INTERNATIONAL UNIVERSITY – VNU HCMC SCHOOL OF BUSINESS

PROBLEMS FOR THE FINAL EXAM (SEMESTER 2, 2012-2013)

CHAPTER 9 - LAYOUT STRATEGY Problem 1: Case: State Automobile License Renewals (p. 382) Problem 2: adapted from Problem 1 A license-renewal process has the following steps and associated times required to perform each step. A review of the jobs indicated that step 1, reviewing renewal applicatins for correctness, had to be performed before any other step. Step 6, issuing temporary licenses, could not be performed untill all the other steps were completed. Each step was assigned to a different clerk. Automobile License-Renewal Process Times Step Average Time to

Perform (sec) 1. Review renewal application for correctness

15

2. Process and record payment 30 3. Check file for violations and restrictions

60

4. Conduct eye test 40 5. Photograph applicant 20 6. Issue temporary license 30 Questions:

a) Where may the bottleneck (long queue), if any, occur in the existing work process during the peak-demand time?

b) What is the maximum number of applications per hour that can be handled by the present process?

c) Assuming the addition of a second clerk to check file for violations, what is the maximum number of applications the process can handle?

d) How would you suggest modifying the process to accommodate 120 applications per hour?

Problem 3: See Problem 9.16 (p. 380) Problem 4: adapted from Problem 3 Tailwind, Inc. produces high-quality but expensive training shoes for runners. The Tailwind shoe, which sells for $210, contains both gas and liquid-filled compartments to provide more stability and better protection against knee, foot, and back injuries. Manufacturing the shoes requires 10 separate

tasks. There are 400 minutes available for manufacturing the shoes in the plant each day. Daily demand is 60. The information for the tasks is as follows: Task Performance

Time (min) Task must follow task listed below

A 1 _ B 3 A C 2 B D 4 B E 1 C, D F 3 A G 2 F H 5 G I 1 E, H J 3 I

a) Draw the precedence diagram b) Assign tasks to the minimum feasible number of workstations according to the “ranked

postioned weight” decision rule. c) What is the efficiency of the process? d) What is the idle time per cycle?

Problem 5 (P 9.17 - textbook) Problem 6a An assemply line in a can-producing factory requires the following activities. The factory operates 8 hours per day, 5 days a week.

Task Time (minutes) Predecessor(s) A 1 B 1 C 1 B D 2 B E 1 B F 2 C, D, E G 1 A H 1 G I 1 H J 1 I K 2 F L 2 J, K M 1 L

a) Draw the precedence diagram b) Without balancing the assemly line, what is the weekly production rate? c) Balance the assembly line. What is the new weekly production rate? d) If the weekly demand is 3,000 cans, what is the greatest possible cycle time. e) Assign tasks to the minimum feasible number of workstations.

Problem 6b: An assemply line in a can-producing factory requires the following activities. The factory operates 5 hours per day, 5 days a week.

Task Time (minutes) Predecessor(s) A 2 B 2 C 2 B D 3 B E 2 B F 3 C, D, E G 1 A H 1 G I 3 H J 1 I K 2 F L 2 J, K M 1 L

a) Draw the precedence diagram b) Without balancing the assemly line, what is the weekly production rate? c) Balance the assembly line. What is the new weekly production rate? d) If the weekly demand is 3,600 cans, what is the greatest possible cycle time. e) Assign tasks to the minimum feasible number of workstations.

