Refer to Examples 1 to 4 and Solved Problem 13.1.

Note the change to part a

a) Develop another plan for the Mexican roofing manufacturer. For this plan, plan 5, the firm wants to maintain a constant workforce of eight, using overtime to meet remaining demand. Is this plan preferable?

b) The same roofing manufacturer has yet a sixth plan. A constant workforce of seven is selected, with the remainder of demand filled by subcontracting.

c) Is this better than plans 15?

A Jurez, Mexico, manufacturer of roofing supplies has developed monthly forecasts for a family of products. Data for the six-month period January to June are presented in Table 13.2. The firm would like to begin development of an aggregate plan. EXAMPLE 1 Graphical Approach to Aggregate Planning for a Roofing Supplier Month Jan. Feb, Demand per Day (computed) 41 39 Production Days 22 18 21 21 22 38 Expected Demand 900 700 800 1200 1500 1100 6200 Mar. Apr. 57 May 68 June 55 20 124 Table 13.2 Monthly Forecasts APPROACH Plot daily and average demand to illustrate the nature of the aggregate planning problem. SOLUTION First, compute demand per day by dividing the expected monthly demand by the num- ber of production days (working days) each month and drawing a graph of those forecasted demands Forecast demand 70 60 Level production, using average monthly forecast demand Production rate per working day 50 40 30 Jan. Mar. May June T 22 Feb. 7 18 Y 21 Apr. 21 22 20 Month = Number of working days 124 (Figure 13.3). Second, draw a dotted line across the chart that represents the production rate required to moet average demand over the six-month period. The chart is computed as follows: 6200 Total expected demand Average requirement 50 complete units per day Number of production days INSIGHT Changes in the production rate become obvious when the data are graphed. Note that in the first three months, expected demand is lower than average, while expected demand in April, May, and June is above average. LEARNING EXERCISE If demand for June increases to 1200 (from 1100), what is the impact on Figure 13.3? Answer: The daily rate for June will go up to 60, and average production will increase to 50.8 (-6300/124).] RELATED PROBLEMS 13.1 EXAMPLE 2 Plan 1 for the Roofing Supplier-A Constant Workforce Table 13.3 Cost Information One possible strategy (call it plan 1) for the manufacturer described in Example 1 is to maintain a con- stant workforce throughout the six-month period. A second (plan 2) is to maintain a constant workforce at a level necessary to meet the lowest demand month (March) and to meet all demand above this level by subcontracting. Both plan 1 and plan 2 have level production and are, therefore, called level strate- gies. Plan 3 is to hire and lay off workers as needed to produce exact monthly requirementsa chase strategy. Table 13.3 provides cost information necessary for analyzing these three alternatives: Inventory carrying cost $5 per unit per month Subcontracting cost per unit $20 per unit Average pay rate $10 per hour ($80 per day) Overtime pay rate $17 per hour (above 8 hours per day) Labour-hours to produce a unit 1.6 hours per unit Cost of increasing daily production rate $300 per unit (hiring and training) Cost of decreasing daily production rate (layoffs) 5600 per unit ANALYSIS OF PLAN 1 APPROACH Here we assume that 50 units are produced per day and that we have a constant workforce, no overtime or idle time, no safety stock, and no subcontractors. The firm accumulates inventory during the slack period of demand, January through March, and depletes it during the higher-demand warm season, April through June. We assume beginning inventory = 0 and planned ending inventory = 0. SOLUTION We construct the table below and accumulate the costs: Monthly Production Production at Demand Inventory Ending Month Days 50 Units per Day Forecast Change Inventory Jan. 22 1100 900 + 200 200 Feb. 18 900 700 +200 400 Mar. 21 1050 800 +250 650 Apr. 1050 1200 -150 500 May 22 1100 1500 -400 100 June 20 1000 1100 -100 0 1850 21 Total units of inventory carried over from one month to the next month = 1850 units Workforce required to produce 50 units per day = 10 workers Because each unit requires 1.6 labour-hours to produce, cach worker can make 5 units in an 8-hour day. Therefore, to produce 50 units, 10 workers are needed. Finally, the costs of plan 1 are computed as follows: S9250 99 200 Cost Inventory carrying Regular-time labour Other costs (overtime, hiring, layoffs, subcontracting) Total cost Calculations (= 1850 units carried X $5 per unit) (= 10 workers X $80 per day X 124 days) 0 S108 450 INSIGHT Note the significant cost of carrying the inventory. ANALYSIS OF PLAN 2 APPROACH Although a constant workforce is also maintained in plan 2, it is set low enough to meet demand only in March, the lowest demand-per-day month. To produce 38 units per day (800/21) in-house. 