Chapter 13 Aggregate Planning Essay 3

125) Houma Containers, Inc., makes industrial fiberglass tanks that are used on offshore oil platforms. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $400. Overtime cost is 150% of regular time cost. Subcontracting is available in substantial quantity but at a very high cost, $1100 per unit. Holding costs are $200 per tank per month; back orders cost the firm $1000 per unit per month. Houma's management believes that the transportation algorithm can be used to optimize this scheduling problem. The firm has no beginning inventory and anticipates no ending inventory. Demand Regular capacity Overtime capacity Subcontract cap. March 300 200 50 150 April 500 200 50 100 May 300 250 50 100 June 350 250 50 150 a. How many units will be produced on regular time in June? b. How many units will be produced by subcontracting over the four-month period? c. What will be the inventory at the end of April? d. What will be total production from all sources in April? e. What will be the total cost of the optimum solution? f. Does the firm utilize the expensive options of subcontracting and back ordering? When; why? 36 Answer: (a) 250; (b) 350; (c) 0, and 50 units are back ordered; (d) 350; (e) $935,000; (f) they use subcontracting every month; there are back orders in April filled with May production. The firm has so little excess capacity, even with the short -term options, that it must utilize almost every unit available, which forces the use of the more expensive options. The data table and solution table appear below. Diff: 2 Topic: Methods for aggregate planning AACSB: Analytic Skills Objective: LO13-4 37 126) Fred's Fabrication has the following aggregate demand requirements and other data for the upcoming four quarters. Quarter 1 2 Demand 700 900 3 4 1200 600 Previous quarter's output Beginning inventory Stockout cost Inventory holding cost Hiring workers Laying off workers Subcontracting cost Unit cost 800 units 0 units $100 per unit $10 per unit at end of quarter $20 per unit $40 per unit $200 per unit $100 per unit Which of the following production plans is better: Plan A–chase demand by hiring and layoffs; Plan B–pure level strategy, or Plan C–700 level with the remainder by subcontracting? Answer: Plan A has cost of $378,000, plan B has cost of $368,500, and plan C has cost of $425,000. Plan B has the lowest cost. Note that Plan C has an ending inventory of 100 units, which is the result of level production which exceeds demand in the last quarter. Plan A -- Chase strategy Plan B -- Level production, 850 per quarter 38 Plan C -- 700 units level, with subcontracting Diff: 2 Topic: Methods for aggregate planning AACSB: Analytic Skills Objective: LO13-4 127) Byron's Manufacturing makes tables. Demand for the next four months and capacities of the plant are shown in the table below. Unit cost on regular time is $40. Overtime cost is 150% of regular time cost. Subcontracting is available in substantial quantity at $75 per unit. Holding costs are $5 per table per month; back orders cost the firm $10 per unit per month. Byron's management believes that the transportation algorithm can be used to optimize this scheduling problem. The firm has 50 units of beginning inventory and anticipates no ending inventory. Demand Regular capacity Overtime capacity Subcontract cap. March 400 400 100 150 April 600 400 100 50 May 600 400 100 50 June 700 400 100 50 a. How many units will be produced on regular time in June? b. How many units will be produced by subcontracting over the four-month period? c. What will be the inventory at the end of April? d. What will be total production from all sources in April? e. What will be the total cost of the optimum solution? f. Does the firm utilize the expensive options of subcontracting and back ordering? When; why? 39 Answer: (a) 400; (b) 250; (c) 0; (d) 550; (e) Total Cost = $109,750; (f) The firm uses subcontracting, but not backordering; there is no production in one month for "delivery" in an earlier month. Subcontracted quantities are 100 in March, 50 each in April, May, and June. The data and solution tables appear below. Diff: 2 Topic: Methods for aggregate planning AACSB: Analytic Skills Objective: LO13-4 40 128) A small private university normally charges the same price –$200–per credit -hour for all courses and for all students. While the university is pretty near capacity in the fall and spring, it finds that its classrooms are only about 60 percent occupied during the summer session. A student of operations management (who has recently read this chapter) wonders if yield management might be useful to both the university and its students alike. This student, with help from some economics majors, estimates a demand curve for summer course enrollment. Points on this demand curve include 9000 credit -hours at the current rate of $200, 12,000 credit hours at $180, 15,000 credit-hours at $160, and 18,000 credithours at $140. Based on this demand curve, what price point would best serve the university, if its objective is the greatest revenue for the summer session? Answer: The student must consider that since 9000 hours is 60 percent of capacity there is a classroom capacity of 15,000 credit -hours during the summer session. The lowest price generates the most revenue, but it is based on 18,000 credit-hours, which is beyond capacity. At $200 per credit hour, revenues would be $1,800,000; at $180, revenues would be $2,160,000; at $160, revenues would be $2,400,000; and at $140, demand exceeds capacity. The $160 price point yields the most revenue of the feasible price points. Diff: 2 Topic: Yield management AACSB: Analytic Skills Objective: LO13-5 129) A professional services firm is investigating yield management as a means of taking advantage of unused capacity. Analysts for this firm estimate a demand curve for the firm's service, which is sold by the hour. Points on this demand curve include 9000 hours at the current rate of $60 per hour, 9500 hours at $55, 10,000 hours at $50, and 10,500 hours at $45. Based on this demand curve, what price point would be best for the firm, if its objective is maximum revenue? Answer: The yields of these price points are as follows: at $60 per hour, revenue is $540,000; at $55, revenue is $522,500; at $50, revenue is $500,000; and at $45, revenue is $472,500. The firm would be well advised not to lower its price, since that will not