Problem 9.19 (textbook, p.381) a) Precedence Diagram b) CT=(1/96)*60*24=15 min/unit c) CT=10, OR=1/10 per minute or (1/10)*24*60 per day d) CT=10, min # of stations = 50/10 = 5

CHAPTER 12 - INVENTORY MANAGEMENT Problem 12.37 (textbook, p. 521) Emarpy Appliance is a company that produces all kinds of major appliances. Bud Banis, the president of Emarpy, is concerned about the production policy for the company’s best-selling refrigerator. The annual demand for this has been about 8,000 units each year, and this demand has been constant throughout the year. The production capacity is 200 units per day. Each time production starts, it costs the company $120 to move materials into place, reset the assembly line, and clean the equipment. The holding cost of a refrigerator is $50 per year. The current production plan calls for 400 refrigerators to be produced in each production run. Assume there are 250 working days per year.

a) What is the daily demand of this product? b) If the company were to continue to produce 400 units each time production starts, how many

days would production continue?

c) Under the current policy, how many production runs per year would be required? What would the annual setup cost be?

d) If the current policy continues, how many refrigerators would be in inventory when production stops? What would the average inventory level be?

e) If the company produces 400 refrigerators at a time, what would the total annual setup cost and holding cost be?

f) If Bud Banis wants to minimize the total annual inventory cost, how many refrigerators should be produced in each production run? How much would this save the company in inventory costs compared to the current policy of producing 400 in each production run.

Solution: a) Daily demand d=D/250=8,000/250=32 b) Q/p=400/200 = 2 c) D/Q=8,000/400=20 Annual S = 20*120=2400 d) Max. Inv. Level = Q(1-d/p)=400(1-32/200) = 336 Average inventory level = 336/2=168 e) (168)50+20(120)=$10,800 f) Q=[2(8,000)120/50(1-32/200)]=213.81

INDEPENDENT DEMAND INVENTORY

Problem 1a Below is a partial listing of the items on a firm’s computer printout of inventory. Using annual dollar value as the criterion, arrange these items into an A-B-C classification. Assign three items to the B category. Part Number

Unit Price

Annual Volume

C150 $1 30,000 C175 2 7,000 MM09 200 400 TL44 4 6,000 MT45 70 3,00 T418 30 3,000 C110 3 5,000 UN04 3 6,000 UN12 60 2,000 BA28 60 2,000 T400 5 4,000

Solution to Problem 1 Part Number

Unit Price

Annual Volume

Amount in $

% explained

C150 $1 30,000 $30,000 4% C175 2 7,000 $14,000 2% MM09 200 400 $80,000 11% TL44 4 6,000 $24,000 3% MT45 70 3000 $210,000 28% T418 30 3,000 $90,000 12% C110 3 5,000 $15,000 2% UN04 3 6,000 $18,000 2% UN12 60 2,000 $120,000 16% BA28 60 2,000 $120,000 16% T400 5 4,000 $20,000 3% TOTAL 68,400 741,000 100% Sorted by % explanation

Part Number

Unit Price

Annual Volume

Amount in $

% explained

Cumulative %

Class

MT45 70 3000 $210,000 28% 28% A UN12 60 2,000 $120,000 16% 45% A BA28 60 2,000 $120,000 16% 61% A T418 30 3,000 $90,000 12% 73% A MM09 200 400 $80,000 11% 84% B C150 $1 30,000 $30,000 4% 88% B TL44 4 6,000 $24,000 3% 91% B T400 5 4,000 $20,000 3% 94% C UN04 3 6,000 $18,000 2% 96% C C110 3 5,000 $15,000 2% 98% C C175 2 7,000 $14,000 2% 100% C TOTAL $741,000 100%

Problem 2a – Probabilistic Model Gemtronics Corporation produces electrical components for appliance and automotive industries. Previous daily demand for part XK202 has shown little seasonal variation, but has been normally distributed with a mean of 700 per day and a standard deviation of 100. The company works 250 days per year. Ten days’ lead time is required to schedule, wait for an available machine, and set up for a production run. The cost to initiate a production run is approximately $200, and the production rate for part XK202 is 4,000 per day. The holding cost for each unit of this product is $0.25 per year.

