MGT 3110: Exam 3 Study Guide

Discussion questions

  1. What is the purpose of safety stock in the ROP model?
  2. Define aggregate production plan? What is the objective and what are the requirements for developing one?
  3. What are demand options for aggregate planning? Give examples and discuss the effects of each.
  4. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this approach.
  5. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this approach.
  6. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this approach.
  7. Define independent and dependent demand items.
  8. What is Master Production Schedule?
  9. What is Bill of Materials?
  10. What is Low-Level coding and what how is it used?
  11. What are the benefits of MRP?
  12. What are the inputs required for MRP?
  13. What is “Lot Sizing” in MRP?
  14. What are the reasons for using a lot sizing method other than Lot-for-lot?

Problems

  1. The Winfield Distributing Company has maintained an 80% service level policy for inventory of string trimmers. Mean demand during the reorder period is 130 trimmers, and the standard deviation is 80 trimmers. What is the value of ROP and SS?
  1. The new office supply discounter, Paper Clips, Etc. (PCE), sells a certain type of ergonomically correct office chair which costs $300. The annual holding cost rate is 40%, annual demand is 600, and the order cost is $20 per order. The store is open 300 days per year and PCE has decided to establish a customer service level of 90%.
  1. Suppose that the lead time is a constant 4 days and the demand is variable with a standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?
  2. Suppose that the lead time is a variable with an average of 4 days and standard deviation of 3 days. Further suppose that the demand is constant. What is the safety stock and reorder point?
  3. Suppose that the lead time is a variable with an average of 4 days and standard deviation of 3 days. Further suppose that the demand is also variable with a standard deviation of 2.4 chairs per day. What is the safety stock and reorder point?
  1. A warehouse store sells laser printer cartridges in bulk. The company places restocking orders 1000 boxes at a time. The annual demand is 7000 boxes. The demand during lead time is given below. The average demand during lead time is 60 boxes. Assume holding cost of $5 per box per year and a stock out cost of $50 per box.

Demand during lead time / Probability
40 / 0.1
50 / 0.2
60 / 0.2
70 / 0.2
80 / 0.2
90 / 0.1

Determine the least cost safety stock and the corresponding ROP.

  1. An oyster bar buys fresh oysters for $3 per pound and sells them for $10 per pound. Unsold oyster at the end of the day is sold to a grocery store for $1.20 per pound. The daily demand is estimated to be 150 pounds with a standard deviation of 12 pounds. How many pounds of oysters must be ordered each day?
  1. Leisure Travels, Inc. manufactures and sells Recreation Vehicles. The demand for the next four quarters is forecasted as 160, 180, 220, and 200. The labor required to produce one unit is 100 hours. Each worker works 8 hours per day for 65 days per quarter. Regular wages is $15 per hour and O.T. wages is $20 per hour. O.T. is limited to 20% regular hours. Limited subcontracting is available at the rate of $2500 per unit. Holding cost per unit per quarter is $100. Cost of hiring a worker is $350 and firing worker will cost $500. The company currently has 30 employees.
  1. Determine the production rate per worker per day and per quarter.
  2. Determine the regular time wage per worker per day and per quarter.
  3. Determine the O.T. cost per unit.
  4. Develop a “Chase” plan and the corresponding cost summary.
  5. Develop a “Level” plan and the corresponding cost summary.
  6. Develop a “Mixed” plan with a constant work force of 31 workers, but produce only what the net demand is each month, i.e. not accumulate any inventory in excess of the safety stock. If regular time capacity is not sufficient, use O.T. production first and use subcontracting only of O.T. capacity is not enough to make up the shortage.
  1. Consider the following data for an Aggregate Planning problem

