PRODUCTION AND OPERATIONS MANAGEMENT INDIVIDUAL ASSIGNMENT TOPICS

ECE 6B

1. A farming conglomerate has a large cow-calf operation. The manager expects the hay crew to place

1,750 bales of hay in the barn daily during harvest. The contract costs for labor only are $180/day

(for a crew of four). In the past four days 8,100 bales have been harvested. What is the farm

manager’s labor efficiency variance for the hay crew? Would you suggest any action based on this

figure?

2. Direct time study for a job resulted in the following times:

Cycle

Average Cycle Time (in minutes)

1 1.321

2 1.411

3 1.704

4 1.175

A pre-determined time standard was set at 2,128 TMU/cycle, which converts to 1.275

minutes/cycle. What time standard would you recommend? Justify your choice.

3. Develop an employee/ machine activity chart to show how a multipage term paper should be copied

on a coin-operated photocopy machine. Use a layout diagram. Assume there are ample coins and

that the stack of pages is unstapled at the start of the task.

4. Job Analysis reveals that during a typical 8-hour workday a man-machine operation typically

experiences various unavoidable delays totaling 40 minutes and one equipment setup changeover

of 20 minutes. Operators need 20 minutes for personal time and take two 15-minute coffee breaks.

Standard time per cycle (to produce one unit) is 10 minutes. How many units are produced by an

operator rated at 85%? At 115%?

5. A student facing mid-term exams decides to start studying in earnest. After one day in the library,

the student is dismayed to find that, at her current rate of studying, she will not be ready to take the

exams until four days after they are over. A friend volunteers to do a work sample and finds the

following:

Study Period No. of observations No. of observations during which study

occurred

1 11 8

2 23 11

3 7 3

As a percentage of her study period time, what portion of time is she studying?

6. Filing clerks in a state department of welfare were considered to be working any time that had

paper in their hands. Observations were made for seven days. Results are given below. What

portion of time is spent in working? What work measurement technique is this? How might one

alternatively define working?

Day No. of observations No. of observations during which work

occurred

1 14 10

2 17 10

3 10 5

4 23 14

5 14 10

6 11 9

7 19 13

7. Several laboratory technicians in a hospital are responsible for running the highly automated

“Chemistry 12” blood profile text. An experienced technician was monitored over a two-week

period (70 hours). The analyst studying the job found that the technician performed 412 blood

profile tests, working 60 percent of the time and idle the rest. Some idleness was due to waiting for

the automated equipment to complete the test. The technician was rated at 85 percent, but the

analyst was uncertain about this rating because of the automated equipment. Allowances are set at

.10.

a) Determine a standard time for a standard blood profile test.

b) How could the analyst be more certain about the worker rating?

8. A post office mail room receives mail and cancels the postage stamps. After first simplifying work,

you make a direct time study of the simplified job and obtain the following times in minutes:

CYCLE

Task Description 1 2 3 4 5

1 Empty mail bags .16 .31 .14 .15 .16

2 Straighten mail .60 .60 .60 .60 .60

3 Carry trays to reader .34 .36 .35 .37 .38

4 Cancellation machine .50 .50 .50 .50 .50

5 Empty trays .24 .24 .48 .27 .25

You further determine the following information about this job:

1. Tasks 2 and 4 are machine-controlled and cannot be speeded up by the operator.

2. You observed two irregularities while timing the job. These task times vary by more

than 20% of each task’s average time.

3. You rated the operator at 120% when he was working.

4. Management and the worker’s union have negotiated the following allowances for

this job:

Personal – 30 minutes/8-hour shift

Unavoidable day – 40 minutes/8-hour shift

Fatigue - .10

5. An operator on this job earns $5/hour

6. Material cost per unit is $.50

7. Total overhead cost is added in at a rate of 150 percent of the sum of direct labor

and material cost.

a) How many pieces should each operator produce during an 8-hour shift?

b) What is the total standard cost per piece?