(a) Compute the optimal production quantity for this item (b) Compute a reorder level that will provide a 0.96 probability of meeting customer demand

during the lead time. (Hint: Use the normal distribution table, for 0.95 Z-value is 1.65; for 0.96 Z-value is 1.76) Problem 2b – Probabilistic Model Alien Auto Co. distributes parts for foreign cars in a large midwestern city. Demand for a particular size of oil filter has been uniform. The lead time to obtain the filters in one month, and the average use rate is 600 per month. The lead-time use is normally distributed with a standard deviation of 70 units. Order cost is $12 and holding cost $0.40 a year per filter. The estimated cost of a stockout is $1.50 per filter.

(a) What is the EOQ? (b) How many orders per year will be placed at this EOQ? (c) What is the optimum probability of a stockout? (d) What is the optimum reorder level? (e) How much will Alien Auto spend per year to hold inventory on this filter if it implements the

values you determined above/

Problem 3a Because of theft, vandalism, abuse and normal wearouts, a large hotel replaces approximately 260 color television sets per year. Ordering cost is $65 for each order, and annual holding cost is $40 per set. Lead-time demand can be described by a normal distribution with a mean of 8 and standard deviation of 3.5 sets. The manager of housekeeping is willing to accept an average shortage of 2 sets per lead time due to the ability to transfer sets among rooms, except for a relatively few times when the rooms are completely booked.

a. What is the economic order quantity of televisions? b. How many orders per year will be made? c. What is the expected number of units short per year? d. What ROP should be used to achieve the desired protection? e. What is the risk of a stockout during lead time for the ROP?

Problem 4 A professional football team uses large quantities of adhesive tape during and immediately preceding the football season. Daily usage tends to be normal with a mean of 40 rolls and a standard deviation of 6 rolls. Ordering lead time is also approximately normal, and it has a mean of 3 days and a standard deviation of ½ day. The front office wants a stockout risk of 2%. a. What ROP is appropriate? b. By how much could safety stock reduced if there were some way to reduce the lead-time variability to zero? What effect on safety stock would result if a constant lead time of 1 day could be achieved? Problem 5 Hoa Phat Furniture Company produces a wide variety of furniture products. The production rate for one model of bookcase is 24 units per day (250 working days per year). The sales rate for this case is 7 units per day. It costs $72 per production equipment setup and the cost to hold a case for a year is $18. a. What is the annual demand for the case? b. To minimize the total annual inventory cost, how many cases should be produced in each production run? c. What is the maximum number of cases that will be in inventory at Hoa Phat Co.? d. How many production runs of cases will Hoa Phat have in a year? Solution:

Parameter Value Parameter Value Demand rate(D) 1750 Optimal production quantity (Q*) 140.59 Setup/Ordering cost(S) 72 Maximum Inventory Level (Imax) 99.58 Holding cost(H) 18 Average inventory 49.79 Daily production rate(p) 24 Production runs per period (year) 12.45 Days per year (D/d) 250 Annual Setup cost 896.24 Daily demand rate 7 Annual Holding cost 896.24 Unit cost 0 Unit costs (PD) 0 Total Cost 1792.48

Problem 6 (problem 13-14, Russel & Taylor) The TransCanada Lumber Company and Mill possesses 10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging company’s supplier begines delivery to to the lumber mill at the rate of 60 logs per day. The lumber mill has determined that the ordering cost is $1600 per order, and the cost of carrying logs in inventory before they are processed is $15 per log on an annual basis. Determine the following:

a. The optimal order size b. The total inventory cost associated with the optimal order quantity c. The number of operating days between orders. d. The number of operating days required to receive an order. Problem 7 (adapted from 13-22, Russel & Taylor’s textbook) Nhu Lan Bakery can make cake at the rate of 116 frozen cakes per day. It operates six days a week, 52 weeks per year. The bakery sets up the cake-production operations and produces until a predetermined number (Q) have been produced. When not producing cakes, the bakery uses its personnel and facilities for producing other bakery items. The setup cost for a production run of cakes is $700. The cost of holding frozen cakes in storage is $9 per cake per year. The annual demand for frozen cakes, which is constant over time, is 8,000 cakes. Determine the following: a) Optimal production run quantity (Q) b) What is the annual setup cost? c) What is the annula holding cost? d) Optimal number of production runs per year