Cost data / Demand forecast
Wage/hour / $8.50 / Month / Demand / Days
OT pay rate / $10.00 / January / 1000 / 20
Subcontracting cost/unit / $25.00 / February / 800 / 18
Carrying cost / $10.00 / March / 1100 / 22
Hiring cost/unit / $200.00 / April / 1200 / 20
Firing cost/unit / $400.00 / May / 1300 / 22
Other data / Initial condition
Labor-hours/unit / 2 / Workers on roll / 8
Hours/day / 8 / Current production rate / 50
OT Limit / 15% / Current inventory / 50
Safety stock / 10
  1. Determine the production rate per worker per day.
  2. Determine the regular time wage per worker per day.
  3. Determine the O.T. cost per unit.
  4. Develop a “Chase” plan and the corresponding cost summary.
  5. Develop a “Level” plan and the corresponding cost summary. (Round up the production rate per day)
  6. Develop a “Mixed” plan with a constant work force of 12 workers, but produce only what the net demand is each month, i.e. not accumulate any inventory in excess of the safety stock. If regular time capacity is not sufficient, use O.T. production. Consider any shortage over and above OT capacity is subcontracted.
  1. Consider the following Solver model for an aggregate planning problemgivebn in the next page.

Determine the excel formula for the following cells:

B18
B19
B20
B23
E23
F23
B24
B31
C31
F31
G31
H31
B32
B37
B38
B39
B40
B41
B42
B43
  1. What is the Solver Target cell?
  2. What are the Solver changing cells?
  3. What are the Solver constraints?
  4. What options of Solver must be checked?

  1. A Bill of Materials is desired for a bracket (A) that is made up of a base (B), two springs (C) and four clamps (D). The base is assembled from one clamp (D) and two housings (E). Each clamp has one handle (F) and one casting (G). Each housing has two bearings (H) and one shaft (I).
  1. Develop a product structure tree.
  2. The lead time for the parts are given below. Develop a time-phased product structure.
  3. The available inventory for each part is given in the table below. Determine the net requirement quantities of all parts required to assemble 50 units of bracket A.

Item / Lead time / Available
A / 1 / 5
B / 2 / 5
C / 3 / 10
D / 2 / 20
E / 1 / 50
F / 2 / 150
G / 1 / 50
H / 1 / 5
I / 2 / 0
  1. A product (A) consists of a base (B) and a casting (C). The base consists of a plate (P) and three fasteners (F). The lead time, current on-hand inventory and scheduled receipts are given below. All components are lot for lot. The MPS requires start of production of 100 units of product A in week 4 and 150 in week 6. Produce the MRP for the upcoming six weeks. Produce a list of all planned order releases.

Part / Lead time / On-hand / Scheduled receipts
B / 1 / 100 / 50 in week 1
C / 3 / 30 / 20 in week 1, 30 in week 2
P / 2 / 0 / 50 in week 1
F / 4 / 0 / 30 in week 1, 40 in week 3
  1. For the following item the inventory holding cost is $0.80 per week and the setup cost is $300. Determine the lot sizes and total cost for this item under (i) Lot-for-Lot, (ii) EOQ, and (iii) PPB methods

Item / LT = / 1
Week: / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Gross requirement / 100 / 250 / 200 / 150 / 250 / 200 / 200 / 150
Scheduled receipts
Projected on-hand / 100
Net Requirement
Planned receipts
Planned order releases

Answers to discussion questions

  1. What is the purpose of safety stock in the ROP model?

The purpose of safety stock is to decrease the probability of stock out during lead time of a replenishment order, which increases the probability of meeting demand, aka service level.

  1. Define aggregate production plan? What is the objective and what are the requirements for developing one?

Aggregate production plan is a plan of overall production level, prepared over a rolling horizon of 12 to 18 monthly periods, or 4 to 6 quarterly periods.

The objective is to minimize cost by adjusting production rates, labor levels, inventory levels, overtime work, subcontracting rates.

The requirements for developing an aggregate production plan include:

  • a logical overall unit for measuring sales and output
  • a forecast of demand for the planning horizon in these aggregate terms
  • standard hours to produce one unit of the product in these aggregate term
  • cost data such as wages (regular time, overtime, and subcontracting), inventory carrying cost, and hiring/firing costs
  1. What are demand options for aggregate planning? Give examples and discuss the effects of each.

Demand options are techniques used to even out fluctuations in demand. Following are some examples.

  • Back ordering during high- demand periods (Effective if substitute products are not available, but may result in loss of customer orders to competition and lost customer good will)
  • Counter-seasonal product mix (effective in reducing huge ups and downs in demand , but may lead to products or services outside the company’s areas of expertise
  • Economic incentives such as discounts (loss of profit)
  1. Describe “Chase” strategy for aggregate planning and discuss the advantages and disadvantages this approach.