9. Randolf Corporation has estimated its aggregate demand for the coming year as follows:

Month Productive

days Demand (in units)

Month Productive

days Demand (in units)

Jan 22 8,000 July 22 26,000

Feb 19 12,000 Aug 11 16,000

Mar 21 18,000 Sept 21 18,000

Apr 22 20,000 Oct 22 14,000

May 21 28,000 Nov 18 9,000

June 21 25,000 Dec 21 7,000

Currently, there are 100 employees whose normal productivity is 12 units/day/employee. Daily

capacity can be increased up to 30% by working overtime at an additional cost of $2/unit.

Regular time salaries average $30/day/employee. Costs of storing units in inventory are

$2/unit/month. Inventory shortages cost $10/unit short. Costs of hiring and training are

$300/employee, and layoff costs are $200/employee. Additional capacity is available by

subcontracting to a local manufacturer at a cost of $8/unit. Currently, Randolf has 5000 units in

inventory. Develop a good plan for next year’s aggregate output.

10. An office equipment repair company has sales/service offices throughout North Carolina. The

company services such products as typewriters, dictating equipment, photocopiers, and small

computers. The following is the demand forecast for the next year in bimonthly groups. Each two-

month period has 43 productive days.

Period Forecasted Demand

(in units of work)

Jan – Feb 210

Mar – Apr 245

May – June 260

July – Aug 250

Sep – Oct 235

Nov – Dec 220

a) Graph the cumulative demand in relation to the cumulative productive days.

b) Assume that an employee contributes 344 working hours each two months and that each unit

requires 30 standard hours to produce. Assuming no overtime or part-time employees, calculate

the number of employees required each period.

c) The company employs enough people to meet peak demand without overtime, hiring, or firing

to meet demand changes. With a correct labor rate of $8.25/hour, what will be the bimonthly

and annual labor costs? What is the extra cot incurred for this employment policy?

11. A manufacturing firm is trying to schedule production for the coming three months. Product

demand for each of the next three months is forecasted as 300, 250, and 325 units respectively.

Currently, 95 units are available in finished goods inventory at the factory. At the end of the three-

month scheduling period, the company wants to have 120 finished units available and to have

supplied all units demanded (backorders are not allowed). Regular shift operations are capable of

producing 200 units/ month at a cost of $10/unit. Overtime operations can supply up to 100 units/

month at $15 cost/unit. Inventory costs are $ 2/unit/month for finished goods. Structure this

scheduling problem in a transportation linear programming format. Create and interpret an initial

feasible solution.

12. Jobs arriving at Joanna’s Downtown Upholstery Shop are processed and due as shown:

Waiting job (numbered in order of arrival)

317 318 319 320

Processing Time (in days) 12 11 14 2

Due Date (in days from now) 20 20 18 8

a) How many processing sequences are possible for these four days?

b) Apply the first-come-first-served priority sequencing rule, and calculate average job lateness.

Now apply the shortest processing time rule, and calculate the average job lateness. Which rule

is better in terms of average job lateness? Will that always be the better rule regardless of the

data?

13. Given the following data for waiting jobs at a work center, calculate system performance using first-

come-first-served, last-come-first-served, and shortest processing time sequencing rules.

Waiting job (numbered in order of arrival)

P Q R S T

Processing Time (in days) 12 4 16 6 7

Due Date (in days from now) 22 14 26 16 17

14. Suppose for the following waiting jobs, setup costs incurred between any two jobs are as follows:

Successor job

Predecessor job

P Q R S T

P - $120 $90 $80 $30

Q 100 - 20 70 60

R 10 50 - 100 80

S 50 90 80 - 40

T 80 70 60 60 -

Assuming job P is being processed now, apply the next best (NB) rule and determine the

resulting total setup cost. How does this setup cost compare with the setup cost resulting from

the SPT rule?

15. Airline Industries is an intermittent manufacturing facility, processing jobs to customer order.

Currently, eight open orders are waiting processing. All jobs must be processed at the same facility.

Waiting job (numbered in order of arrival)

A B C D E F G H

Processing Time (in days) 23 16 5 31 11 20 2 27

Due Date (in days from now) 28 35 15 40 30 45 8 50

a) Develop a Gantt load chart for the facility.

b) How many different processing sequences are possible?

c) Develop a visual load profile for infinite loading; the work center’s capacity is five days of

processing per week.

