Krajewski Ism Ch16

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Chapter

16

Scheduling

DISCUSSION QUESTIONS

1. The optimizing approach, of course, would give the optimal schedule for a group of jobs. However, implementing the model would be difficult. For example, significant amounts of data would need to be maintained and updated each time the model was used. There would also likely be circumstances when the schedule would have to be manually adjusted to account for unexpected happenings. Of course, the model’s assumptions (linearity or nonlinearity, deterministic or stochastic, and so forth) could come into serious question.

The dispatching approach does not claim to provide an optimal solution, but it is much easier to implement and “adjusts” to unexpected happenings as they occur. The optimizing approach might prove to be the better choice in environments where there are few new job arrivals during the week (or they can be held until the next scheduling session) and there are few unexpected disruptions to the process. The dispatching approach is likely to be the better choice in dynamic environments where control of the schedule is difficult without making changes periodically.

Technology and software advances for real-time scheduling may offer the best of both approaches.

2. Priority systems affect operations performance and aid management in making operational decisions. They facilitate prioritizing of work in the organization, as all the work to be performed in the organization cannot be done at the same time. The choice of priority system also helps management to focus and consciously decide on the scheduling system that will emphasize the performance criteria it considers to be important. By providing guidance for the numerous routine decisions associated with determining the sequence in which jobs are to be processed, priority systems allow managers to spend more time with strategic issues.

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PROBLEMS

1. Michaels Distribution Center

Day M T W Th F S Su Requirements 6 3 5 3 7 2 3 M T W Th F S Su Employee 6 3 5 3 7 2 3 1 5 2 4 2 6 2 3 2 4 1 3 1 5 2 3 3 3 1 3 0 4 1 2 4 2 0 2 0 3 1 2 5 1 0 2 0 2 0 1 6 0 0 1 0 1 0 1 7

The number of employees is 7. They are scheduled to take the boxed days off. 2. Cara Ryder’s ski school needs 11 instructors.

a. Alternative 1. The heuristic does have a number of different solutions. M T W Th F S Su Instructor 7 5 4 5 6 9 8 1 6 5 4 5 5 8 7 2 5 4 4 5 5 7 6 3 5 4 4 4 4 6 5 4 4 4 4 4 3 5 4 5 3 3 4 4 3 4 3 6 3 3 3 3 2 3 3 7 2 2 2 2 2 3 3 8 2 2 2 1 1 2 2 9 1 1 1 1 1 2 1 10 1 1 0 0 0 1 0 11

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460 z PART 3 •Managing Value Chains

b. Instructors are scheduled to take the boxed days off in the solution shown in part (a).

M T W Th F S Su On-duty 7 5 4 5 6 9 8 Requirements 7 5 4 5 6 9 8 Slack 0 0 0 0 0 0 0 Alternative 2 (Optional) M T W Th F S Su Instructor 7 5 4 5 6 9 8 1 6 5 4 5 5 8 7 2 5 4 4 5 5 7 6 3 5 4 4 4 4 6 5 4 4 3 4 4 4 5 4 5 4 3 3 3 3 4 4 6 3 3 3 3 2 3 3 7 2 2 2 2 2 3 3 8 2 2 2 1 1 2 2 9 1 1 1 1 1 2 1 10 1 1 0 0 0 1 1 11

Instructors are scheduled to take the boxed days off.

M T W Th F S Su

On-duty 7 5 4 5 6 9 8

Requirements 7 5 4 5 6 9 8

Slack 0 0 0 0 0 0 0

3. The environmentally progressive Mayor of Massilon, Ohio

a. We used Workforce Scheduler Solver in OM Explorer to arrive at the minimum number of collectors. For each employee, the bold values show his or her two off-days.

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Solver Workforce Scheduler Enter data in yellow shaded areas. Enter your base requirements for the days of the work week.

M T W Th F S Su

Base Requirements 12 7 9 9 5 3 6

Employee 1 12 7 9 9 5 3 6 Employee gets F/S off.

Employee 2 11 6 8 8 5 3 5 Employee gets S/Su off.

Employee 7 6 1 3 3 2 3 3 Employee gets T/W off.

Employee 8 5 1 3 2 1 2 2 Employee gets Th/F off.

Employee 9 4 0 2 2 1 2 1 Employee gets T/W off.

Employee 11 2 0 1 0 0 1 0 Employee gets Th/F off.

The minimum number of employees is 12. However, many schedules (particular assignments of on-duty periods) are possible.

b. The work schedule for the analysis in part (a) is to assign employees the boxed days off.

On-duty 12 10 10 10 7 4 7

Slack 0 3 1 1 2 1 1

c. We can use the heuristic method again to find whether we can get by with fewer employees. One solution follows.