Chase strategy matches output rates to demand forecast for each period by varying the workforce levels or vary production rate.

Advantage: Very low inventories

Disadvantage: Requires frequent hiring and firing of workers

  1. Describe “Level” strategy for aggregate planning and discuss the advantages and disadvantages this approach.

Level strategy uses uniform production rate. Fluctuations in demand is managed through accumulation of inventory during lean demand periods.

Advantage: Stable production leads to better quality and productivity

Disadvantage: High levels of inventory

  1. Describe “Mixed” strategy for aggregate planning and discuss the advantages and disadvantages this approach.

Mixed strategy maintains uniform production rate, but does not build inventory. Overtime and subcontracting is used to meet demand.

Advantage: Stable production leads to better quality and productivity and low levels of inventory

Disadvantage: Use of overtime and/or subcontracting may increase cost and may lead to quality related problems

  1. Define independent and dependent demand items.

Finished products whose demand is independent of production decisions are called “Independent demand” items. Items for which demand can be directly calculated from production decisions are called “Dependent demand” items. These are raw-materials and parts required for the production of the finished goods.

  1. What is Master Production Schedule?

Master Production Schedule specifies production quantities of each Independent Demand item for a planning horizon of 12 to 15 weeks. Total of MPS quantities must be in accordance with the aggregate production plan.

  1. What is Bill of Materials?

Bill of materials is structured list of components, ingredients, and materials needed to make an end product. Items needed to produce a given part are called components or “children”. The part into which the components go us called “Parent”. The BOM also gives the number of units of a child item needed to produce one unit of the parent item.

  1. What is Low-Level coding and what how is it used?

A level code starting from zero at the top of the BOM tree and incremented by 1 going down each level of the BOM tree is assigned. Then, the lowest level at which an item appears is called Low-Level code. The MRP computations are processed one level at a time, starting from level zero.

  1. What are the benefits of MRP?
  • Better response to customer orders
  • Faster response to market changes
  • Improved utilization of facilities and labor
  • Reduced inventory levels
  1. What are the inputs required for MRP?
  • Master Production Schedule
  • Bill of Materials
  • Inventory status
  1. What is “Lot Sizing” in MRP?

The process of combining net requirements into production lots is called lot sizing.

  1. What are the reasons for using a lot sizing method other than Lot-for-lot?
  • Lot-for-lot often requires too many lots that may not be economically justifiable
  • Sometime lot-for-lot generates absurdly small lots

Answers to problems

1.GivendL = 130, dLT = 80, and for 80% service level, Z = 0.84

ROP = 130 + 0.84 x 80 = 197.2, or round up to 198 for at least 80% service level

2.

d = D/No. of days per year = 600/300 = 2 per day

Z for 90% service level = 1.285

a.Given: L = 4 days Constant, d = 2.4 per day, therefore dLT = 2.4 = 4.8

Safety stock = Z dLT = 1.285 x 4.8 = 6.2 or 7 (round up for at least 90% service level)

ROP = dL + SS = (2 chairs/day * 4) + 7 = 15

b.Given: L = 4 days with L = 3 and demand is constant, dLT = 2 (3) = 6

Safety stock = Z dLT = 1.285 x 6 = 7.7 or 8 (round up for at least 90% service level)

ROP = dL + SS = (2 chairs/day * 4) + 8 = 16

c.Given: L = 4 days with L =3 , and d = 2.4 per day, therefore dLT = = 7.684

Safety stock = Z dLT = 1.285 x 7.684 = 9.9 or 10 (round up for at least 90% service level)

ROP = dL + SS = (2 chairs/day * 4) + 10 = 18

3. Number of orders per year = 7, H = $5, S = $50

ROP / Safety stock / Carrying cost / Expected stock out / Stock out cost/order / Stock out cost/year / Total cost
60 / 0 / 0 / (10x.2 + 20x.2 + 30x.1) = 9 / 9 x $50 = $450 / $3,150 / $3,150
70 / 10 / 10 x $5 = $50 / (10x.2 + 20x.1) = 4 / 4 x $50 = $200 / $1,400 / $1,450
80 / 20 / 20 x $5 = $100 / (10x.1) = 1 / 1 x $50 = $50 / $350 / $450
90 / 30 / 30 x $5 = $150 / 0 / 0 / $0 / $150

Least cost safety stock = 30, ROP = 90

4.

