【導(dǎo)讀】priceincreases.duction.demand.carryingcosts.zero).

　　

【正文】 constraint. The mix dictates a production rate of 1,600 units of Part A per day. At this rate, all 800 hours available of the drummer constraint are used. The fabrication constraint would use hours at this rate, leaving hours of excess capacity. The drummer constraint sets the production rate for the entire factory, 1,600 units of A per day. The rope concept simply means that the production rate of the fabrication process is controlled by tying the release of materials to assembly’s rate of production. The daily release of materials to the fabrication process should be enough to produce only 1,600 ponents. The buffer means that there should be a supply of ponents in front of the drummer process (assembly) so that production can continue should the supply of parts to assembly be interrupted. Thus, a 2,400ponent inventory is required. This protects throughput in case production or supply is interrupted. The length reflects the time thought necessary to restore most production interruptions. 3. The use of local labor efficiency measures would encourage the fabrication process to produce at a higher rate than the drummer rate (it has excess capacity) and so would run counter to the TOC objectives. In fact, efficient use of labor in fabrication would cause a buildup of about 266 units per day of workinprocess inventory—a very expensive oute. 497 21–18 Concluded 4. Adding a second shift of 50 workers for the assembly process creates an additional 400 hours of assembly resource. There would now be 1,200 hours of assembly resource available. The assembly constraint now appears as follows: (1/2)X + (2/3)Y ? 1,200 The new constraint graph appears below. (Units are in hundreds.) 05101520250 2 4 6 8 10 12 14 16 18 20 22 24 26A CB Point C is now optimal: X = 2,400, Y = 0. The contribution margin before the increase in the labor cost of the second shift is $48,000 ($20 ? 2,400). Thus, the daily contribution margin increases by $16,000 ($48,000 – $32,000). Since the cost of adding the extra shift of 50 workers is $4,800, the improvement in profit performance is $11,200 ($16,000 – $4,800). 498 21–19 1. Dept. 1 Dept. 2 Dept. 3 Total Product 401 (500 units): ........................Labor hoursa 1,000 1,500 1,500 4,000 ................... Machine hoursb 500 500 1,000 2,000 Product 402 (400 units): ........................Labor hoursc 400 800 — 1,200 ................... Machine hoursd 400 400 — 800 Product 403 (1,000 units): ........................Labor hourse 2,000 2,000 2,000 6,000 ....................Machine hoursf 2,000 2,000 1,000 5,000 Total labor hours....................... 3,400 4,300 3,500 11,200 Total machine hours ................ 2,900 2,900 2,000 7,800 a2 ? 500。 3 ? 500。 3 ? 500. d1 ? 400。 1 ? 400. b1 ? 500。 1 ? 500。 2 ? 500. e2 ? 1,000。 2 ? 1,000。 2 ? 1,000. c1 ? 400。 2 ? 400. f2 ? 1,000。 2 ? 1,000。 1 ? 1,000. The demand can be met in all departments except for department 3. Production requires 3,500 labor hours in department 3, but only 2,750 hours are available. 2. Product 401: CM/Unit = $196 – $103 = $93 CM/DLH = $93/3 = $31 Direct labor hours needed (Dept. 3): 3 ? 500 = 1,500 Product 402: CM/Unit = $123 – $73 = $50 Requires no hours in Department 3 Product 403: CM/Unit = $167 – $97 = $70 CM/DLH = $70/2 = $35 Direct labor hours needed (Dept. 3): 2 ? 1,000 = 2,000 Production should be equal to demand for Product 403 as it has the highest contribution margin per unit of scarce resource. After meeting demand, any additional labor hours in Department 3 should be used to produce Product 401 (2,750 – 2,000 = 750。 750/3 = 250 units of 401). Contribution to profits: Product 401: 250 ? $93 = $ 23,250 499 Product 402: 400 ? $50 = 20,000 Product 403: 1,000 ? $70 = 70,000 Total contribution margin... $113,250 21–19 Concluded 3. Let X = Number of Product 401 produced Let W = Number of Product 402 produced = 400 units Let Y = Number of Product 403 produced Max Z = $93X + $70Y + $50W (objective function) Subject to: 2X + Y ? 1500 (machine constraint) 3X + 2Y ? 2,750 (labor constraint) X ? 500 (demand constraint) Y ? 1,000 (demand constraint) W = 400 Corner Point X Y W Z = $93X + $70Y + $50W ................ A 0 0 400 $ 20,000 ................B 500 0 400 66,500 ................C 500 500 400 101,500 ................D 250 1,000 400 113,250* ................ E 0 1,000 400 90,000 *The optimal output is: Product 401: 250 units Product 402: 400 units Product 403: 1,000 units At this output, the contribution to profits is $113,250. 500 02004006008001 ,0 0 01 ,2 0 01 ,4 0 01 ,6 0 00 100 200 300 400 500 600 700 800 900 1 ,0 0 0A BDEC 501 21–20 1. Potential daily sales: Frame X Frame Y Sales........................ $ 40 $ 55 Materials ................. 20 25 ...... CM per unit $ 20 $ 30 Daily demand ........ ? 200 ? 100 ....... Daily profit $ 4,000 + $ 3,000 = $7,000 potential Process Resource Demands Resource Supply Cutting .......... X: 15 ? 200 = 3,000 Y: 10 ? 100 = 1,000 4,000 4,800 Welding......... X: 15 ? 200 = 3,000 Y: 30 ? 100 = 3,000 6,000 4,800 Polishing ...... X: 15 ? 200 = 3,000 4,800 Painting ........ X: 10 ? 200 = 2,000 Y: 15 ? 100 = 1,500 3,500 4,800 Bountiful cannot meet daily demand. The welding process requires 6,000 minutes but only has 4,800 available. All other processes have excess capacity. Thus, welding is the bottleneck. The contribution margin per unit of welding resource (minutes) for eac