M T W Th F S Su Employee 8 7 7 7 7 7 7 1 7 6 6 6 6 7 7 2 6 5 5 6 6 6 6 3 5 5 5 5 5 5 5 4 4 4 4 4 4 5 5 5 3 3 3 4 4 4 4 6 2 3 3 3 3 3 3 7 2 3 2 2 2 2 2 8 1 2 1 1 1 2 2 9 0 1 0 1 1 1 1 10 0 1 0 0 0 0 0 11

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i. Only 11 employees would be needed now. Total slack generated from this work schedule is:

M T W Th F S Su

On-duty 9 7 9 8 8 7 7

Slack 1 0 2 1 1 0 0

ii. With preference to S-Su pairs.

M T W Th F S Su Employee 8 7 7 7 7 7 7 1 7 6 6 6 6 7 7 2 6 5 5 6 6 6 6 3 5 5 5 5 5 5 5 4 4 4 4 4 4 5 5 5 3 3 3 4 4 4 4 6 2 3 3 3 3 3 3 7 2 2 2 2 2 2 3 8 1 1 1 1 2 2 2 9 0 0 1 1 1 1 1 10

The number of employees needed is reduced to 10, and no slack is generated from this solution.

M T W Th F S Su

On-duty 8 7 7 7 7 7 7

Slack 0 0 0 0 0 0 0

iii. Because each employee requires a truck, the number of trucks needed would be 8 to cover Monday, even though the actual number of employees available would be 9 in the solution (i). Assuming that extra employees are put to work doing some support activities, the smoothing of the workload will result in a reduction of 4 trucks over the requirements schedule in part (a).

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4. Hickory Company a. FCFS: SPT: EDD: Job Start Time Flow Time Job Start Time Flow Time Job Start Time Flow Time 1 0 10 2 0 3 2 0 3 2 10 13 5 3 10 1 3 13 3 13 28 4 10 19 3 13 28 4 28 37 1 19 29 4 28 37 5 37 44 3 29 44 5 37 44 b. FCFS: SPT: EDD:

Average flow times 26.4 21.0 25.0

Average early time 0.4 3.4 1.0

Average past due 11.0 8.6 10.2

Average WIP inv. 3.0 2.4 2.8

Average total inv. 3.1 2.8 3.0

c. The rules perform as expected, except for SPT on the average past due measure. Typically EDD will do better here. Nonetheless, SPT does well on flow times, WIP, and inventory levels.

5. Drill press

a., b. The following tables give the solutions to parts (a) and (b) using the Single Machine Scheduler from OM Explorer.

Solver - Single Machine Scheduler

Enter data in yellow shaded areas.

Single or Multiple Operations Multiple Operations

Operation Time to Number of Shop Time

Time at Due Date Operations Remaining

Job Curr. Station (weeks) Remaining (weeks) CR S/RO

AA 4 5 3 4 1.25 0.33

BB 8 11 4 6 1.83 1.25

CC 13 16 10 9 1.78 0.70

DD 6 18 3 12 1.50 2.00

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Solver—Singe Machine Scheduler

FCFS: SPT: EDD: S/RO: CR:

Job Start

Time Flow Time Job Start Time Flow Time Job Start Time Flow Time Job Start Time Flow Time Job Start Time Flow Time

AA 0 4 EE 0 2 AA 0 4 AA 0 4 AA 0 4 BB 4 12 AA 2 6 EE 4 6 CC 4 17 DD 4 10 CC 12 25 BB 6 12 BB 6 14 EE 17 19 CC 10 23 DD 25 31 CC 12 20 CC 14 27 BB 19 27 BB 23 31 EE 31 33 DD 20 33 DD 27 33 DD 27 33 EE 31 33 FCFS: SPT: EDD: S/RO: CR:

Average Flow TImes 21.0 14.6 16.8 20.2 20.0

Average Early TIme 0.2 2.2 0.4 1.8 0.2

Average Past Due 9.8 5.4 5.8 10.6 8.8

Average WIP Inv. 3.2 2.2 2.5 3.1 3.0

Average Total Inv. 3.2 2.5 2.6 3.3 3.1

c. Priority planning with an MRP system relies on proper timing of materials. Planners manipulate scheduled due dates to match material need dates with order due dates. Consequently, priority rules incorporating due dates would be most useful in communicating these changes to the shop floor. Of those listed in this problem, EDD, S/RO, and CR would work best.