Cs = Lost profit = Selling price per unit – Cost per unit = 10 – 3 = $7

Co = Cost/unit – salvage value/unit = 3 – 1.20 = $1.80

Optimum service level = 7/(7 + 1.80) = 0.795 = 79.5%

From normal table, for 79.5% service level, Z = 0.83

Order quantity =  + Z  = 150 + 0.825 (12) = 159.9 or 160

5.

Hiring cost/worker = / 350 / Worker hours/quarter = / 520
Firing cost/worker = / 500 / Standard hours/unit = / 100
RT Wage/hour = / 15 / Holding cost = / 100
OT wage rate/hour = / 20
Sub-contracting cost/unit = / 2500
  1. Production rate/worker/day = 8 hours per day/100 hours per unit = 0.08 per worker/day

Production rate/worker/quarter = 0.08/worker/day x 65 days/quarter = 5.2/worker/ quarter

  1. Wage rate per worker per day = $15/hour x 8 hours/day = $120

Wage rate per worker per quarter = $15/hour x 8 hours/day x 65 days/quarter = $7800

  1. OT cost/unit = $20/hour x 100 hours/unit = $2000

d. Chase plan

Period / Demand / Production required / Workers needed / Workers needed (Rounded) / Hired workers / Fired workers
30
1 / 160 / 160–(0–0) = 160 / 160/5.2=30.77 / 31 / 1 / 0
2 / 180 / 180 / 180/5.2=34.62 / 35 / 4 / 0
3 / 220 / 220 / 220/5.2=42.31 / 43 / 8 / 0
4 / 200 / 200 / 200/5.2=38.46 / 39 / 0 / 4
148 / 13 / 4
Cost summary
Regular wages / 148 workers-quarters x $7800 = / 1,154,400
O.T. cost =
S.C. cost
Hiring cost / 13 workers x $350 = / 4,550
Firing cost / 4 workers x $500 = / 2,000
Carrying cost
Total cost / $1,160,950
  1. Level Plan
Sum of demand = 760
Average demand = 760/4 = 190 i.e. = production per quarter
Period / Demand / RT Production / E.I.
0
1 / 160 / 190 / 30
2 / 180 / 190 / 40
3 / 220 / 190 / 10
4 / 200 / 190 / 0
Average demand = / 190 / 760 / 80
Workers needed/quarter = / 36.54
Workers rounded up = / 37
Cost summary
Regular wages / 37 workers x 4 quarters x $7800 = / 1,154,400
O.T. cost =
S.C. cost
Hiring cost / (37 workers – 30 workers) x $ 350 = / 2,450
Firing cost / -
Carrying cost / 80 x $100 = / 8,000
Total cost / $1,164,850

f. Mixed plan

Plan C
No. of workers = 31
Production per quarter with 31 workers = 31 x 5.2 = 161.2 or 161
O.T. capacity/quarter = 161 x 20% = 32
Period / Demand / Production capacity / RT Production / Shortage / O.T Capacity / O.T. Production / S.C.
1 / 160 / 161 / Min(160,161) =160 / 160 – 160=0 / 32 / 0 / 0
2 / 180 / 161 / Min(180,161) =161 / 180-161=19 / 32 / Min(19,32)=19 / 0
3 / 220 / 161 / Min(220,161) =161 / 220-161=59 / 32 / Min(59,32)=32 / 59-32=27
4 / 200 / 161 / Min(200,161) =161 / 200-161=39 / 32 / Min(39,32)=32 / 39-32=7
643 / 83 / 34
Cost summary
Regular wages / 31 workers x 4 quarters x $7800 = / 967,200
O.T. cost = / 83 units x $2000 / 166,000
S.C. cost / 34 units x $2500 = / 85,000
Hiring cost / (31 – 30) x $350 = / 350
Firing cost / -
Carrying cost / -
Total cost / $1,218,550

6.

