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OPERATIONS MANAGEMENT (MGCR-472-061)

AGGREGATE PLANNING AND MATERIAL REQUIREMENTS PLANNING PRACTICE QUESTIONS

Problem 1. Leather-All produces a line of handmade leather products. At the present time, the company is producing only belts, handbags, and attaché cases. The predicted demand for the three products over a six-month planning horizon is as follows:

DEMAND

MONTH WORK DAYS

BELTS BAGS CASES

1 22 2,000 1,250 240

2 20 2,800 780 380

3 20 2,500 1,425 210

4 24 3,400 745 75

5 21 3,000 635 126

6 17 2,600 475 145

The belts require an average of 2 hours to produce, the handbags 3 hours, and the attaché cases 6 hours. All of the workers have the skill to work any product. Leather-All has currently 35 regular time workers who each have a share in the firm and cannot be fired. There are an additional 25 locals that are available and can be hired for short periods at higher cost. Regular employees earn a base monthly salary calculated on the basis of the regular working hours for the month at $8.5 per hour (even if they need to work less). They, in addition, receive an overtime salary calculated on the basis of the monthly overtime hours they work at $14 per hour.

Regular time comprises a 7-hour workday and due to union contracts, regular time workers can work at most 2 hours per day on overtime. The additional temporary workers are hired for $11 per hour and are kept on the payroll for at least one full month. The cost of hiring and firing of these workers is negligible. Temporary workers do not work overtime. Leather-All also recognizes that in certain months it can manufacture more than what is needed, in order to accumulate inventory for future months.

The accountant of the company estimates that 1 worker-hour worth of inventory has a cost of $1 per month. Likewise, Leather-All recognizes that some demand can be backordered. The estimated cost of backordering 1 worker-hour worth of demand is $10 per month. The production chief of Leather-All is totally confused and asks for your help.

a) Using worker hours as the aggregate measure of production, convert the forecasted demands to demands in terms of aggregate units. Also, convert the amount of capacity (regular time, overtime, temporary worker) available in terms of aggregate units.

b) Determine the optimal aggregate production plan for Leather-All assuming that demands cannot be backordered.

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Problem 2. Psychics of the World Inc. wants an aggregate plan for their organization. Given the nature of the business, Psychics has decided that back orders are not acceptable. If a caller cannot be handled immediately, the call is lost sale. Psychics has predicted the following number of calls; May-8000 calls, June-5000 calls, July-6000 calls, August-7000 calls, September-6000 calls, October-8000 calls, November-10,000 calls, December-12,000 calls. Psychics of the World pays each of their 48 employees $4,000 per month. Each psychic works for 160 regular-time hours per month or 40 regular-time hours per week. The regular-time labor cost of a call is $20, the overtime labor cost per call is $30. Each psychic is expected to serve 200 callers per month. The management has limited overtime to 50 calls per month per psychic. It costs $3,000 to hire a new psychic and $2,000 to fire a psychic.

a) Develop a level aggregate without inventory, without back orders, and without overtime. b) Using the same problem data, develop an aggregate plan using a level workforce supplemented by

overtime. Minimize the wasted capacity. No back orders are permitted.

Problem 3. The Bloomington Bike Company produces two models: the Basic and the Supra. Herb Hoosier, the owner, plans to assemble 15 Basics and 10 Supras each week during periods 4 to 8. Product structure trees for each bike are shown below:

B S

X M W K(2) F

F

W(2) Q

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Develop a materials requirement plan for component parts K and W over the next eight weeks. Data on all lead times, current inventory and ordering rules are given below: Scheduled receipts are: Period 1: 20 B’s, 18 W’s; Period 2: 20 S’s, 15 F’s.