Solution

Parameter Value Parameter Value Demand rate(D) 8000 Optimal production quantity (Q*) 1263.95 Setup/Ordering cost(S) 700 Maximum Inventory Level (Imax) 984.57 Holding cost(H) 9 Average inventory 492.28 Daily production rate(p) 116 Production runs per period (year) 6.33 Days per year (D/d) 312 Annual Setup cost 4430.54 Daily demand rate 25.64 Annual Holding cost 4430.54 Unit cost 0 Unit costs (PD) 0 Total Cost 8861.09 Problem 8 (Basic EOQ): A coffee shop in San Francisco sells Cappuccino at a fairly steady rate of 1000 pounds annually. Assume one pound of Cappuccino is made from 0.25 pound of some certain coffee beans. The beans are purchased from a local supplier for $2.70 per pound. The setup cost for this coffee shop to place an order from its supplier is $50. The holding cost for coffee beans is based on a 20 percent annual interest rate. a. Determine the optimal order quantity for the coffee beans. (10 points) b. If the replenishment lead time is three weeks, determine the reorder level based on the on-hand inventory. (5 points) c. The current reorder policy is to buy the coffee beans once a year, what is the additional cost incurred by this policy. (10 points)

Solution a. D = 1000(0.25)=250 pounds per year S = $50 per order H = $0.20(2.7) per unit per year

HDS2* =Q = 215 pounds

b. The reorder point should be ROP = 250*3/52 = 14.42 ≈ 15 c. Average annual cost for setup cost and holding cost under optimal order policy is

19.1162*

** =+= HQS

QDC

Average annual cost for setup cost and holding cost under current order policy is

5.11754.02

25050250250

2=+=+= HQS

QDC

Additional cost is 117.5 - 116.19 = 1.3 Problem 9 Gamestop buys Wii from Nintendo. Since Wii sells very well in US, Nintendo wants to discourage large amount purchases, so a reverse quantity discount is applied. In particular, when the order quantity is less than 1500 (include 1500), the unit cost is $150, while if the order quantity is higher than 1500, the unit cost is $160. Suppose the setup cost for Gamestop to place an order is $1600, and the annual demand is 50000. Holding costs are based on a 10 percent annual interest rate. How many Wii’s should Gamestop order each time? Solution

D= 50,000 50,000 S= 1,600 1,600 I= 0.1 0.1 of price

Max Q'ty Min Q'ty 1,500 1,501

Unit price, P 150 160 Q* 3,266 3,162 Order Q’ty (adjusted) 1,500 3,162 Annual Setup cost 53,333 25,298 Annual Holding cost 11,250 25,298 Product Cost 7,500,000 8,000,000 Total cost 7,564,583 8,050,596

The order quantity of 1500 is optimal solution because its total cost is cheaper.

CHAPTER 14 – INVENTORY FOR DEPENDENT DEMAND Problem 1a: Daily demand for an item is shown here. Assume a holding cost of $0.50 per unit per day, a setup cost of $100 per setup, a lead time of one day and 70 units on hand.

Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements

50 30 25 35 40 50 35 45 70 75

a) Develop a lot-for-lot solution b) Calculate total inventory-related costs for the data above.

Problem 1b: Daily demand for an item is shown here. Assume a holding cost of $0.50 per unit per day, a setup cost of $100 per setup, a lead time of one day and 70 units on hand.

Period 1 2 3 4 5 6 7 8 9 10 Gross Requirements

50 30 25 35 40 50 35 45 70 75

c) Develop an EOQ solution d) Calculate total inventory-related costs for the data above.