7.6 workers are needed. (You can think of this as seven full-time workers and one part-timer.) All other demand is met by subcontracting. Subcontracting is thus required in every other month. No inventory holding costs are incurred in plan 2. SOLUTION Because 6200 units are required during the aggregate plan period, we must compute how many can be made by the firm and how many must be subcontracted: In-house production = 38 units per day * 124 production days = 4712 units Subcontract units = 6200 - 4712 = 1488 units EXAMPLE 3 Plan 2 for the Roofing Supplier-Use of Subcontractors Within a Constant Workforce The costs of plan 2 are computed as follows: Cost Calculations Regular-time labour $ 75 392 (= 7.6 workers X 580 per day X 124 days) Subcontracting 29 760 (= 1488 units x 20 per unit) Total cost $105 152 INSIGHT Note the lower cost of regular labour but the added subcontracting cost. LEARNING EXERCISE If demand for June increases to 1200 (from 1100), what is the change in cost (all other things being oqual)? [Answer: Subcontracting requirements increase to 1588 at $20 per unit for a subcontracting cost of 531 760 and a total cost of $107 152. RELATED PROBLEMS 13.2, 13.3, 13.4, 13.5, 13.6, 13.7.13.8, 13.9, 13.10. 13.11, 13.12. 13.19 EXAMPLE Plan 3 for the Roofing Supplier-Hiring and Layoffs Table 13.4 Cost Computations for Plan 3 ANALYSIS OF PLAN 3 APPROACH The final strategy, plan 3. involves varying the work- force size by hiring and layoffs as necessary. The production rate will equal the demand, and there is no change in production from the previous month, December SOLUTION Table 13.4 shows the calculations and the total cost of plan 3. Recall that it costs $600 per unit produced to reduce production from the previous month's daily level and $300 per unit change to increase the daily rate of production through hirings. Basic Production Extra Extra Cost Cost of Cost of Daily (demand x 1.6 Increasing Decreasing Forecast Production hr per unit Production Production Month (units) Rate $10 per br) (hiring cost) (layoff cost) Total Cost Jan. 900 41 $14 400 $ 14400 Feb. 700 39 11 200 $1200 (= 2 X $60,0) 12 400 38 12 800 $600 (= 1 X $600) 13.400 Apr. 1200 57 19 200 $5700 (= 19 x $300) 24 900 May 1500 68 24 000 $3300 (= 11 X 5300) 27 300 June 1100 SS 17600 $7800 (= 13 X $600) 25 400 $99 200 $9000 S9600 $11780) Thus, the total cost, including production, hiring, and layoff, for plan 3 is $117 800. Mar 800 INSIGHT Note the substantial cost associated with changing (both increasing and decreasing the production levels LEARNING EXERCISE If demand for June increases to 1200 (from 1100), what is the change in cost? [Answer: Daily production for June is 60 units, which is a decrease of 8 units in the daily pro- duction rate from May's 68 units, so the new June layoff cost is $4800 (= 8 X $600), but an additional production cost for 100 units is $1600 (100 X 1.6 X 510), willia tutal plan 3 usef $116,400.1 RELATED PROBLEMS 13.2, 13.3, 13.4, 13.5, 13.6, 13.7, 13.8. 13.9. 13.10, 13.11, 13.12.13.19 Day SOLVED PROBLEM 13.1 The roofing manufacturer described in Examples 1 to 4 of this overtime whenever necessary to meet demand. Use the information chapter wishes to consider yet a fourth planning strategy (plan 4). found in Table 13.3. Again, assume beginning and ending invento- This one maintains a constant workforce of eight people and uses ries are equal to zero. SOLUTION Employ eight workers and use overtime when necessary. Note that carrying costs will be encountered in this plan. Production at 40 Beginning- Forecast Overtime Production Units per of-Month Demand This Production Ending Month Days Inventory Month Needed Inventory Jan. 22 880 900 20 units 0 units Feb. 18 720 0 700 O units 20 units Mar. 21 840 800 units 60 units Apr. 21 840 60 1200 300 units 0 units May 22 880 0 1500 620 units O units June 20 800 0 1100 300 units 0 units 1240 units 80 units Carrying cost totals = 80 units X $5/unit/month = $400 Regular pay: & workers * $80/day x 124 days = 579 360 Overtime pay: To produce 1240 units at overtime rate requires 1240 x 1.6 hours/unit = 1984 hours. Overtime cost = $17/hour 1984 hours = $33 728 20 Plan 4 Costs (workforce of 8 plus overtime) $ 400 (80 units carried X $5/unit) 79 360 (8 workers x $80/day x 124 days) 33 728 (1984 hours x $17/hour) Carrying cost Regular labour Overtime Hiring or firing Subcontracting Total costs Plan 2 is still preferable at $105 152. 0 0 $113 488