Chapter 2 - Production Planning system PDF

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CHAPTER 22 If the opening inventory is 400 units, demand is 900 units, and production is 700 units, what will be the ending inventory? Ending inventory = opening inventory + production – demand = 400 + 700 – 900 = 200 units 2. A company wants to produce 500 units over the next 3 months at a uniform ...

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CHAPTER 2 2.1 If the opening inventory is 400 units, demand is 900 units, and production is 700 units, what will be the ending inventory? Ending inventory = opening inventory + production – demand = 400 + 700 – 900 = 200 units 2.2. A company wants to produce 500 units over the next 3 months at a uniform rate. The months have 19, 20, and 21 working days, respective! On the average, how much should the company produce each day to level production? Total Production = 500 units Total working days = 19 + 20 + 21 = 60 days Average daily production = 500 / 60 = 8.33 Answer. Average daily production = 8.3 units 2.3. A company plans to produce 25,000 units in a 3-month period. The months have 22, 21, and 20 working days respectively. What should the average daily production be? Total Production; = 25,000 units Total working days = 22 + 21 + 20 = 63 days Average daily production = 25,000 / 63 = 396.8 units 2.4. In problem 2.2, how much will be produced in each of 3 Months? Month 1 = working days * production / day = 19 days * 8.33 units = 158 Month 2 = 20 days * 8.33 units = 166 Month 3 = 21 days * 8.33 units = 174 2.5. In problem 2.3, how much will be produced in each of the 3 months? Month 1 = working days * production / day = 22 days * 396.8 units = 8729.6 units Month 2 = 21 days * 396.8 units = 8332.8 units Month 3 = 20 days * 396.8 units = 7936 units 2.6. A production line is to run at 1000 units per month. Sales are forecast as shown in the following. Calculate the expected period-end inventory. The opening inventory is 600 units. All periods have the same number of working days.

Period 1 2 3 4 Forecast 750 700 1050 1600 Planned Production 1000 1000 1000 1000 Planned 600 850 900 550 0 inventory Ending inventory period = opening inventory + production – demand

5 1000 1000 600

6 850 1000 750

Total 5950 6000

= 600 + 1000 – 750 = 850 Answer. For period 1, the ending inventory is 850 units. 2.7. A company wants to develop a level production plan for a family of products. The opening inventory is 100 units, and an increase to 150 units is expected by the end of the plan. The demand for each period is given in what follows. How much should the company produce each period? What will be the ending inventories in each period? All periods have the same number of working days. Period 1 2 3 Forecast Demand 100 120 125 Planned Production 125 125 125 Planned 100 125 105 100 inventory Total Production required = 700 + 150 – 100 = 750

4 130 125 95

5 115 125 110

6 110 125 115

TOTAL 700 750

Production each period = 750 / 6 = 125 units Ending inventory = opening inventory + production – demand Ending inventory after the 1st period = 100 + 125 – 100 = 125 Ending inventory (period 2) = 100 + 125 – 120 = 105 2.8. A company wants to develop a level production plan for a family of products. The opening inventory is 450 units, and a decrease to 200 units is expected by the end of the plan. The demand for each of the periods is given in what follows. All periods have the same number of working days. How much should the company produce each period? What will be the ending inventories in each period? Do you see any problems with the plan? Total Production required = 5,600 + 200 – 450 = 5,350 units Production each period = 5,350 / 6 = 891.7 cases Ending inventory = opening inventory + production – demand Ending inventory after the first period = 450 + 1300 – 500 = 1,250 Ending inventory (2 period) = 1,250 + 891.7 – 1200 = 941.7 Ending inventory is 200 units Period Forecast Demand Planned Production Planned 500 inventory

1 1300 891.7 1,250

2 1200 891.7 941.7

3 800 891.7 1341.7

4 600 891.7 1541.7

5 800 891.7 1341.7

6 900 891.7 1241.7

TOTAL 5,600 5,350

The only problem I see with this plan is production staying efficient during period 1 & 2 with have to produce a greater amount than the rest of the periods. The ending inventory at period 2 is 0 so that could be a problem to not have any in stock, but these periods already have to produce a greater amount. Depending on production capacity period 1 & 2 planned production could be increased if the department can stay on schedule. Periods 3 – 6 planned production could decrease than if periods 1 & 2 were increased. 2.9. A company wants to develop a level production plan. The beginning inventory is zero. Demand for the next four periods is given in what follows. a. What production rate per period will give a zero inventory at the end of period 4? Total monthly production = 32/4 = 8 Production Rate of 8 per period will give a zero inventory at the end of period 4 b.When and in what quantities will back orders occur? Ending inventory after the first period = 0 + 8 – 9 = -1 c. What level production rate per period will avoid back orders? What will be the ending inventory in period 4? Period 1 Forecast Demand 9 8 Planned Production Planned 0 -1 inventory Ending inventory (2nd period) = 0 + 8 – 5 = 3