6. Bycraft Enterprises

Job Total Processing Time (hours)

1 50(.06) + 4 = 7.0 2 120(.05) + 3 = 9.0 3 260(.03) + 5 = 12.8 4 200(.04) + 2 = 10.0

a. Using SPT

Job Arrival Start Finish Flow (hr) Past Due (hr)

1 9:00 A.M.(M) 9:00 A.M.(M) 4:00 P.M.(M) 7.0 0.0

2 10:00 A.M.(M) 4:00 P.M.(M) 1:00 A.M.(T) 15.0 3.0

4 12:00 P.M. (M) 1:00 A.M.(T) 11:00 A.M.(T) 23.0 9.0

3 11:00 A.M.(M) 11:00 A.M.(T) 11:48 P.M.(T) 36.8 24.8

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Monday Tuesday

8–12 12–4 4–8 8–12 12–4 4–8 8–12 12–4 4–8 8–12

Job 1 Job 2 Job 4 Job 3

7 hours 9 hours 10 hours 12.8 hours

Using EDD

Job Arrival Start Finish Flow Past Due

(hr) (hr) 1 9:00 A.M.(M) 9:00 A.M.(M) 4:00 P.M.(M) 7.0 0.0 2 10:00 A.M.(M) 4:00 P.M.(M) 1:00 A.M.(T) 15.0 3.0 3 11:00 A.M.(M) 1:00 A.M.(T) 1:48 P.M.(T) 26.8 14.8 4 12:00 P.M.(M) 1:48 P.M.(T) 11:48 P.M.(T) 35.8 21.8 Total 84.6 39.6 Monday Tuesday 8–12 12–4 4–8 8–12 12–4 4–8 8–12 12–4 4–8 8–12

Job 1 Job 2 Job 3 Job 4

7 hours 9 hours 12.8 hours 10 hours

b. SPT EDD

Average flow time (hours) 20.45 21.15 Average hours past due 9.20 9.90

c. EDD minimizes the maximum number of due hours and the variance of the past-due hours; however, EDD does worse with regard to average flow times and average hours past due. Consequently, in this example EDD does better with respect to some customer service measures but does worse with respect to inventory. SPT processes some jobs and gets them out of inventory quickly, assuming jobs can be shipped on completion whether or not they are due. Typical trade-offs involve customer service and inventory investment.

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7. Refer to Gantt chart in Fig. 16.8

A Job 1 Job 2 Job 3 Idle

B Idle Job 1 Job 2 Job 3

Machine

0 1 2 3 4 5 6 7 8 9

a. To minimize the makespan if each job must be processed on machine A first, we can use Johnson’s rule:

Process Time (hr)

Job Machine A Machine B

1 2 1

2 1 4

3 3 2

The optimal sequence would be 2–3–1. The revised Gantt chart is:

A Job 2 Job 3 Job 1 Idle

B Idle Job 2 Job 3 Job 1

Machine

0 1 2 3 4 5 6 7 ₈

The makespan is now 8 hours, which is an improvement of 1 hour.

b. Now suppose that the only restriction is that no job may be processed on different machines at the same time. One of several schedules that yield a makespan of 7 hours is given following:

A Job 2 Job 3 Job 1

B Job 1 Job 2 Job 3

Machine

0 1 2 3 4 5 6 7

Idle

With the restriction of flow from machine A to machine B removed, we are able to utilize the first hour on machine B. This is why we could beat the schedule in part (a).

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8. Manufacturer of small-boat sails

Job 1 2 3 4 5 6 7 8 9 10

Operation 1 1 5 8 3 9 4 7 2 4 9

Operation 2 8 3 1 2 8 6 7 2 4 1

a. One possible sequence is 1–8–6–7–5–9–2–4–10–3

b. Machine 1 Machine 2

Job Start Finish Start Finish

1 0 1 1 9 8 1 3 9 11 6 3 7 11 17 7 7 14 17 24 5 14 23 24 32 9 23 27 32 36 2 27 32 36 39 4 32 35 39 41 10 35 44 44 45 3 44 52 52 53

The Gantt chart is shown following. Oper 1 0 5 10 15 20 25 30 35 40 45 50 55 1 8 6 7 5 9 2 10 3 4 3 Oper 2 8 6 7 5 9 2 4 Idle 10 1

9. McGee Parts Company

a. To minimize the makespan if each job must be deburred prior to heat treatment, we can use Johnson’s rule:

Processing Time Days

Job Debur Heat Treat

1 2 6 2 3 5 3 7 4 4 3 8 5 1 5 6 8 2

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b. The Gantt chart is shown following. The orders can be shipped in 31 working days.

Debur ₅ ₁ ₂ ₄ ₃ ₆ Heat Treat-ment 5 1 2 4 3 6 | | | | | | | | | | | | | | | | | 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 10. Reliable Manufacturing Job 1 2 3 4 5 6 7 8 Department 12 2 4 7 5 4 10 8 2 Department 22 3 6 3 8 2 6 6 5 a. SPT. Department 12 Department 22

Process Begin End Flow Process Begin End Flow

Job Time Time Time Time Time Time Time Time

1 2 0 2 2 3 2 5 5 8 2 2 4 4 5 5 10 10 5 4 4 8 8 2 10 12 12 2 4 8 12 12 6 12 18 18 4 5 12 17 17 8 18 26 26 3 7 17 24 24 3 26 29 29 7 8 24 32 32 6 32 38 38 6 10 32 42 42 6 42 48 48 141 186

i. Average flow time in Department 12 = (141/8) = 17.625 days ii. Makespan = 48 days