16. Data Systems, Inc., processes all incoming jobs through two work centers, A and B. Each job goes

first through A, and then through B. Five jobs await processing.

Waiting job S T U V W

Processing Time (in days) in A 16 3 21 31 6

Processing Time (in days) in B 7 9 5 17 13

Assign a job sequence that minimizes the flow time of the last job processed. What is the total

flow time for this sequence?

17. Ten new projects await processing at Environmental Impact Affiliates. All projects must be evaluated

first empirically and then legally. Estimates of processing times (in days) for the empirical and legal

phases are:

Waiting job A B C D E F G H I J

Empirical phase 20 18 7 30 10 20 3 25 14 24

Legal phase 7 21 36 9 12 17 8 22 17 12

a) Develop a Gantt load chart for the work centers (empirical and legal).

b) Find the processing sequence that minimizes the flow time of the last project processed. What is

this flow time?

c) Draw the Gantt chart for scheduling based on the results for part (b).

18. First National Bank has four new tellers with varying skills who are to be assigned to the main bank

or one of the branches. The criterion for assigning tellers to locations is minimal customer waiting

time. Customer waiting time (in sec) is shown in the table below for each of four locations and teller

skills. Make teller assignments, using the assignment algorithm that will minimize overall waiting

time. What is the total waiting time index for the optimal assignments?

Teller Skill

Location A B C D

Main bank 50 70 40 100

Southwest branch 70 40 70 70

Clearwater branch 90 70 50 50

Northgate branch 80 60 70 50

19. A local bakery, Harry’s, orders 100 50-pound bags of flour every three months.

a) What is the average inventory for three months (in bags)?

b) What is the average inventory for a year (in bags)?

c) What is the average monthly inventory (in pounds)?

20. Delicious Donut shop requires 50 bags of flour every three months. The costs of ordering are

12/order, and carrying charges are 22% of the flour cost. A bag of flour costs $27. Flour can be

delivered virtually instantaneously from a local warehouse. Determine the operating doctrine for a

quantity/reorder point inventory system.

21. Use the graphical method to estimate Q* for the following situation, in which delivery is

instantaneous and usage rate is constant throughout the year.

D= 10,000 units, R= 0 units I= .25, C= $100/unit

Procurement cost/order= $.50 + $.50/unit in the order

22. A textile manufacturer is interested in optimally determined inventories for cutting operations for a

children’s product line. The production manager would like to establish the optimal reorder point

and order quantity for each item in the line. Garment 78A201, a typical product, is demanded

uniformly throughout the year; total annual demand is 14,000 items. The production rate is 2,000

items/ month. Sewing, the operation following cutting, is staffed to meet annual demand exactly.

Setup costs for cutting are $240, and the cost of carrying one item for a year is $.50. Since cutting

and sewing are done in the same plant, delivery of cut items to sewing is essentially instantaneous.

Determine the cutting operation operating doctrine for garment 78A201.

23. A missile manufacturer requires an electrically wired subassembly for final assembly. Annual

subassembly demand is 480 “wire bundles”; order costs are $85; carrying costs are 75% of average

inventory investment; and bundles cost $1,125 each. Delivery time is known with certainty to be 21

days. Establish the optimal operating doctrine.

24. Buster’s Inc., is interested in the economical order quantity for a production subassembly that is

currently purchased from another company. The final assembly made by Buster’s is for their parent

company, under an annual contract, with the year’s demand set at 125,000 units. Two purchased

subassemblies are required for each final assembly. The cost of a subassembly is $15, and the cost

of placing an order with the supplier is $35. The annual inventory holding charge is $5. Buster’s

currently orders 1,500 units at one time. Can you save Buster’s any money by recommending a new

order quantity? If so, how much can be saved and what quantity should be ordered?

