MGT 3110: Exam 2 Study Guide

1. A company has 12 items in its inventory. Using the data given below classify the items into A, B, and C classes.

SKU Annual usage (units) Unit $ valueD120 6850 1.20E111 371 8.60C140 1292 13.18E151 62 91.80B180 12667 3.20B120 9625 10.18E149 7010 1.27A180 5100 0.88E110 258 62.25A155 862 18.10F120 1940 0.38B150 967 2.20

2. Herbert Adams sells bicycles. One particular model is highly popular with annual sales of 2,000 units per year. Annual holding cost is $200 per unit and the ordering cost is $40. The store is open 250 days a year.a. What is the economic order quantity?b. What is the average number of orders per year?c. What is the average time between orders in days?d. What is the annual total cost?

3. Montegut Manufacturing produces a product for which the annual demand is 10,000. Production averages 100 per day, while demand is 40 per day. Holding costs are $1.50 per unit per year; set-up costs $200.00. If they wish to produce this product in economic batches, what size batch should be used? What is the length of time in days to producing one lot? What is the maximum inventory level? What is the time between orders in days? How many order cycles are there per year? Determine the total annual inventory cost?

4. The annual demand, ordering cost, and the inventory carrying cost rate for a certain item are D = 600 units, S = $10/order and holding cost is 30% of item price. Price is established by the following quantity discount schedule. What should the order quantity be in order to minimize the total annual cost?

Quantity 1 to 49 50 to 249 250 and upUnit price $5.00 $4.50 $4.10

5. A warehouse store sells laser printer cartridges in bulk. The company places restocking orders 1000 boxes at a time. The annual demand is 8000 boxes. The demand during lead time is given below. The average demand during lead time is 60 boxes. Assume holding cost of $50 per box per year and a stock out cost of $40 per box.

Demand during lead time Probability40 0.150 0.260 0.270 0.280 0.290 0.1

Determine the least cost safety stock and the corresponding ROP.

6. 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?

7. 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%.a. 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?b. 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?

c. 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?

8. 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. Determine the pounds of oysters that must be ordered each day if the daily demand follows normal distribution with mean of 150 pounds and standard deviation of 12 pounds.

9. 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.a. Determine the production rate per worker per day and per quarter.b. Determine the regular time wage per worker per day and per quarter.c. Determine the O.T. cost per unit.d. Develop a “Chase” plan and the corresponding cost summary. Round up workers needed.e. Develop a “Level” plan and the corresponding cost summary. f. 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. Round to 2 decimal places.

10. Consider the following Solver model for an aggregate planning problem given in the next page.a. What is the Solver Target cell?b. What are the Solver changing cells?c. What are the Solver constraints?d. What options of Solver must be checked?

e. Determine the excel formula for the following cells:

B17 F29B18 G29B19 H29

B22 G33E22 B35B23 B36C26 B37D26 B38E26 B39B29 B40C29 B41

11. A concert organizing company wishes to study the effect of discount pricing on net revenue generated. Currently the company charges uniform fee of $100 per ticket and has averaged 500 tickets sold. The company is considering a three tier pricing structure, (a) a deeply discounted $70 per ticket if purchased at least 1 month in advance, (b) $90 per ticket if purchase at least a week in advance and $120 at the box office on the day of the event. The company has estimated a demand of 300 tickets sold at least a month in advance, 200 at least a week in advance and 100 on the day of the event. The company estimates the variable cost to be $3 per ticket under all the three prices. Using the yield revenue approach determine what the effect of the proposed price structure will be on net revenue.

12. 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). a. Develop a product structure tree.b. The lead time for the parts are given below. Develop a time-phased product structure.c. 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 AvailableA 1 5B 2 5C 3 10D 2 20E 1 50F 2 150G 1 50H 1 5I 2 0

13. 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 receiptsB 1 100 50 in week 1C 3 30 20 in week 1, 30 in week 2P 2 0 50 in week 1F 4 0 30 in week 1, 40 in week 3

14. 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) POQ methods.

Item LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receiptsProjected on-hand 100Net RequirementPlanned receiptsPlanned order releases

15. Consider the following planned and actual hours of input and output.

Week ending 1 2 3 4 5 6Planned input 500 800 700 600 600 800Actual input 700 700 700 800 600 500Planned output 650 650 650 650 650 700Actual output 600 700 800 700 650 500

Prepare the Input/Output Control chart for this workstation. Assume an initial actual backlog of 120 hours and zero for the two cumulative deviations.

16. The following jobs are waiting to be processed on day 50Job Production days needed Date job dueA 30 90B 20 215C 40 175D 35 180

Sequence the jobs in the order of SPT, EDD, and Critical Ratio, and compute (i) Average flow time, (ii) Average lateness, (iii) Average number of jobs in the system, and (iv) Utilization, for each of the three schedule of jobs.