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b. Johnson’s rule minimizes makespan time when scheduling two facilities. First we establish the sequence of jobs based on Johnson’s rule:

Department # 12 1 8 2 4 6 7 3 5

Department # 22 1 8 2 4 6 7 3 5

Department #1 Department #22

Process Begin End Flow Process Begin End Flow

Job Time Time Time Time Time Time Time Time

1 2 0 2 2 3 2 5 5 8 2 2 4 4 5 5 10 10 2 4 4 8 8 6 10 16 16 4 5 8 13 13 8 16 24 24 6 10 13 23 23 6 24 30 30 7 8 23 31 31 6 31 37 37 3 7 31 38 38 3 38 41 41 5 4 38 42 42 2 41 43 43 161 206

i. Average flow time for Department 12 = (161/8) = 20.125 days. ii. Makespan = 43 days.

iii. Sum of job-days = 206

c. The SPT rule results in a lower inventory of uncompleted jobs (see sum of job-days). Johnson’s rule minimizes makespan for a set of jobs over a group of machines. However, to implement Johnson’s rule, the informational requirements increase and the cost of applying the priority rule increases. The trade-off is between improving the overall utilization of the whole facility (2 machines) versus the optimum utilization of an individual facility.

The implication for centralized priority planning is that the additional information requirement may increase the cost. However, centralized planning allows better overall performance and control by higher management.

11. Little 6, Inc.

Time M T W Th F S Su

Personal tax returns 1.5 24 14 18 18 10 28 16 Corporate tax returns 4.0 18 10 12 15 24 12 4 Total hours required 108 61 75 87 111 90 40 Accountants 10.0 11 7 8 9 12 9 4

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a. We used the Employee Scheduling method in the text to schedule accountants. Tie-breaking preference was given to S-Su pairs of days off. For each employee, the box represents his or her two off-days.

M T W Th F S Su Accountant 11 7 8 9 12 9 4 1 10 6 7 8 11 9 4 2 9 5 6 7 10 9 4 3 8 5 6 6 9 8 3 4 7 4 5 5 8 8 3 5 6 4 5 4 7 7 2 6 6 3 4 3 6 6 2 7 5 3 4 2 5 5 1 8 4 2 3 1 4 5 1 9 3 1 3 1 3 4 0 10 3 0 2 0 2 3 0 11 2 0 1 0 2 2 0 12 1 0 1 0 1 1 0 13 0 0 0 0 0 1 0 14

This schedule calls for 14 accountants.

b. Three part-time accountants working on the “X” days, as shown following, could be effectively used to replace the three full-time accountants numbered 12 through 14.

M T W Th F S Su Accountant

X off off off X X off PT1

X off X off X off off PT2

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12. Return to Problem 1. We use the same method except now the requirement is to have four consecutive days off. The “boxed” days are the off-days in the schedule below.

Employee M T W Th F S Su 1 6 3 5 3 7 2 3 2 6 3 4 2 6 2 3 3 5 2 3 2 6 2 3 4 5 2 2 1 5 2 3 5 4 1 1 1 5 2 3 6 4 1 1 1 4 1 3 7 4 1 1 1 3 0 2 8 3 0 1 1 3 0 1 9 3 0 0 0 2 0 1 10 2 0 0 0 2 0 0 11 1 0 0 0 2 0 0 12 1 0 0 0 1 0 0 13 0 0 0 0 1 0 0

It will take 13 employees to cover this set of requirements on a part-time basis. If the requirement of 4 consecutive days off could be adjusted for several employees, the number of required employees could be significantly reduced.

M T W Th F S Su

On-duty employees 6 4 7 4 7 5 6

Slack 0 1 2 1 0 3 3

13. Standard Components

Shop Time Slack per

Work Time Due Date Remaining Operations Slack Remaining Critical

Job (days) (days) (days) Remaining (days) Operation Ratio

1 1.25 6 2.5 5 3.5 0.700 2.40 2 2.75 5 3.5 7 1.5 0.214 1.43 3 2.50 7 4.0 9 3.0 0.333 1.75 4 3.00 6 4.5 12 1.5 0.125 1.33 5 2.50 5 3.0 8 2.0 0.250 1.67 6 1.75 8 2.5 6 5.5 0.917 3.20 7 2.25 7 3.0 9 4.0 0.444 2.33 8 2.00 5 2.5 3 2.5 0.833 2.00

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Rule Sequence

FCFS 1 2 3 4 5 6 7 8

Due date 6 5 7 6 5 8 7 5

Completion 1.25 4.00 6.50 9.50 12.00 13.75 16.00 18.00 Days past due 0 0 0 3.50 7.00 5.75 9.00 13.00

