers. Exhibit 4 AGGREGATE PLAN FOR MACPHERSON REFRIGERATION LIMITED Month Dec Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Totals Production Plan 4400 4400 6000 8000 6600 11800 13000 11200 10800 7600 6000 5600 95400 240 160 Shipment Forecast Production Plan Shipments Inventory Extraordinary Labour Costs Number of Workers Hirings Layoffs Worker Months Overtime Cost of Alternative 4 Hiring Costs Layoff Costs Inventory Holding Costs Labour Costs Regular Overtime TOTAL COSTS X 1800 X 1200 X 8 X 2400 X 3300 2 On December 31 finished goods inventory was predicted to be 240 units. On December 31 the workforce was predicted to be 160 workers