CHAPTER 15 – SCHEDULING Problem 1a: Nam has four jobs waiting to be run this morning. He has four printing presses available. However, the presses are of different vintage and operates at different speeds. The approximate times (in minutes) required to process each job on each press are given next. Assign jobs to presses to minimize the press running times. PRESS JOB 1 2 3 4 A 10 50 40 20 B 40 45 50 35 C 30 70 35 25 D 60 45 70 40 Solution: Optimal cost = $125 Press 1 Press 2 Press 3 Press 4 A Assign 10 50 40 20 B 40 45 50 Assign 35 C 30 70 Assign 35 25 D 60 Assign 45 70 40

Problem 1b: Nguyen has four jobs waiting to be run this morning. He has four printing presses available. However, the presses are of different vintage and operates at different speeds. The approximate times (in minutes) required to process each job on each press are given next. Assign jobs to presses to minimize the press running times. PRESS JOB 1 2 3 4 A 30 18 26 17 B 23 22 32 25 C 17 31 24 22 D 28 19 13 18 Solution: Optimal cost = $69 Press 1 Press 2 Press 3 Press 4 A 30 18 26 Assign 17 B 23 Assign 22 32 25 C Assign 17 31 24 22 D 28 19 Assign 13 18 Problem 2a. The following set of seven jobs is to be processed through two work centers at a printing company. The sequence is first printing, then binding. Processing time at each of the work centers is shown below.

JOBS A B C D E F G

Printing (hours)

14 6 3 6 9 3 6

Binding (hours)

3 9 10 6 9 5 8

a) What is the optimal sequence for these jobs? b) Draw Gantt chart for these work centers. c) What is the total length of time of this optimal solution? Solution a) C – F – B – D – G – E – A b)

c) The seven jobs are completed in 53 hours.

Problem 2b. The following set of seven jobs is to be processed through two work centers. The sequence is first work center 1, then work center 2. Processing time at each of the work centers is shown below.

JOBS A B C D E F G

Work center 1 (hours)

3 11 15 6 12 5 8

Work center 2 (hours)

4 10 11 7 10 6 9

a) What is the optimal sequence for these jobs? b) Draw Gantt chart for these work centers. c) What is the total length of time of this optimal solution?

Solution:

a) A – F – D - G – C – E – B b) Gantt Chart:

c) The seven jobs are completed in 70 hours. CHAPTER 10 and SUP 10 Problem 1: A brake system installer in an auto factory has an actual average time of 10 minutes on her task. The performance rating of the worker timed was estimated at 110%. Practice in this department is to allow 9% for the constant allowances. There is currently no variable allowance. a. Find the normal time for the operation. b. Compute the standard time for the operation. c. Recompute the standard time if a variable allowance of 7% is factored in.

Answer: a) Normal time: 11 minutes; b) Standard time: 12.09 minutes; c) New standard time: 12.10 minutes

EXAMS Problem 1a. (10 points) Casumina Company produces a type of tire called CA120A. The annual demand at its distribtuion center is 12,400 tires per year. The transport and handling costs are $2600 each time a shipment of tires is ordered at the distribution center. The annual carrying cost is $3.75 per tire.

a. Determine the optimal order quantity and the minimum total annual cost. (2.5 pt) b. What is the maximum inventory level and average inventory? (2.5 pt) c. Draw a graph showing total inventory cost, total holding cost, total ordering cost and optimal

inventory level. (2.5 pt) d. The company is thinking about relocating its distribution center, which would reduce

transport and hanling costs to $1,900 per order but increase carrying costs to $4.5 per tire per year. Should the company relocate based on inventory costs. (2.5 pts)

Solution D = 12,400 units/year; S = $2600/unit/year; H = $3.75/unit/year

a. Optimal order quantity (Q*) 4,146.65 Annual Setup cost 7,774.96 Annual Holding cost 7,774.96 Total Cost 15,549.92 b. Maximum Inventory Level (Imax) 4146.65 Average inventory 2073.32

c.

d. Parameter Value Demand rate(D) 12400 Setup/Ordering cost(S)

1900

Holding cost(H) 4.5 Parameter Value Optimal order quantity (Q*)