SPT 1 6 8 7 3 5 2 4

Due date 6 8 5 7 7 5 5 6

Completion 1.25 3.00 5.00 7.25 9.75 12.25 15.00 18.00 Days past due 0 0 0 0.25 2.75 7.25 10.00 12.00

EDD 2 5 8 1 4 3 7 6

Due date 5 5 5 6 6 7 7 8

Completion 2.75 5.25 7.25 8.50 11.50 14.00 16.25 18.00 Days past due 0 0.25 2.25 2.50 5.50 7.00 9.25 10.00

S/RO 4 2 5 3 7 1 8 6

Due date 6 5 5 7 7 6 5 8

CR 4 2 5 3 8 7 1 6

Due date 6 5 5 7 5 7 6 8

a. Relative performance. The following table shows that FCFS and SPT result in the lowest proportion of past jobs completed. SPT results in the lowest average past due, whereas EDD results in the lowest level of maximum past due.

Rule % of Jobs

Past Due Average Past Due (days) Maximum Past Due (days)

FCFS 62.5% 4.781 13.00

SPT 62.5% 4.031 12.00

EDD 87.5% 4.594 10.00

S/RO 87.5% 5.406 11.25

CR 87.5% 5.469 10.25

b. All of these rules result in some jobs being past due. If customers can tolerate a small amount of past due but would be very upset and likely to move their business elsewhere if jobs are extremely past due, then SPT would be a good rule to use.

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14. Penultimate Support Systems

Model A B C D

Fabrication 12 24 6 18

Assembly 8 30 12 15

Using Johnson’s rule, the sequence of Models is C–B–D–A.

Fabrication

0 10 20 30 40 50 60 70 80

C B D A Idle

Assembly C Idle B D A

Fabrication Assembly Job Start Finish Start Finish

C 0 6 6 18

B 6 30 30 60

D 30 48 60 75 A 48 60 75 83

The duration of this schedule (83 hours) is longer than can be completed within two 40-hour shifts.

15. Eight jobs processed on three machines

Job 1 2 3 4 5 6 7 8

Machine 1 2 5 2 3 1 2 4 2

Machine 2 4 1 3 5 5 6 2 1

Machine 3 6 4 5 2 3 2 6 2

a. Using SPT for M2, the makespan for the eight jobs is 38 hours.

Sequence 2–8–7–3–1–4–5–6 M1 0 3 6 9 12 15 18 21 24 27 30 33 6 1 7 8 Idle 2 M2 36 39 3 7 8 2 Idle 1 M3 2 am 4 5 6 3 7 2 8 Idle 1 4 5 6 7 am 3 4 5

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b. We can use Johnson’s rule with some modifications. For example, we sum the processing times of M1 and M2 and then sum the processing times of M2 and M3 as follows: Job M1 + M2 M2 + M3 1 6 10 2 6 5 3 5 8 4 8 7 5 6 8 6 8 8 7 6 8 8 3 3

By Johnson’s rule, the revised schedule is 8–3–1–5–7–6–4–2. The Gantt chart is shown following. If we start the M2 schedule at 7:00 A.M., M1 begins at 5:00 A.M. The result is a makespan of 35 hours. Note that Johnson’s rule utilizes M2 better than when SPT was used for scheduling.

M1 0 3 6 9 12 15 18 21 24 27 30 33 2 7 3 Idle 8 M2 36 39 5 1 3 8 Idle 7 M3 2 A.M. 7 A.M. 6 4 2 5 8 7 6 4 6 4 2 1 5 3 1 Idle Idle

16. Two operations scheduled through three machines a. Job schedules using four rules:

i. SPT:

M1 Schedule M2 Schedule

Start Finish Start Finish

Job Time Time Job Time Time

2 0 2 8 0 2 6 2 5 7 2 6 3 5 9 9 6 12 4 9 14 10 12 20 1 14 20 5 20 27

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Arrival Process Job Start Finish Hours Past

Job Time Time Sequence Time Time Early Due

2 2 1 2 2 3 15 — 8 2 10 8 3 13 18 — 6 5 1 6 13 14 15 — 7 6 6 4 14 17 — 1 3 9 7 7 17 23 19 — 9 12 9 10 23 25 15 — 4 14 3 1 25 29 — 16 10 20 2 5 29 33 — 3 1 20 4 3 33 40 — 18 5 27 4 9 40 49 — 1 Total 82 39 Average 8.2 3.9 ii. EDD: M1 Schedule M2 Schedule

Start Finish Start Finish

Job Time Time Job Time Time

1 0 6 8 0 2 4 6 11 10 2 10 2 11 13 7 10 14 3 13 17 9 14 20 6 17 20 5 20 27 M3 Schedule