2 5 8 3

3 9 8 -1

4 9 8 -1

TOTAL 32 32

2.10. If the cost of carrying inventory is $50 per unit per period and stock out cost $500 per unit, what will be the cost of the plan developed in problem 2.9a? What will be the cost of the plan developed in 2.9c? There is a stock out of 1 unit in period of time. The cost will be: Stock out cost: 1 * $500 = $500 Carrying cost: 3 * $50 = $150 Total cost: $500 + $50 = $650 Total period inventory = 0 + 5 + 3 + 4 = 12 units The cost will be = $50 * 12 = $600 Since there are no stockouts this will be the total cost of the plan. Answer Total cost for plan in question 2.9a = $650 Total cost for plan in question 2.9c = $600 2.11. A company wants to develop a level production plan for a family of products. The opening inventory is 100 units, and an increase to 130 units is expected by the end of the plan. The demand for each month is given in what follows. Calculate the total production, daily production, and production and ending inventory for each month Period

May

Jun

Jul

Aug

TOTAL

Working Days 21 Forecast Demand 115 Planned Production 203.9 Planned 100 188.9 inventory Opening Inventory = 100 units

19 125 184.49 248.4

20 140 194.2 302.6

10 150 97.1 249.7

70 530 679.69 989.6

Ending inventory = 250 units Total production = 530 + 250 – 100 = 680 units Average Total Production = 680 / 70 = 9.71 units/ day Production Each Month: May = 21 * 9.71 = 203.91 Jun = 19 * 9.71 = 184.49 Jul = 20 * 9.71 = 194.2 Aug = 10 * 9.71 = 97.1 Ending Inventory in each month Ending inventory = Open inventory + Production – Demand May = 100 + 203.91 – 115 = 188.9 Jun = 188.9 + 184.49 – 125 = 248.4 Jul = 248.4 + 194.2 – 140 = 302.6 Aug = 302.6 + 97.1 – 150 = 249.7 2.12. A company wants to develop a level production plan for a family of products. The opening inventory is 500 units, and a decrease to 100 units is expected by the end of the plan. The demand for each of the months is given in what follows. How much should the company produce each month? What will be the ending inventory in each month? Do you see any problems with the plan? Period Jan Working Days 20 Forecast Demand 1200 874 Planned Production Planned 500 174 inventory Opening Inventory = 500 units

Feb 22 1300 961.4 164.6

Mar 20 800 874 -90.6

Ending inventory = 100 units Total Production (TP) = 5600 + 100 – 500 = 5200 units Average Total production (ATP) = 5200 / 119 = 43.7 units/days Production Each Month: Jan = 20 * 43.7 = 874

Apr 20 700 874 83.4

May 18 700 786.6 170

Jun 19 900 830.3 100.3

TOTAL 119 5600 5200.3 782.9

Feb = 22 * 43.7 = 961.4 Mar = 20 * 43.7 = 874 Apr = 20 * 43.7 = 874 May = 18 * 43.7 = 786.6 Jun = 19 * 43.7 = 830.3 Ending inventory in each month Ending inventory = Opening inventory + Production – Demand Jan = 500 + 874 – 1200 = 174 Feb = 174 + 961.4 – 1300 = -164.6 Mar = -164.6 + 874 – 800 = -90.6 Apr = -90.6 + 874 – 700 = 83.4 May = 83.4 + 786.6 – 700 = 170 Jun = 170 + 830.3 – 900 = 100.3 2.13. Because of its labor contract, a company must hire enough labor for 100 limits of production per week on one shift or 200 units per week on two shifts. It cannot hire, lay off, or assign' Overtime. During the fourth week, workers will be available from another department to work part or all of an extra shift (up to 100 units). There is a planned shutdown for maintenance in the second week, which will cut production to half. Develop a production plan. The opening inventory is 200 units, and the desired ending inventory is 300 units. Period Forecast Demand Planned Production Planned 300 inventory Opening inventory = 200

1 120 660 840

2 160 880 1560

3 240 1320 2640

4 240 1320 3720

5 160 880 4440

6 160 880 5160

TOTAL 1080

Planned inventory = 300 Labor contract = 100 limits of production per week for one shift and 200 for two shifts Total Production = 300 + 1080 – 200 = 1180 units Average Weekly level production = 1180 / 5.5 = 214.5 units ~ 215 units Number of weeks available for production = 5.5 The nearest quantity that can be produced is 200 units on two shifts. In the second week there is a shutdown so production in that week that will be only 100 units. Total production so far = 5 * 200 + 100 = 110 units The balance of 80 units can be made in week four when extra help in available. Opening inventory = 200 units

Production each week: 1. = 120 * 5.5 = 660 2. = 160 * 5.5 = 880 3. = 240 * 5.5 = 1320 4. = 240 * 5.5 = 1320 5. = 160 * 5.5 = 880 6. = 160 * 5.5 = 880 Ending inventory in each month Ending inventory = Opening inventory + Production – Demand 1. 2. 3. 4. 5. 6.

