OPERATIONS MANAGEMENT (MGCR-472-061) - PageOut

Problem 1.
OPERATIONS MANAGEMENT (MGCR-472-061)
AGGREGATE PLANNING AND MATERIAL REQUIREMENTS PLANNING
PRACTICE QUESTIONS
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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Problem 1.
SOLUTIONS
(a) Month Belts Hours Bags Hours Cases Hours Total
1 2,000 4,000 1,250 3,750 240 1,440 9,190
2 2,800 5,600 780 2,340 380 2,280 10,220
3 2,500 5,000 1,425 4,275 210 1,260 10,535
4 3,400 6,800 745 2,235 75 450 9,485
5 3,000 6,000 635 1,905 126 756 8,661
6 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 3,850
2 20 4,900 1,400 3,500
3 20 4,900 1,400 3,500
4 24 5,880 1,680 4,200
5 21 5,145 1,470 3,675
6 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 COST
Demand 9,190 10,220 10,535 9,485 8,661 7,495
Production
Regular Time@$8.5 5,390 4,900 4,900 5,880 5,145 4,165 $258,230
Overtime@$14 1,105 1,400 1,400 0 0 0 $54,670
Temporary@$11 3,850 3,500 3,500 3,801 3,675 2,975 $234,311
Inventory End 0 1,155 735 0 196 355 0
Inventory Aver.@$1 577.5 945.0 367.5 98.0 275.5 177.5 $2,441
Total $549,652 TOTAL
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.
a)
Period May June July August September October November December
Service 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 -
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.
Total Cost Calculation
Regular-time Labor Cost
60 Psychics @ $4,000 for 8 periods $ 1,920,000
Hiring Costs
12 Psychics @ 3,000 $ 36,000
Total Costs $ 1,956,000
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) 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.
Period May June July August September October November December
Service 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 Cost
48 Psychics @ $4,000 for 8 periods $ 1,536,000
Overtime Cost
2800 calls @ $30 $ 84,000
Total Costs $ 1,620,000
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.
Item: B
Lot Size Rule: L4L
Lead Time: 2 weeks
1 2 3 4 5 6 7 8
Gross 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
Item: S
Lot Size Rule: L4L
Lead Time: 2 weeks
1 2 3 4 5 6 7 8
Gross 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
Item: K
Lot Size Rule: L4L
Lead Time: 1 week
1 2 3 4 5 6 7 8
Gross 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
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For instance: Period 3 gross requirement is 31=2*(13 of K)+(5 of B)
Item: W
Lot Size Rule: FOQ=12 units
Lead Time: 2 weeks
1 2 3 4 5 6 7 8
Gross Requirements 0 0 31 55 55 15 0 0
Scheduled Receipts 18
Projected Available (2) 20 20 1 6 11 8 8 8
Planned Orders 12 60 60 12
Planned orders are multiples of 12, fixed order quantity size.
Problem 4.
Item: Robot
Lot Size Rule: L4L
Lead Time: 2 weeks
1 2 3 4 5 6 7 8
Gross 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
Item: C
Lot Size Rule: L4L
Lead Time: 1 week
1 2 3 4 5 6 7 8
Gross 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
Item: G
Lot Size Rule: FOQ=80 units
Lead Time: 2 weeks
1 2 3 4 5 6 7 8
Gross 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
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)
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ROBOT
B G C(3)
E F G(2)
H
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.
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
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