Arrival Due Job Start Finish Hours Past

Job Time Date Sequence Time Time Early Due

8 2 31 8 2 12 19 — 1 6 13 1 12 16 — 3 10 10 40 4 16 19 — 3 4 11 16 2 19 20 — 2 2 13 18 3 20 27 — 5 7 14 42 6 27 28 1 — 3 17 22 5 28 32 — 2 6 20 29 10 32 34 6 — 9 20 48 7 34 40 2 — 5 27 30 9 40 49 — 1 Total 28 16 Average 2.8 1.6

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476 z PART 3 •Managing Value Chains iii. S/RO:*

M1 Schedule

Start Finish

Job S/RO Job Time Time

1 1.5 1 0 6 2 7.5 4 6 11 3 5.5 3 11 15 4 4.0 2 15 17 5 9.5 5 17 24 6 12.5 6 24 27 M2 Schedule Start Finish

Job S/RO Job Time Time

7 16.0 8 0 2 8 9.5 10 2 10

9 16.5 7 10 14

10 15.0 9 14 20

M3 Schedule

Arrival Job Start Finish Hours Past

Job Time S/RO Sequence Time Time Early Due

8 2 19 8 2 12 19 — 1 6 –3 1 12 16 — 3 10 10 0 4 16 19 — 3 4 11 –3 3 19 26 — 4 7 14 4 2 26 27 — 9 3 15 –4 5 27 31 — 1 2 17 –9 6 31 32 — 3 9 20 –1 7 32 38 4 — 5 24 –1 10 38 40 — — 6 27 –3 9 40 49 — 1 Total 23 24 Average 2.3 2.4

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iv. CR:*

M1 Schedule

Start Finish

Job CR Job Time Time

1 1.3 1 0 6 2 6.0 3 6 10 3 2.0 4 10 15 4 2.0 5 15 22 5 2.7 2 22 24 6 7.3 6 24 27 M2 Schedule Start Finish

Job CR Job Time Time

7 4.2 8 0 2

8 2.6 9 2 8

9 3.2 10 8 16

10 4.0 7 16 20

M3 Schedule

Arrival Job Start Finish Hours Past

Job Time CR Sequence Time Time Early Due

8 2 2.90 8 2 12 19 — 1 6 0.25 1 12 16 — 3 9 8 0.89 4 16 19 — 3 3 10 0.43 3 19 26 — 4 4 15 0.00 2 26 27 — 9 10 16 1.00 5 27 31 — 1 7 20 1.67 6 31 32 — 3 5 22 0.75 7 32 38 4 — 2 24 –8.00 10 38 40 — — 6 27 –2.00 9 40 49 — 1 Total 23 24 Average 2.3 2.4

*_{Note: The S/RO and CR ratios at M3 are calculated each time the machine is available to}

process another job. Only the jobs in queue at that instant are evaluated. The values in the S/RO and CR columns are the values at the time the jobs were selected for processing.

b. EDD minimizes the past due but results in producing product early. If the product will have to be held in inventory and has a high inventory carrying cost, S/RO or CR minimizes early production.

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CASE: FOOD KING

*

A. Synopsis

The Food King case is set in the grocery supermarket industry where competition is severe and profit margins are a very small percentage of revenues. The principal in the case, Marty Moyer, has recently been promoted to the position of store manager at a large, flagship store in Columbia, South Carolina. Competitive positioning of the supermarket chain’s service package has just been revised, and the store has recently adopted a 24-hour-a-day, 7-days-a-week open-door policy. The problem facing Marty is to develop a work schedule for the stocking/bagging employees that will satisfy competitive priorities and, at the same time, control costs.

B. Purpose

This case is designed to expose students to issues pertaining to scheduling workers in a service environment where demand typically exhibits large fluctuations over very short periods of time within a day or even within a shift.

Specific issues the case is meant to illustrate include:

Adjusting capacity to meet demand, given workforce scheduling constraints

concerning:

—Organizational policies —Legal restrictions

—Behavioral/psychological factors —Minimizing cost

Seeing how the scheduling of workers impacts the ability of organizations to meet

competitive priorities.

Receiving enough information concerning demand, work policies, and costs to enable

students to develop a work schedule.

Rotating versus fixed work schedules within the context of meeting behavioral needs

of the younger workers specifically.

Appropriate measures for determining the effectiveness of the resulting schedule with

respect to meeting the competitive priorities of Food King. C. Analysis

The analysis should begin with a discussion of the target market and the accompanying shopper priorities. The issue here is translating customer requirements into organizational competitive priorities. Customer requirements given in the case were:

Cleanliness

Availability

Timely service

Reasonable prices

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These requirements can be associated with the following competitive priorities:

1. Quality: Food King must maintain the quality of the service delivery package, which includes both high-performance design and service delivery process factors. Facilities that are easy to keep clean, don’t look messy and cluttered, and are flexible with respect to changing displays and stocking locations should be designed. Stockers/baggers are the primary labor input in the housekeeping service process. 2. Flexibility: The many aspects of flexibility will impact virtually all of the customer

requirements listed. The facilities must be designed to adapt to changing customer grocery item mixes. The store must keep the shelves stocked with what the customers want. Shelf space allocations, in-store displays, and the grocery item mix will be constantly changing.