17. An antique restoration operation uses a two-step sequence that all jobs in a certain category follow. For the group of jobs listed.a. Find the sequence that will minimize total completion time.b. Determine the amount of idle time for workstation 102.

c. What jobs are candidates for splitting‘? Why? If they were split, how much would idle time and makespan time be reduced? Assume the very first job can be split 50% and the remaining jobs can be spit 60%.

JOB TIMES (minutes)A B C D E

Workstation 101 27 18 70 26 15Workstation 102 45 33 30 24 10

Answers

1.

No. SKU

Annual usage

(units) Unit $ valueAnnual Dollar

volume Dollar %Cum. %

for $Cum. % for

no. of items Class1 B120 9625 10.18 97,982.50 44.4% 44.4% 8.3% A2 B180 12667 3.20 40,534.40 18.4% 62.8% 16.7% A3 C140 1292 13.18 17,028.56 7.7% 70.5% 25.0% B4 E110 258 62.25 16,060.50 7.3% 77.8% 33.3% B5 A155 862 18.10 15,602.20 7.1% 84.9% 41.7% B6 E149 7010 1.27 8,902.70 4.0% 88.9% 50.0% B7 D120 6850 1.20 8,220.00 3.7% 92.6% 58.3% C8 E151 62 91.80 5,691.60 2.6% 95.2% 66.7% C9 A180 5100 0.88 4,488.00 2.0% 97.3% 75.0% C

10 E111 371 8.60 3,190.60 1.4% 98.7% 83.3% C11 B150 967 2.20 2,127.40 1.0% 99.7% 91.7% C12 F120 1940 0.38 737.20 0.3% 100.0% 100.0% C

220565.66 100%

2. D = 2000, No. of days = 250, H = $200, S = $40

a. EOQ =

b. N = D/Q = 2000/28 = 71.4

c. d = D/No. of days per year = 2000/250 = 8, T = Q/d = 28/8 = 3.5 days

d. Annual total cost = (D/Q)S + (Q/2)H = (2000/28)40 + (28/2)200 = $5,657

3. D = 10,000, H = $1.50, S = $200, p = 100/day, d = 40/day

EPQ = √ 2DS

H (1−dp)=√ 2 (10000 )200

1.50(1− 40100

) = 2108

Production time = Q/p = 2108/100 = 21.08 days

Imax = (Q/p)(p - d) = (2108/100)(100 - 40) = 1264.80

Average number of orders per year = D/Q = 10000/2108 = 4.74

Time between orders = Q/d = 2108/40 = 52.7 days

√ 2(2000 )40200=28

Annual holding cost = (Imax/2) x H = (1264.80/2) x 1.50 = $948.60

Annual setup cost = (D/Q) x S = (10000/2108) x 200 = $948

Total cost = 948.60 + 948 = $1,896.60

4.

D = 600 S = 10 Holding cost = 30%

Q Price Holding cost Formula Q Candidate Q

1 - 49 5.00 1.50 89Formula Q > upper limit -- not a candidate -

50 - 249 4.50 1.35 94Formula Q is within range, = Candidate Q = Formula Q 94

250 & above 4.10 1.23 99

Formula Q < lower limit, Candidate Q = lower limit 250

Q Price Candidate Q Ordering cost Holding cost Item cost Total cost1 – 49 5.00 -50 - 249 4.50 94 63.83 63.45 2700 2827.28>= 250 4.10 250 24.00 153.75 2460 2637.75EOQ = 250 @ P = $4.10

5. Number of orders per year = 8000/1000 = 8, H = $50, Cs = $40

ROPSafety stock Carrying cost Expected stock out Stock out cost/year Total cost

60 0 0 (10x.2 + 20x.2 + 30x.1) = 9 9 x 8 x 40 = $2,880 $2,88070 10 10 x $50 = $500 (10x.2 + 20x.1) = 4 4 x 8 x 40 = $1,280 $1,78080 20 20 x $50 = $1000 (10x.1) = 1 1 x 8 x 40 = $320 $132090 30 30 x $50 = $1500 0 $0 $1500

Least cost safety stock = 20, ROP = 80

6. Given dL = 130, dLT = 80, and for 80% service level, Z = 0.84ROP = 130 + 0.84 x 80 = 197.2, or round up to 198 for at least 80% service level

7. 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 = 4.8Safety 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 = √4 (2.4)2+2232 = 7.684Safety 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

8. Cs = Lost profit = Selling price per unit – Cost per unit = 10 – 3 = $7Co = Cost/unit – salvage value/unit = 3 – 1.20 = $1.80Optimum service level = 7/(7 + 1.80) = 0.795 = 79.5%

From normal table, for 79.5% service level, Z = 0.83Stock = + Z = 150 + 0.825 (12) = 159.9 or 160