=300 + 660 – 120 = 840 = 840 + 880 – 160 = 1560 = 1560 + 1320 – 240 = 2640 = 2640 + 1320 – 240 = 3720 = 3720 + 880 – 160 = 4440 = 4440 + 880 – 160 = 5160

2.14. If the opening backlog is 500 units, forecast demand is 700 units, and production is 800 units, what will be the ending backlog? Projected backlog = old backlog + forecast – production = 700 + 500 - 800 = 400 units 2.15. The opening backlog is 800 units. Forecast demand is shown in the following. Calculate the weekly production for level production if the backlog is to be reduced to 100 units. Period Forecast Demand Planned Production Project 800 Backlog Opening backlog = 800 units

1 750 750 800

2 700 750 750

3 550 750 550

4 700 750 500

5 600 750 350

Backlog to be reduced = 100 units Total Production Backlog = Forecast Demand + Open Backlog – Ending Backlog = 3800 + 800 – 100 = 4500 ATP Backlog = 4500 / 6 = 750 units Ending Backlog = Opening Backlog + Forecast Demand – Production 1. = 800 + 750 – 750 = 800 2. 800 + 700 – 750 = 750 3. 750 + 550 – 750 = 550 4. 550 + 700 – 750 = 500 5. 500 + 600 – 750 = 350 6. 350 + 500 – 750 = 100

6 500 750 100

TOTAL 3800 4500 3050

2.16. The opening backlog is 1100 units. Forecast demand is shown in the following. Calculate the weekly production for level production if the backlog is to be increased to 1200 units. Period Forecast Demand Planned Production Project 1100 Backlog Opening backlog = 1100

1 1200 1117 1183

2 1100 1117 1166

3 1200 1117 1249

4 1200 1117 1332

5 1100 1117 1317

6 1000 1117 1199

TOTAL 6800 6702

Backlog is to be increased = 1200 Total Production Backlog = Forecast demand + Open Backlog – Ending Backlog 6800 + 1100 – 1200 = 6700 units ATP backlog = 6700 / 6 = 1116.7 units ~ 11117 Ending Backlog = Opening backlog + Forecast Demand – Production 1. 1100 + 1200 – 1116.7 = 1183.3 ~ 1183 2. 1183.3 + 1100 – 1116.7 = 1166 3. 1166.6 + 1200 – 1116.7 = 1249 4. 1249.9 + 1200 – 1116.7 = 1333 5. 1333.2 + 1100 – 1116.7 = 1317 6. 1316.5 + 1000 – 1116.7 = 1199 2.17. For the following data, calculate the number of workers required for level production and the resulting month-end inventories. Each worker can produce 15 units per day, and the desired ending inventory is 9000 units. Month 1 2 3 Working Days 20 24 12 Forecast Demand 28000 27500 28500 Planned Production 29400 35280 17640 Planned 11250 12650 20430 9570 Inventory Total Production = 112500 + 9000 – 11250 = 110,250 units Average Total Production = 110250 / 75 = 1470 Number of workers required = 1470 / 15 = 98 workers Actual Daily production = 98 * 15 = 1470 units Production Each Month: 1. 2. 3. 4.

= 20 * 1470 = 29400 24 * 1470 =35280 12 * 1470 = 17640 19 * 1470 = 27930

Ending inventory = open inventory + Production – Demand 1.

11250 + 29400 – 28000 = 12650 units

4 19 28500 27930 9000

TOTAL 75 112,500 110250 51650

2. 3. 4.

12650 + 35280 – 27500 = 20430 units 20430 + 17640 – 28500 = 9570 units 9570 + 27930 – 28500 = 9000 units

2.18. For the following data, calculate the number of workers required for level production and the resulting month-end inventories. Each worker can produce 9 units per day, and the desired ending inventory is 800 units. Why is it not possible to reach the exact ending inventory target? Month 1 2 Working Days 20 24 Forecast Demand 2800 3000 3060 3672 Planned Production Planned 1000 1260 1932 Inventory Total Production = 17900 + 800 – 1000 = 17700

3 12 2700 1836 1068

4 22 3300 3366 1134

5 20 2900 3060 1294

6 19 3200 2907 1001

TOTAL 117 17900 17901

Daily Production = 17700 / 117 = 151.28 units Number of workers required = 151.28 / 9 = 16.81 ~ 17 workers Actual Daily production 17 * 9 = 153 units Production each month: 1. 20 * 153 = 3060 2. 24 * 153 = 3672 3. 12 * 153 = 1836 4. 22 * 153 = 3366 5. 20 * 153 = 3060 6. 19 * 153 = 2907 Ending inventory: 1. 1000 + 3060 – 2800 = 1260 2. 1260 + 3672 – 3000 = 1932 3. 1932 + 1836 – 2700 = 1068 4. 1068 + 3366 – 3300 = 1134 5. 1134 + 3060 – 2900 = 1294 6. 1294 + 2907 – 3200 = 1001 It is not possible to meet the ending inventory target because of the extra fraction of a worker needed. The only way to do it would be to reduce the number of workers to 16 at some point....