ITEM LEADTIME (WKS) ON HAND LOT-SIZING RULE

B 2 5 Lot-for-lot

S 2 2 Lot-for-lot

X 1 5 Q = 25

W 2 2 Multiples of 12

F 1 10 Q = 30

K 1 3 Lot-for-lot

Q 1 15 Q = 30

M 1 0 Lot-for-lot

Problem 4. Assume that you are the manager of Assembly Inc. You have just received an order for 40 units of an industrial robot which is to be delivered at the start of week 7 of your schedule. Using the following information, determine how many units of subassembly G to order and the timing of those orders given that subassembly G must be ordered in multiples of 80 units and all other components are ordered lot-for-lot. Assume that the components are used only for this particular robot.

ITEM LEADTIME (WKS) ON HAND COMPONENTS

Robot 2 10 B, G, C(3)

B 1 5 E, F

C 1 20 G(2), H

E 2 4 --

F 3 8 --

G 2 15 --

H 1 10 --

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Problem 5. A manager has prepared a forecast of expected aggregate demand for the next six months. Develop an aggregate plan to meet this demand given this additional information: A level regular time production rate of 100 units per month will be used. Backorders are allowed and they are charged at a rate of $8 per unit per month. Inventory holding costs are $1 per unit per month. Determine the cost of this plan if regular time cost is $20 per unit and beginning inventory is zero. Month 1 2 3 4 5 6 Forecast 80 100 120 110 100 90 Problem 6. A producer of lawn mowers and leaf blowers, must develop an aggregate plan given the forecast for engine demand shown in the table below. The department has a normal capacity of 130 engines per month. Normal output has a cost of $60 per engine. The beginning inventory is zero engines. Overtime has a cost of $90 per engine. Develop a chase plan that matches the forecast using overtime and slack time, and computer the total cost of your plan.

Month 1 2 3 4 5 6 7 8 Total Forecast 120 135 140 120 125 125 140 135 1,040

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SOLUTIONS

Problem 1. Problem 2. a) Here we are using a level plan. Since inventory and back orders are not permitted, find the period with

the highest demand- December has demand of 12,000 calls which is the aggregate production rate. 12,000 calls divided by 200 calls per psychic per month gives us 60 psychics. So we hire 60-48=12 psychics.

This plan appears to waste substantial capacity – 34,000 more calls could have been handled. Total calls demanded were 62,000 whereas we had 96,000.

a)Period May June July August September October November DecemberService Calls 8,000 5,000 6,000 7,000 6,000 8,000 10,000 12,000

Regular Time Capacity (calls) 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000

Wasted Capacity (calls) 4,000 7,000 6,000 5,000 6,000 4,000 2,000 -

Total Cost Calculation Regular-time Labor Cost60 Psychics @ $4,000 for 8 periods 1,920,000$

Hiring Costs12 Psychics @ 3,000 36,000$

Total Costs 1,956,000$

(a) Month Belts Hours Bags Hours Cases Hours Total1 2,000 4,000 1,250 3,750 240 1,440 9,1902 2,800 5,600 780 2,340 380 2,280 10,2203 2,500 5,000 1,425 4,275 210 1,260 10,5354 3,400 6,800 745 2,235 75 450 9,4855 3,000 6,000 635 1,905 126 756 8,6616 2,600 5,200 475 1,425 145 870 7,495

Month Work Days Reg.Cap. OT Cap. Temp. Cap.1 22 5,390 1,540 3,8502 20 4,900 1,400 3,5003 20 4,900 1,400 3,5004 24 5,880 1,680 4,2005 21 5,145 1,470 3,6756 17 4,165 1,190 2,975

Total 124 30,380 8,680 21,700

(b) No backorders 0 1 2 3 4 5 6 COSTDemand 9,190 10,220 10,535 9,485 8,661 7,495ProductionRegular Time@$8.5 5,390 4,900 4,900 5,880 5,145 4,165 $258,230Overtime@$14 1,105 1,400 1,400 0 0 0 $54,670Temporary@$11 3,850 3,500 3,500 3,801 3,675 2,975 $234,311

Inventory End 0 1,155 735 0 196 355 0Inventory Aver.@$1 577.5 945.0 367.5 98.0 275.5 177.5 $2,441Total $549,652 TOTAL

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b) Here we use a level workforce. Aggregate production rate is 9,000 calls. We don’t need to hire or fire

since overtime will match the volume of calls – each psychic can provide up to 250 calls per period. This plan reduces the wasted regular-time capacity by 16,400 calls. Total cost is $300,000 less than the previous plan. Overtime is needed only in 2 periods so it should not create morale problems. This plan is an improvement but better plans are possible. Problem 3.