3. Fast and convenient delivery: Perhaps on par with flexibility, the ability to provide fast, convenient service is important. The store recently established a 7-day, 24-hour open policy in response to customer and competitive requirements. Other aspects of fast delivery service include not having to wait at service counters (i.e., meat, deli, or bakery) or at the checkout counters.

4. Low Cost: The grocery store industry traditionally operates on very low profit margins. Customers may be willing to pay some premium for higher quality and faster service, but the issue is how much? This is one of the key trade-offs facing Food King. Stockers and baggers can be added to help meet each of the other competitive priorities, but then overall costs would rise.

Following a discussion of the trade-offs present in establishing the competitive priorities for Food King, students’ attention should be directed to the development of a work schedule for stockers/baggers. This note contains one possible solution in Exhibits TN.1 through TN.7. Also attached is Appendix A, a student solution that contains two methods of approaching the schedule.

The solution in the teaching note is based on the following assumptions:

1. Full-time employees were assigned shifts of eight consecutive hours, each with two consecutive days off.

2. Part-time workers were scheduled in four-hour blocks of time.

3. The number of part-time hours worked could not exceed 50 percent of that of the full-time staff.

4. Standard full-time shifts began at 8 A.M., 4 P.M., and 12 A.M.

5. Maximize the use of full-time employees without creating a large amount of excess capacity.

6. Utilize part-time employees to avoid excess capacity and to lower labor costs.

The solution presented in the exhibits was developed using a modified version of the “minimize total slack capacity” approach outlined in Chapter 17, Scheduling. The differences are that two consecutive four-hour blocks were used to identify the minimum requirement pairs. The work schedule for full-time employees is provided in Exhibit

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TN.1 with the procedure for the traditional shift schedules of 8:00 A.M., 4:00 P.M., and 12:00 A.M. given in Exhibits TN.2, TN.3, and TN.4. Twenty-two full-time stockers/baggers are utilized in this schedule. Eight will work from 8:00 A.M. to 4:00 P.M. with four having Sunday and Monday off and four having Wednesday and Thursday off. Six employees will work from 4:00 P.M. to 12:00 A.M. Two will have Wednesday and Thursday off, two will have Sunday and Monday off, and one will have Tuesday and Wednesday off.

Six employees will work the 12:00 A.M. to 8:00 A.M. shift with three having Saturday and Sunday off. Two employees will have Tuesday and Wednesday off and one will have Thursday and Friday off. The 21st and 22nd full-time employees were determined by creating a special 12:00 P.M. to 8:00 P.M. shift, as seen in Exhibit TN.5.

Exhibit TN.6 represents the remaining requirements after the 22 full-time employees had been scheduled. In order to cover these requirements, 12 part-time employees were scheduled. These workers represent 9.4-20 hour per week part-time employee equivalents. The part-time schedule is provided in Exhibit TN.7. The total costs of this schedule in labor cost dollars is:

22 FT × 40 hrs/wk × $5.25/hr = $4,620

9.4 PT × 20 hrs/wk × $4.50hr = 846

$5,466

Of course there are many other combinations of part-time workers available. The configuration of part-time workers will change depending on the rules of thumb used to assign workers. However, if 22 full-time workers are employed, you need the equivalent of 9.4 part-time workers, each working 20 hours per week. General rules for the configuration in Exhibit TN.7 were to allocate 20 hours per worker when possible; do not allocate more than 8 hours in any one day, and try to spread like time slots across multiple days.

D. Recommendations

Once a schedule similar to the one provided in this note is developed, you can readily test its ability to cover expected demand and calculate the labor costs involved. There are no specified legal restrictions presented in this case, but there are organizational policies to consider with respect to limiting part-time employees to 50 percent of the hours of full-time employees and keeping part-full-time hours to 20 or fewer per employee. The solution presented has 22 full-time and 12 part-time employees scheduled, but some part-time employees work fewer than 20 hours per week. The effective full-time equivalent number of part-time employees is actually 9.4, well below the 50 percent target.

When students are convinced that the schedule meets demand, costs, and organ-izational guidelines, attention usually shifts toward the behavioral and psychological factors associated with the schedule. Therefore, additional recommendations will usually focus on the following issues:

Should employees be rotated through the schedule in some manner to provide more

fairness in days off and shifts?

Are there other ways to assign individual employees to work schedules? Seniority?

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Can employees swap days and shift times on a limited basis?

What would be the impact of utilizing extended shift times, such as 10 hours?

Having weekends off is usually a consideration brought up by the students. In the schedule provided, only three full-time employees have the whole weekend off, and they work the 12:00 A.M. to 8:00 A.M. shifts.