25. Ward Paper Box Company supplies a particular candy box to Russell Stover Candy Company,

delivering 200 one-pound candy boxes/ day. The machine that produces these boxes has a capacity

of 1,000 boxes/ day. In the past, Ward has always run the machine one day a week to satisfy the

weekly demand of 1,000 boxes over a 5-day work week (50 weeks a year). Setup costs are $100/run,

and carrying costs are $.05/box/ day.

a) Find the economic order quantity for this candy box.

b) What is the cost savings in a year by ordering the economic order quantity rather than following

current policy?

26. A fast-food outlet uses 220 breakfast paper cartons/ day. The outlet plans to be open 365 days a

year. The cartons cost $.35/dozen; ordering costs are $15/order; and carrying costs are 70% of the

item (since space is a premium).

a) Find the economic order quantity if delivery is instantaneous.

b) Currently, cartons are ordered every 14 days. Relate current ordering quantity, optimal order

quantity, current total costs, and optimal total costs. What does this mean?

27. A dairy that supplies a large number of retail outlets uses a certain ingredients at the rate of 1,500

pounds/day, 250 days/year. Delivery is virtually constant and requires two days. A two-day usage of

safety stock is set up by management and cannot be changed. Ordering costs are $40/order, and the

cost of carrying inventory charge is $0.001/ pound/day. Determine the following:

a) Economic order quantity

b) Reorder point

c) Maximum inventory level

d) Total annual carrying costs.

28. Often variances for production are computed and the results are used for subsequent production

control.

a) Compute the raw material price and usage (quantity) variance and the direct labor quantity

variance for Milton Industries’ key product, shown below. State the variance as favorable or

unfavorable.

Standard for 1,000 units Actual for 1,000 units

Raw materials: Price

Quantity

$1.20/ pound $1.40/ pound

1 pound/ unit 1,100 pounds

Direct labor: Price

Quantity

$6.00/ hour $6.00/ hour

2.37 hour/ unit 2,172 hours

b) For each measure in part (a), would you take action as a manager?

c) Write the general formula you used to compute this variance.

29. Actual daily demand and lead-time distributions are given below. What is expected demand during

lead time? What is the minimum that demand during lead time will ever be?

Range of Actual Daily Demand

(in units)

Days Demand Fits Range

Actual Lead time

(in days)

Number Lead Times

20- 40 4 1 3

41- 60 3 2 2

61- 80 3 4 2

30. An electrical motor housing has an annual usage rate of 75,000 units/ year, an ordering cost of $20,

and annual carrying charge of 15.4 % of the unit price. For lot sizes of fewer than 10,000, the unit

price is $.50; for 10,000 or more, the unit price is $.45. Delivery lead time is known with certainty to

be two weeks. Determine the optimal operating doctrine.

31. Daily demand for a manufactured part is normally distributed with a daily mean of 80 cases and a

standard deviation of 30 cases. Supply is virtually certain, with a lead time of three days. The cost of

placing an order is $15, and annual carrying charges are 20 percent of the unit price of $6.50. We

want a 90% service level at our warehouse for customers who place orders during the reorder

period. Service level is interpreted as the probability that there will be a stock-out of any size during

lead time. Backorders are allowed. Once stocks are depleted, orders are filled as soon as the stocks

arrive. We can assume orders arrive 200 days throughout the year. Determine the operating

doctrine for this manufactured part.

32. The daily demand for a component assembly item is normally distributed with a mean of 120 and

standard deviation of 15. Furthermore, the source of supply is reliable and maintains a constant lead

time of four days. If the cost of placing the order is $45 and annual carrying charges are $0.75/ unit,

find the order quantity and reorder point to provide an 85 percent service level. Service level is

interpreted as the probability that there will be a stock-out of any size during lead time. Unfilled

orders are filled as soon as an order arrives. Assume sales occur over the entire year.

33. A florist orders flowers weekly. Demand for carnations varies uniformly from 18 to 30 dozen a week.

Carnations cost $7/dozen and sell for an average price of $11/dozen, some sold individually and

some sold in arrangements. Salvage is virtually zero after a week’s storage. Establish the ordering

quantity for carnations. Explain your results in terms the florist will understand.