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

a. Production rate/worker/day = 8 hours per day/100 hours per unit = 0.08 per worker/dayProduction rate/worker/quarter = 0.08/worker/day x 65 days/quarter = 5.2/worker/ quarter

b. Wage rate per worker per day = $15/hour x 8 hours/day = $120Wage rate per worker per quarter = $15/hour x 8 hours/day x 65 days/quarter = $7800

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

d. Chase plan

Period DemandProduction

requiredWorkers needed

Workers needed (Rounded)

Hired workers

Fired workers

30

1 160160–(0–0) =

160 160/5.2=30.77 31 1 02 180 180 180/5.2=34.62 35 4 03 220 220 220/5.2=42.31 43 8 04 200 200 200/5.2=38.46 39 0 4

148 13 4

Cost summaryRegular wages 148 workers-quarters x $7800 = 1,154,400O.T. cost =S.C. costHiring cost 13 workers x $350 = 4,550Firing cost 4 workers x $500 = 2,000Carrying costTotal cost $1,160,950

e. Level PlanSum of demand = 760Average demand = 760/4 = 190 i.e. = production per quarter

Period Demand RT Production E.I.0

1 160 190 302 180 190 403 220 190 104 200 190 0

No. of workers needed = 190/5.2 = 36.54 or 37Cost summaryRegular wages 37 workers x 4 quarters x $7800 = 1,154,400Hiring cost (37 workers – 30 workers) x $ 350 = 2,450Firing cost -Carrying cost 80 x $100 = 8,000Total cost $1,164,850

f. Mixed PlanNo. of workers = 31Production per quarter with 31 workers = 31 x 5.2 = 161.2O.T. capacity/quarter = 161.2 x 20% = 32.2

Period Demand Production capacity RT Production1 160 161.2 Min(160,161.2) =1602 180 161.2 Min(180,161.2) =161.23 220 161.2 Min(220,161.2) =161.24 200 161.2 Min(200,161.2) =161.2

643.6

Shortage O.T Capacity O.T. Production S.C.160 – 160=0 32.2 0 0

180-161.2=18.8 32.2 Min(18.8,32.2) = 18.8 0220-161.2=58.8 32.2 Min(58.8,32.2)=32.2 58.8 – 32.2=26.8200-161.2=38.8 32.2 Min(38.8,32.2)=32.2 38.8 - 32.2=6.8

82.8 33.6

Cost summaryRegular wages 31 workers x 4 quarters x $7800 = 967,200O.T. cost = 82.8 units x $2000 165,600S.C. cost 33.6 units x $2500 = 84,000Hiring cost (31 – 30) x $350 = 350Firing cost -Carrying cost -

A

B C2

D4

F

E2

H2 I

D1

GF G

Total cost $1,217,150

10.

B17 (B13*B12)/B11 F29 E4 a. B41b. C22:D25, D29:E32c. D29:D32 <= H29:H32

G29:G32 >= E13C22:D25 = Integer (if needed)D29:E32 = Integer (if needed)

d. Changing cells non-negativeSimplex LP

B18 B13*B3*B12 G29 SUM(B29:E29)-F29B19 B11*B4 H29 C29*$B$14B22 E11 G33 SUM(G29:G32)E22 B22+C22-D22 B35 E26*B18B23 E22 B36 D33*B19C26 SUM(C22:C25) B37 E33*B5D26 SUM(D22:D25) B38 C26*B7E26 SUM(E22:E25) B39 D26*B8B29 E12 B40 G33*B6C29 E22*$B$17 B41 SUM(B35:B40)

11. Current pricing:Price = $100Demand = 500Revenue = 500 x $100 = 50,000Variable cost = $3 x 500 = 1500Net revenue = 50,000 – 1,500 = $48,500

Proposed pricing:Price 70 90 120Demand 300 200 100Revenue 21000 18000 12000

Total revenue = 51000Variable cost = $3 x 600 tickets sold = 1800Net revenue = 51,000 – 1,800 = $49,200

12. (a)

(b).

F

D

G

B

H

E

I

C A

F

D

G

1 2 3 4 5 6 7Lead time = 7 weeks

(c)Part Gross Available Net

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

13.1 2 3 4 5 6

MPS start for A 100 150

Item B GR = Lead time = 1Week: 1 2 3 4 5 6Gross requirement 0 0 0 100 0 150Scheduled receipts 50Projected on-hand 100 100 150 150 150 50 50Net requirement 100Planned receipts 0 0 0 0 0 100Planned order releases 0 0 0 0 100 0

Item C Lead time = 3Week: 1 2 3 4 5 6Gross requirement 0 0 0 100 0 150Scheduled receipts 20 30Projected on-hand 30 30 50 80 80 0 0Net requirement 20 150Planned receipts 0 0 0 20 0 150Planned order releases 20 0 150 0 0 0