raise revenue. The lower prices will generate more demand, and utilize some unused capacity, but the firm's revenues will fall. (Demand in this case is pretty inelastic). Diff: 2 Topic: Yield management AACSB: Analytic Skills Objective: LO13-5 41 130) A large consulting firm is deciding on if its workforce should be expanded, maintained, or decreased. Suppose that demand is given in week long projects, and that a consultant can work on 3 projects each month (1 week off for personal leave and/or other duties such as conferences, etc). Currently there are 25 consultants. Ten consultants are trained for LEAN and 15 for Six Sigma, with 5 of those consultants being overlaps (the consultant is trained for BOTH LEAN and Six Sigma). Assume that all consultants can do the general work. Complete the table (the forecast period is an upcoming month) and prepare a recommendation. Best Likely Worst Max Forecast Forecast Forecast Demand (# (# (# in # of Category projects) projects) projects) people LEAN 42 24 12 Six Sigma 45 36 30 General 75 60 57 Number of Qualified People Answer: Best Likely Worst Max Forecast Forecast Forecast Demand (# (# (# in # of Category projects) projects) projects) people LEAN 42 24 12 14 Six Sigma 45 36 30 15 General 75 60 57 25 Number of Qualified People 10 15 25 NOTE: Student responses will vary but should follow the same principles. Under the likely condition (24+36+60)/3 = 40 total consultants are needed but only 25 are available. Under the worst forecast 33 consultants are needed total but again only 25 are available. Thus the firm should hire more consultants, but which type? 4 additional LEAN trained consultants are needed to meet maximum demand, while the number of Six Sigma consultants is adequate. However, there is an overlap of 5 consultants being counted in each category, so the hiring recommendation must be at least 4 LEAN consultants and then 5 additional consultants that can perform either LEAN or Six Sigma, for a total of 9 trained consultants. To meet likely demand 15 total consultants must be added, so 6 general consultants at a minimum should be hired. Thus the recommendation is for: At least 15 consultants, with a minimum of 4 trained in LEAN and a minimum total of 9 trained in either LEAN or Six Sigma. Diff: 3 Topic: Aggregate planning in services AACSB: Analytic Skills Objective: no LO 42 131) A train company is considering applying yield management principles to its ticket sales. Suppose that there is no variable cost in the operation, only a fixed cost to run each train. The company decides that a student ticket will sell for half the cost of a business ticket. If demand for the business tickets is given by 50-3x where x is the sales price of a business ticket and demand for student tickets is given by 70-y^2 where y is the price of a student ticket how much should the company charge for tickets to maximize revenue? Answer: The crucial step is to relate x and y, using the relation that 2*y=x. Revenue from the business tickets is Demand*cost = x(50-3x) Revenue from the student tickets is demand*cost = y(70-y^2) Total revenue is thus x(50-3x)+y(70-y^2) Substituting yields 2y(50-6y)+y(70-y^2) as total revenue Students must then either graph this function to find its maximum feasible solution, or know that when the derivative is 0 the function is at its local maximum (for the feasible solution range of x and y > 0) The derivative is given by dR/dy=-3y^2-24y+170, using either a calculator solver or the quadratic equation yields y=-12.5 or y=4.52. Since price cannot be negative y must be set at $4.52 and subsequently x is $9.04. Thus the company should charge students $4.52 and business travelers $9.04 *Note- this problem requires use of basic calculus and have content related to, but not expressly performed in, the text. As such they are more difÏcult than usual problems and require reflective thinking on the students' behalf. Diff: 3 Topic: Yield management AACSB: Analytic Skills Objective: LO13-5 132) A manager is applying the transportation model of linear programming to solve an aggregate planning problem. Demand in period 1 is 100 units and in period 2 demand is 150 units. The manager has 125 hours of regular employment available for $10/hour each period. In addition, 50 hours of overtime are available for $15/hour each period. If holding costs are $2 per unit each period, how many hours of regular employment should be used in period 1 (assume demand must be met in both periods 1 and 2 for the lowest possible cost and that production is 1 unit per hour)? Answer: In period 2 all regular work will be used for a total of 125 units. However, 150 are needed and 25 units must be made with either overtime from period 2 or carried from period 1. In period 1 100 units are made with regular work, leaving 25 hours available. The cost to make 25 units and carry them into period 2 is $12/unit (hourly rate + holding cost). The cost to make these units with overtime in period 2 would be $15/unit, so the units should be produced in period 1. Thus the total hours of regular employment should be 125 for both periods 1 and 2. *Note- this problem requires use of basic calculus and have content related to, but not expressly performed in, the text. As such they are more difÏcult than usual problems and require reflective thinking on the students' behalf. Diff: 3 Topic: Methods for aggregate planning AACSB: Analytic Skills Objective: LO13-4 43 133) A manufacturing plant has created the following forecast and would like to apply a graphical aggregate planning method. Complete the table and calculate the difference between Jan.'s forecast demand per working day vs a level production model for the entire period? Month Jan. Feb. Mar. Expected Demand 1800 1400 1600 Demand per Day (to Productio the nearest whole n Days unit) 22 18 21 Expected Demand 1800 1400 1600 Productio n Days 22 18 21 Answer: Month Jan. Feb. Mar. Demand per Day (to the nearest whole unit) 82 78 76 Total expected demand/ Total # working days = level production rate = 79 units/day Thus the difference between Jan. and the level production is 3 units. *Note- this problem requires use of basic calculus and have content related to, but not expressly performed in, the text. As such they are more difÏcult than usual problems and require reflective thinking on the students' behalf. Diff: 3 Topic: Methods for aggregate planning AACSB: Analytic Skills Objective: LO13-4 44