34. Daily demand for pickles for a local chain of fast-food restaurants is normally distributed with a

mean of 30 jars and a standard deviation of 7. Supply is virtually certain with a lead time of two

days; the cost of placing an order is $2.50, and annually carrying charges are 80% of the unit price of

$.60/jar. A 98% service level is desired. Service level is interpreted as the probability that there will

be a stock-out of any size during lead time. The restaurant chain serves 365 days a year.

a) Determine the operating doctrine for ordering pickles.

b) What is the annual cost for pickle buffer stocks? Does this cost seem reasonable for a 98%

service level?

35. For the fast-food restaurant chain in problem 34, suppose that exactly the same situation exists for

coffee as did for pickles, except that coffee costs ten times as much per can as do pickles per jar.

a) What is the operating doctrine for coffee?

b) What is the annual cost for coffee buffer stocks?

c) What conclusions can you reach concerning the effect price has on operating doctrine and

buffer stocks?

36. For the fast-food restaurant chain in problem 34, suppose that exactly the same situation exists for

chocolate syrup as did for pickles, except that chocolate syrup demand is 30 cans/ day with a

standard deviation of 28 cans.

a) What is the operating doctrine for chocolate syrup?

b) What is the annual cost for chocolate syrup buffer stocks?

c) What impact does the variability of demand seem to have on buffer stocks?

37. Bilson, Inc., purchases all metal needed in bar stock form. With an annual demand of 4,500 units, an

ordering cost of $75, and storage costs of 25% of the unit cost, what is the optimal order quantity

given these price breaks?

a) 0-299, $60/unit

b) 300-499, $50/unit.

c) 500 or more, $40/unit.

38. The demand per period for an important inventory item seems to have the following probability

distribution:

Demand (in units)

Probability of Demand

5 .4

6 .2

7 .1

8 .3

All stock to meet the demand for a period must be acquired at the start of the period. The product

costs $5/unit and sells for $8/unit. Any leftover units at the end of a period must be disposed of as

“seconds” at a selling price of $4/unit. On the other hand, if the stock becomes depleted, there is no

cost associated with the shortage.

a) Under these conditions, is it profitable to stock six or seven units at the start of each period?

b) If there were a cost associated with a shortage and a probability of a shortage for each demand

level, how would you modify your answer to part (a)?

39. Demand for the local daily newspaper at a newsstand is normally distributed with a daily mean of

210 copies and standard deviation of 70. A newspaper sells for $.25 cents and costs $.20 to

purchase. Day-old newspapers are very seldom requested, and therefore they are destroyed. What

should the newsstand’s daily order be to maximize profits?

40. A bank purchases promotional ball point pens for $3 each. The company that supplies the pens

suggests that if the imprinted pens were ordered in twice the quantity, a 35% discount could be

arranged. At present the bank orders 100 pens every two months. Ordering costs are $12, and the

bank’s cost of money is 18%. What ordering policy should be followed? Show your analysis to

support your decision.

41. A bank is evaluating teller capacity. Daily demand for teller services is as shown below. The cost of

not serving a customer or having the customer leave angry because of a long wait is estimated to be

high and should be avoided. The cost of a teller is $75/day. A teller typically generates $250/day in

revenue. Develop a decision rule for the bank to follow in comparing current capacity with the most

economical capacity

Average Daily Demand (in no. of busy tellers)

Days Demand Fits Range

0 0

1-2 13

3-4 21

5-6 10

7 or more 6

42. You have a product whose average weekly sales are 600 units. By looking at records of past demand,

you find that the demand pattern has followed the distribution below:

Weekly Demand Above (in units)

Percent of the Time Demand Above

400 100

450 90

500 79

550 64

600 50

650 22

700 8

750 3

800 0

The cost of carrying an item on inventory for one year is $1.30. Order cost is fixed at $72. Lead

time is constant at one week. The stock-out policy has been set to allow two stock-outs/ year on

average. Determine the order quantity and the safety stock that minimize the variable costs.