Item P Lead time = 2Week: 1 2 3 4 5 6Gross requirement 0 0 0 0 100 0Scheduled receipts 50Projected on-hand 0 0 50 50 50 50 0Net requirement 50Planned receipts 0 0 0 0 50 0Planned order releases 0 0 50 0 0 0

Item F Lead time = 4Week 1 2 3 4 5 6Gross requirement 0 0 0 0 300 0Scheduled receipts 30 40Projected on-hand 0 0 30 30 70 70 0Net requirement 230Planned receipts 0 0 0 0 230 0Planned order releases 230 0 0 0 0 0

Planned order releases:A has releases of 100 in week 4, 150 in week 7B has a release of 100 in week 5C has releases of 20 in week 1, 150 in week 3P has a release of 50 in week 3F has a release of 230 in week 1

14. (i) L-4-LItem LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receiptsProjected on-hand 100 100 0 0 0 0 0 0 0Net Requirement 0 250 200 150 250 200 200 150Planned receipts 0 250 200 150 250 200 200 150Planned order releases 250 200 150 250 200 200 150 0

No. of setup = 7Carrying cost = 0Setup cost = 7 x $300 = 2100Total cost = 2100

(ii) EOQ:Total demand for 8 weeks = 1500, d = 1500/8 = 187.5H = $0.80/weekS = 300

Q = √ 2 (187.5 )3000.8

= 375

Item LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receipts 0 0 0 0 0 0 0 0Projected on-hand 100 100 0 125 300 150 275 75 250Net Requirement 0 250 75 0 100 0 125 0Planned receipts 0 375 375 0 375 0 375 0Planned order releases 375 375 0 375 0 375 0 0

Setup cost per week = (d/Q) S = (187.5/375) x 300 = 150Holding cost per week = (Q/2)H per week = (375/2) x 0.80 = 150Total cost per week= 150 + 150 = 300Cost for 8 weeks = Total cost per week x 8 weeks = 300 x 8 = 2400

(iii) POQNo. of periods = EOQ/d = 375/187.5 = 2 weeksItem LT = 1Week: 1 2 3 4 5 6 7 8Gross requirement 100 250 200 150 250 200 200 150Scheduled receipts 0 0 0 0 0 0 0 0Projected on-hand 100 100 0 200 0 250 0 200 0Net Requirement 0 250 0 150 0 200 0 150Planned receipts 0 450 0 400 0 400 0 150

Planned order releases 450 400 400 150

No. of setup = 4Setup cost = 4 x $300 = 1200Sum of ending inventory 650Carrying cost = 650 x 0.8 = 520Total cost = 1720

#15.Week ending 1 2 3 4 5 6Planned input 500 800 700 600 600 800Actual input 700 700 700 800 600 500Cumulative deviation 200 100 100 300 300 0Planned output 650 650 650 650 650 700Actual output 600 700 800 700 650 500Cumulative deviation -50 0 150 200 200 0Backlog 120 220 220 120 220 170 170

#16. SPT

JobProcessing

time (Days)Days till due

dateCompletion time

(Flowtime) LatenessB 20 165 20 0A 30 40 50 10D 35 130 85 0C 40 125 125 0

125 280 10

Average flow time = 70Average lateness = 2.5Average WIP = 2.240Utilization = 44.6%

EDD

JobProcessing

time (Days)Days till due

dateCompletion time

(Flowtime) LatenessA 30 40 30 0C 40 125 70 0D 35 130 105 0B 20 165 125 0

125 330 0

Average flow time = 82.5Average lateness = 0Average no. of jobs in the system = 2.640Utilization = 37.9%

CRJob Processing time Date job due Due date CRA 30 90 40 1.333333B 20 215 165 8.25C 40 175 125 3.125D 35 180 130 3.714286

JobProcessing

time (Days)Days till due

dateCompletion time

(Flowtime) LatenessA 30 40 30 0C 40 125 70 0D 35 130 105 0B 20 165 125 0

125 330 0

Average flow time = 82.5Average lateness = 0Average no. of jobs in the system = 2.640Utilization = 37.9%

#17. JOB TIMES (minutes)A B C D E

Workstation 101 27 18 70 26 15Workstation 102 45 33 30 24 10

a. Schedule: B – A – C – D – E

JobWorkstation 101 Workstation 102

Processing time Finish time Processing time Start time Finish time Idle timeB 18 18 33 18 51 18A 27 45 45 51 96 0C 70 115 30 115 145 19D 26 141 24 145 169 0E 15 156 10 169 179 0

37

b. Total idle time for workstation 102 is 37 minutes

10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180

B A C D E

Idle B A C D EIdle

18 45 115 141 156

18 51 96 115 145 169 179