  1. Production rate/worker/day = 8 hours per day/2 hours per unit = 4 per worker/day
  2. Wage rate per worker per day = $8.50/hour x 8 hours/day = $68
  3. OT cost/unit = 2 hours/unit x $10/hour = $20/unit

d.Chase plan:

Month / Demand / Production / Days / Production rate / Hire / Fire
50
Jan / 1000 / 960 / 20 / 960/20 = 48 / 0 / 2
Feb / 800 / 800 / 18 / 800/18 = 44 / 0 / 4
March / 1100 / 1100 / 22 / 1100/22 = 50 / 6 / 0
April / 1200 / 1200 / 20 / 1200/20 = 60 / 10 / 0
May / 1300 / 1300 / 22 / 1300/22 = 59 / 0 / 1
16 / 7
Production rate / Workers / Workers (Rounded) / Wages
50
48 / 48/4 = 12 / 12 / $16,320
44 / 44/4 = 11 / 11 / $13,464
50 / 50/4 = 12.5 / 13 / $19,448
60 / 60/4 = 15 / 15 / $20,400
59 / 59/4 = 14.75 / 15 / $22,440
$92,072
Cost summary
Regular wages / $92,072
OT cost
Subcontracting
Hiring cost / $3,200.00
Firing cost / $2,800.00
Carrying cost / $500.00
Total cost / $98,572

e. Level plan

Net total demand = 5400 – (50 – 10) = / 5360
Average demand rate /day = 5360/102 days = / 52.5
Production rate/day – rounded up / 53
No. of workers needed = 53/4 = / 13.25
Rounded number of workers = / 14
Month / Demand / Days / Production / E.I.
50
Jan / 1000 / 20 / 53 x 20 = 1060 / 110
Feb / 800 / 18 / 53 x 18 =- 954 / 264
March / 1100 / 22 / 53 x 22 = 1166 / 330
April / 1200 / 20 / 53 x 20 = 1060 / 190
May / 1300 / 22 / 53 x 22 = 1166 / 56
5400 / 102 / 950
Cost summary
Regular wages / $97,104
OT cost
Subcontracting
Hiring cost / $600
Firing cost / $0
Carrying cost / $9,500
Total cost / $107,204

f.Mixed plan

Workers / 12
Production rate/day = 12 x 4 unit/day = / 48
Month / Requirement / Days / Capacity / Production / Shortage
Jan / 960-(0-0)=960 / 20 / 20x48=960 / Min(960,960)=960 / 0
Feb / 800 / 18 / 18x48=864 / Min(800,864)=800 / 0
March / 1100 / 22 / 22x48=1056 / Min(1100,1056)=1056 / 1100-1056=44
April / 1200 / 20 / 20x48=960 / Min(1200,960)=960 / 1200-960=240
May / 1300 / 22 / 22x48=1056 / Min(1300,1056)=1056 / 1300-1056=244
102
Shortage / OT Capacity / OT / SC
0 / 0
0 / 0
1100-1056=44 / 1056x0.15=158 / 44 / 44-44 = 0
1200-960=240 / 960x0.15=144 / 144 / 240 – 144 = 96
1300-1056=244 / 1056x0.15=158 / 158 / 244 – 158 = 86
346 / 182
Cost summary
Regular wages = 12 workers x $68/day x 102 days = / $83,232
OT wages = 346 units x $20 per unit = / $6,920
SC = 182 x $20 = / $4,550
Hiring cost / $0
Firing cost (50 – 48) x $400 / $800
Carrying cost = 10 units x 5 months x $10 = / $500
Total cost / $96,002

7.

B18 / =B14/B13 / b.B43
c.C23:D26, D31:E34
d.D31:D34 <= H31:H34
G31:G34 >= E15
C23:D26 = Integer (if needed)
D31:E34 = Integer (if needed)
e.Assume linear model
Assume non-negative
B19 / =B14*B5
B20 / =B13*B6
B23 / =E13
E23 / =B23+C23-D23
F23 / =E23*F6*$B$18
B24 / =E23
B31 / =E14
C31 / =F23
F31 / =E6
G31 / =B31+SUM(C31:E31)-F31
H31 / =C31*$B$15
B32 / =G31
B37 / =SUMPRODUCT(E23:E26,F6:F9)*B19
B38 / =D35*B20
B39 / =E35*B7
B40 / =C27*B9
B41 / =D27*B10
B42 / =G35*B8
B43 / =SUM(B37:B42)

8.