3,235.91

Annual Setup cost

7,280.8

Annual Holding cost

7,280.8

Total Cost 14,561.59 The total inventory cost of the new option is $14,562, less than $15,549.92 of the current option. Therefore, the company should relocate the distribution center. Problem 1b Bridgestone Corporation produces a type of tire called …. The annual demand at its distribtuion center is 12,000 tires per year. The transport and handling costs are $2000 each time a shipment of tires is ordered at the distribution center. The annual carrying cost is $3 per tire.

a. Determine the optimal order quantity and the minimum total annual cost. (2.5 pt) b. What is the maximum inventory level and average inventory? (2.5 pt)

c. Draw a graph showing total inventory cost, total holding cost, total ordering cost and optimal inventory level. (2.5 pt)

d. The company is thinking about relocating its distribution center, which would reduce transport and hanling costs to $1,500 per order but increase carrying costs to $4 per tire per year. Should the company relocate based on inventory costs. (2.5 pts)

Solution Parameter Value Optimal order quantity (Q*)

4000

Maximum Inventory Level (Imax)

4000

Average inventory

2000

Orders per period(year)

3

Annual Setup cost

6000

Annual Holding cost

6000

Unit costs (PD) 0 Total Cost 12000 Graph

d.

Parameter Value Parameter Value Demand rate(D) 12000 Optimal order

quantity (Q*) 2683.28

Setup/Ordering cost(S)

1500 Maximum Inventory Level (Imax)

2683.28

Holding cost(H) 5 Average inventory

1341.64

Unit cost 0 Orders per period(year)

4.47

Annual Setup cost

6708.2

Annual Holding cost

6708.2

Unit costs (PD) 0 Total Cost 13416.41 The company should relocate the distribution center because the total inventory cost for this option ($13,416) will be higher than that of the current option ($12,000). Problem 2a A big university plans to issue “smart” identification cards to all of its faculty and students. The cards store information on library usage, class schedules, insurance, emergency contacts. They may also be used as debit cards to buy meals and stationery. According to the plan, 60,000 new cards should be issued. The following table shows the relevant steps of the card-issuing steps. Steps Time

(seconds) 1. Review application for correctness 10 2. Verify inofrmation and check for outstanding debt 60 3. Process and record payment 30 4. Take photo 20 5. Attach photo and laminate 10 6. Magnetize and issue card 10

a. Is it possible to process one applicant every minute? Explain. b. How would you assign tasks to wokers in order to process 60 applicants an hour? c. How many workers are required? How efficient is your line? Solution a. Yes. The largest cycle time of the process is 60 seconds or 1 minute. Therefore, the output

rate is 1 student per minute.

b. The number demanded is 60 applicants per hour The desired cycle time is 60 sec/applicant (= 3600 sec/60). Assignment should be as follows. Worker 1: step 1 Worker 2: step 2 Worker 3: step 3, 4, 5 Worker 4: Step 6 c. Four workers should be required. Efficiency rate is 58.33%.

Problem 2b A big university plans to issue “smart” identification cards to all of its faculty and students. The cards store information on library usage, class schedules, insurance, emergency contacts. They may also be used as debit cards to buy meals and stationery. According to the plan, 60,000 new cards should be issued. The following table shows the relevant steps of the card-issuing steps. Steps Time

(seconds) 1. Review application for correctness 10 2. Verify inofrmation and check for outstanding debt 50 3. Process and record payment 28 4. Take photo 18 5. Attach photo and laminate 8 6. Magnetize and issue card 8

d. Is it possible to process one applicant every minute? Explain. e. How would you assign tasks to wokers in order to process 60 applicants an hour? f. How many workers are required? How efficient is your line? Solution c. Yes. The largest cycle time of the process is 60 seconds or 1 minute. Therefore, the output

rate is 1 student per minute. d. The number demanded is 60 applicants per hour The desired cycle time is 60 sec/applicant (= 3600 sec/60). Assignment should be as follows. Worker 1: step 1, step 2 Worker 2: step 3, step 4, step 5 Worker 3: step 6 c. Three workers should be required. Efficiency rate is 67.78 %.