43. The Office Supply Shop estimates that the monthly demand for ballpoint pens has the following

distribution:

Furthermore, the lead time for the ballpoint pens from the distributor has the following

distribution:

(a) If the management wants to have a cycle-service level of 95% for their continuous review

system, what should the re-order point be?

(b) What quantity of safety stock must be held?

44. Wood County Hospital consumes 1,000 boxes of bandages per week. The price of bandages is $35

per box, and the hospital operates 52 weeks per year. The cost of processing an order is $15, and

the cost of holding one box for a year is 15% of the value of the material.

(a) The hospital orders bandages in lot sizes of 900 boxes. What extra cost does the hospital incur,

which it could save by using the EOQ method?

(b) Demand is normally distributed with a standard deviation of weekly demand of 100 boxes. The

lead time is 2 weeks. What safety stock is necessary if the hospital uses a continuous review

system and a 97% cycle-service level is desired? What should be the re-order point?

(c) If the hospital uses a periodic review system, with P = 2 weeks, what should be the target

inventory level, T?

45. Karl’s Copiers sells and repairs photocopy machines. The manager needs weekly forecasts of service

calls so that he can schedule service personnel. The forecast for the week of July 3 was 24 calls. The

manager uses exponential smoothing with α = 0.20. Forecast the number of calls for the week of

August 7, which is next week.

Week Actual Service Calls

July 3 24

Demand (thousands) Probability

5 0.1

10 0.3

15 0.4

20 0.1

Demand (thousands) Probability

5 0.1

10 0.3

15 0.4

20 0.1

25 0.1

Lead time (weeks) Probability

1 0.2

2 0.4

3 0.2

4 0.1

5 0.1

July 10 32

July 17 36

July 24 23

July 31 25

46. The number of heart surgeries performed at Heartville General Hospital has increased steadily over

the past several years. The hospital’s administration is seeking the best method to forecast the

demand for such surgeries in year 6. The data for the past 5 years are shown. Six years ago, the

forecast for year 1 was 41 surgeries, and the estimated trend was an increase of 2 per year.

Year Demand

1 45

2 50

3 52

4 56

5 58

Use exponential smoothing method with α = 0.6 to forecast for the next year.

47. Refer to the data given in question number 46, and forecast the demand using trend adjusted

exponential smoothing with α = 0.6 and β = 0.1.

48. Refer to the data given in question number 46, and forecast the demand using Regression model,

Y = 42.6 + 3.2X, where Y is the number of surgeries and X is the index for the year.

49. Gerald Glynn manages the Michaels Distribution Centre. After careful examination of his database

information, he has determined the daily requirements for part-time loading dock personnel. The

distribution centre operates seven days a week and the daily part-time staffing requirements are-

Day M T W Th F S Su

Requirements 6 3 5 3 7 2 3

Find the minimum number of workers Glynn must hire. Prepare a workforce schedule for these

individuals so that each will have two consecutive days off per week and all staffing

requirements will be satisfied. Give preference to the S-Su pair in case of a tie.

50. Return to problem number 49 and the workforce schedule for part-time loading dock workers.

Suppose that each part-time worker can work only 3 days, but the days must be consecutive. Devise

an approach to this workforce scheduling problem. Your objective is to minimize total slack capacity.

What is the minimum number of clerks needed now and what are their schedules.

51. Cara Ryder manages a ski school in a large resort and is trying to develop a schedule for instructors.

The instructors receive little salary and work just enough to earn room and bread. They do receive

free skiing, spending most of their free time tackling the resort’s black diamond slopes. Hence the

instructors work only 4 days a week. One of the lesson packages offered at the resort is a 4-day

beginner package. Ryder likes to keep the same instructor with a group over the 4-day period, so

she schedules the instructors for 4 consecutive days and then 3 days off. Ryder uses years of

experience with demand forecasts provided by management to formulate her instructor

requirements for the upcoming month.

Day M T W Th F S Su

Requirements 7 5 4 5 6 9 8

Determine how many instructors Ryder needs to employ. Give preference to Saturday and

Sunday off. Specify the work schedule for each employee. How much slack does your schedule

generate for each day?