Period May June July August September October November DecemberService Calls 8,000 5,000 6,000 7,000 6,000 8,000 10,000 12,000

Regular Time Capacity (calls) 9,600 9,600 9,600 9,600 9,600 9,600 9,600 9,600

Wasted Capacity (calls) 1,600 4,600 3,600 2,600 3,600 1,600

Overtime Capacity needed (calls) 400 2,400

Total Cost Calculation Regular-time Labor Cost48 Psychics @ $4,000 for 8 periods 1,536,000$

Overtime Cost2800 calls @ $30 84,000$

Total Costs 1,620,000$

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 15 15 15 15 15

Scheduled Receipts 20

Projected Available (5) 25 25 25 25 0 0 0 0

Planned Orders 5 15 15 15

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 10 10 10 10 10

Scheduled Receipts 20

Projected Available (2) 2 22 22 22 12 0 0 0

Planned Orders 8 10 10

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 16 20 20 0 0

Scheduled Receipts

Projected Available (3) 3 3 3 0 0 0 0 0

Planned Orders 13 20 20

Item: B Lot Size Rule: L4L Lead Time: 2 weeks

Item: S Lot Size Rule: L4L Lead Time: 2 weeks

Item: K Lot Size Rule: L4L Lead Time: 1 week

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For instance: Period 3 gross requirement is 31=2*(13 of K)+(5 of B) Planned orders are multiples of 12, fixed order quantity size. Problem 4. For item G, gross requirements are calculated from Robot and item C as; Period 4 Gross Requirement=2*(70 from C) Period 5 Gross Requirement=1*(30 from Robot)

1 2 3 4 5 6 7 8Gross Requirements 0 0 31 55 55 15 0 0Scheduled Receipts 18

Projected Available (2) 20 20 1 6 11 8 8 8

Planned Orders 12 60 60 12

Item: W Lot Size Rule: FOQ=12 units Lead Time: 2 weeks

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 0 0 0 40 0

Scheduled Receipts

Projected Available (10) 10 10 10 10 10 10 0 0

Planned Orders 30

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 0 90 0 0 0

Scheduled Receipts

Projected Available (20) 20 20 20 20 0 0 0 0

Planned Orders 70

1 2 3 4 5 6 7 8Gross Requirements 0 0 0 140 30 0 0 0

Scheduled Receipts

Projected Available (15) 15 15 15 35 5 5 5 5

Planned Orders 160

Item: Robot Lot Size Rule: L4L Lead Time: 2 weeks

Item: C Lot Size Rule: L4L Lead Time: 1 week

Item: G Lot Size Rule: FOQ=80 unitsLead Time: 2 weeks

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Problem 5.

Month 1 2 3 4 5 6 Costs Forecast 80 100 120 110 100 90 Level Production 100 100 100 100 100 100 $12,000 Beginning Inv. 0 20 20 0 0 0 Ending Inv. 20 20 0 0 0 0 Avg. Inventory 10 20 10 0 0 0 $ 40 Backorder 0 0 0 10 10 0 $ 160 Total $12,200

Problem 6.

ROBOT

B G C(3)

H E F G(2)

Period 1 2 3 4 5 6 7 8 Costs Forecast 120 135 140 120 125 125 140 135 Output

Regular 120 130 130 120 125 125 130 130 $60,600 Overtime 5 10 10 5 $2,700 Subcontract

Beginning Inv. Ending Inv. Avg. Inventory Backorder _________________________________________________________________________________________ Total $63,300