Answer Happy

4. A Juarez, Mexico, manufacturer of roofing supplies has developed monthly forecasts for a family of products. Demand data for the 6-month period January to June are presented in Table 1 below. The firm would like to begin development of an aggregate plan. One possible strategy (call it plan 1) for the manufacturer is to maintain a constant workforce throughout the 6-month period. A second plan (plan 2) is to maintain a constant workforce at a level necessary to meet the lowest demand month (March) and to meet all the demand above this level by subcontracting. Both plan 1 and plan 2 have level production and are, therefore, called level strategies. Plan 3 is to hire and lay off workers as needed to produce exact monthly requirements – a chase strategy. Table 2 provides the cost information necessary for analyzing these three alternatives. In Plan 1 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. Assume beginning inventory = 0 and planned ending inventory = 0. Although in Plan 2 a constant workforce is also maintained 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 7 full-time workers and 1 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. The final strategy, plan 3, involves varying the workforce 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.
(A) Determine the daily and average demand to illustrate the nature of the aggregate planning problem.
(B) Determine the total inventory carried from one month to the next and how large of a workforce do you need to produce 50 units per day.
(C) Determine how many units will be done in house and how many will be subcontracted out. Also, determine the cost of regular-time labor and subcontracting labor.
(D) Determine the optimal costs for plan 3.
(E) Determine the optimal (lowest cost) plan.
Table 1 – Monthly Forecasts
Month​​Expected Demand​​Production Days​​Demand per Day
​​​​​​​​​​(Computed)
Jan​​900​​​​22​​​​41
Feb​​700​​​​18​​​​39
Mar​​800​​​​21​​​​38
Apr​​1200​​​​21​​​​57
May​​1500​​​​22​​​​68
June​​1100​​​​20​​​​55
​​6200​​​​124
Table 2 – Cost Information
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)
Labor 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)​$ 600 per unit