F
D
G
B
H
E
I
C / A
F
D
G
1 / 2 / 3 / 4 / 5 / 6 / 7

Lead time = 7 weeks

Part / Gross / Available / Net
A / 50 / 5 / 50 – 5 = 45
B / 1 x A = 45 / 5 / 45 – 5 = 40
C / 2 x A = 2 x 45 = 90 / 10 / 90 – 10 = 80
D / 4 x A + 1 x B = 4 x 45 + 40 = 220 / 20 / 220 – 20 = 200
E / 2 x B = 80 / 50 / 80 – 50 = 30
F / 1 x D = 200 / 150 / 200 – 150 = 50
G / 1 x D = 200 / 50 / 200 – 50 = 150
H / 2 x E = 2 x 30 = 60 / 5 / 60 – 5 = 55
I / 1 x E = 30 / 0 / 30 – 0 = 30

9.

1 / 2 / 3 / 4 / 5 / 6
MPS start for A / 100 / 150
Item B / Lead time = / 1
Week: / 1 / 2 / 3 / 4 / 5 / 6
Gross requirement / 0 / 0 / 0 / 100 / 0 / 150
Scheduled receipts / 50
Projected on-hand / 100 / 100 / 150 / 150 / 150 / 50 / 50
Net requirement / 100
Planned receipts / 0 / 0 / 0 / 0 / 0 / 100
Planned order releases / 0 / 0 / 0 / 0 / 100 / 0
Item C / Lead time = / 3
Week: / 1 / 2 / 3 / 4 / 5 / 6
Gross requirement / 0 / 0 / 0 / 100 / 0 / 150
Scheduled receipts / 20 / 30
Projected on-hand / 30 / 30 / 50 / 80 / 80 / 0 / 0
Net requirement / 20 / 150
Planned receipts / 0 / 0 / 0 / 20 / 0 / 150
Planned order releases / 20 / 0 / 150 / 0 / 0 / 0
Item P / Lead time = / 2
Week: / 1 / 2 / 3 / 4 / 5 / 6
Gross requirement / 0 / 0 / 0 / 0 / 100 / 0
Scheduled receipts / 50
Projected on-hand / 0 / 0 / 50 / 50 / 50 / 50 / 0
Net requirement / 50
Planned receipts / 0 / 0 / 0 / 0 / 50 / 0
Planned order releases / 0 / 0 / 50 / 0 / 0 / 0
Item F / Lead time = / 4
Week / 1 / 2 / 3 / 4 / 5 / 6
Gross requirement / 0 / 0 / 0 / 0 / 300 / 0
Scheduled receipts / 30 / 40
Projected on-hand / 0 / 0 / 30 / 30 / 70 / 70 / 0
Net requirement / 230
Planned receipts / 0 / 0 / 0 / 0 / 230 / 0
Planned order releases / 230 / 0 / 0 / 0 / 0 / 0

Planned order releases:

A has releases of 100 in week 4, 150 in week 7

B has a release of 100 in week 5

C has releases of 20 in week 1, 150 in week 3

P has a release of 50 in week 3

F has a release of 230 in week 1

10. (i) L-4-L

Item / LT = / 1
Week: / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8
Gross requirement / 100 / 250 / 200 / 150 / 250 / 200 / 200 / 150
Scheduled receipts
Projected on-hand / 100 / 100 / 0 / 0 / 0 / 0 / 0 / 0 / 0
Net Requirement / 0 / 250 / 200 / 150 / 250 / 200 / 200 / 150
Planned receipts / 0 / 250 / 200 / 150 / 250 / 200 / 200 / 150
Planned order releases / 250 / 200 / 150 / 250 / 200 / 200 / 150 / 0
No. of setup = / 7
Carrying cost = / 0
Setup cost = 7 x $300 = / 2100
Total cost = / 2100

(ii) EOQ:

Total demand for 8 weeks = 1500

D (1 year) = (1500/8) x 52 weeks/year = 9750

H (for 52 weeks) = $0.80/week x 52 weeks = $41.60

S = 300

Q = = 375