E. Teaching Suggestions

This is a pretty straightforward case that should be assigned as an overnight exercise. The primary focus, of course, is to challenge the student to adapt scheduling methodologies presented in the text in order to develop an acceptable schedule. The discussion should be sectioned into three stages. First, discuss the requirements being placed on the operating system, and make sure the students see how these customer requirements translate into competitive priorities. Second, go right into the development of a work schedule. Ask students to share their schedules and explain the assumptions and rules of thumb they used to arrive at their schedule. It is helpful if you can have at least two schedules presented so comparisons can be made and students can discuss the trade-offs made. Finally, focus the students’ attention on evaluating the schedule with respect to

organizational policies and the behavioral implications of the schedule. It is easy to use an hour to discuss the case issues completely. I try to allocate 15 minutes to discuss the requirements and competitive priorities; 30 minutes to go over at least two different schedules; and 15 minutes to evaluate the schedules and discuss recommendations beyond the specific worker configuration. It is usually a good idea to have the note solution ready if students are reluctant to offer their solutions. However, make sure that they understand that this is not necessarily “the best” solution, just a feasible one. The best depends on the interpretation and prioritization of the trade-offs that are present.

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EXHIBIT TN.1 Full-Time Work Schedule

Shift Time Employee M T W Th F S Su

8A–4P 1 off X X X X X off

8A–4P 2 X X off off X X X

4P–12A 9 X X off off X X X

4P–12A 10 off X X X X X off 4P–12A 11 off off X X X X X 4P–12A 12 X X off off X X X 4P–12A 13 off X X X X X off 4P–12A 14 X off off X X X X 12A–8A 15 X X X X X off off 12A–8A 16 X off off X X X X 12A–8A 17 X X X X X off off 12A–8A 18 X off off X X X X 12A–8A 19 X X X off off X X 12A–8A 20 X X X X X off off

12P–8p 21 X off off X X X X 12P–8P 22 X X off off X X X

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EXHIBIT TN.2 Full-Time 8:00 A.M.–4:00 P.M. Requirements M T W TH F S Su 8A–12P 6 8 5 5 8 15 4 12P–4P 6 8 5 5 10 15 6 8A–12P 6 7 4 4 7 14 4 12P–4P 6 7 4 4 9 14 6 8A–12P 5 6 4 4 6 13 3 12P–4P 5 6 4 4 8 13 5 8A–12P 5 5 3 3 5 12 3 12P–4P 5 5 3 3 7 12 5 8A–12P 4 4 3 3 4 11 2 12P–4P 4 4 3 3 6 11 4 8A–12P 4 3 2 2 3 10 2 12P–4P 4 3 2 2 5 10 4 8A–12P 3 2 2 2 2 9 1 12P–4P 3 2 2 2 4 9 3 8A–12P 3 1 1 1 1 8 1 12P–4P 3 1 1 1 3 8 3 8A–12P 2 0 1 1 0 7 0 12P–4P 2 0 1 1 2 7 2

Note: Bold pairs indicate chosen minimum requirements for each allocation. Pairs represent 8-hour shifts with

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EXHIBIT TN.3 Full-Time 4:00 P.M.–12:00 A.M. Requirements

M T W Th F S Su 4P–8P 5 6 5 5 15 15 6 8P–12A 4 4 4 4 8 6 4 4P–8P 4 5 5 5 14 14 5 8P–12A 3 3 4 4 7 5 3 4P–8P 4 4 4 4 13 13 5 8P–12A 3 2 3 3 6 4 3 4P–8P 4 4 3 3 12 12 4 8P–12A 3 2 2 2 5 3 2 4P–8P 3 3 3 3 11 11 3 8P–12A 2 1 2 2 4 2 1 4P–8P 3 2 2 2 10 10 3 8P–12A 2 0 1 1 3 1 1 4P–8P 2 2 2 1 9 9 2 8P–12A 1 0 1 0 2 0 0

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EXHIBIT TN.4 Full-Time 12:00 A.M.–8:00 A.M. Requirements M T W Th F S Su 12A–4A 4 4 4 4 5 4 4 4A–8A 8 4 4 8 5 4 4 12A–4A 3 3 3 3 4 4 4 4A–8A 7 3 3 7 4 4 4 12A–4A 2 3 3 2 3 3 3 4A–8A 6 3 3 6 3 3 3 12A–4A 1 2 2 1 2 3 3 4A–8A 5 2 2 5 2 3 3 12A–4A 0 2 2 0 1 2 2 4A–8A 4 2 2 4 1 2 2 12A–4A 0 1 1 0 1 1 1 4A–8A 3 1 1 4 1 1 1 12A–4A 0 0 0 0 0 1 1 4A–8A 2 0 0 3 0 1 1

consecutive days off.

EXHIBIT TN.5 Full-Time 12:00 A.M.–8:00 A.M. Requirements

M T W Th F S Su 12P–4P* 2 0 1 1 2 7 2 4P–8P** 2 2 2 1 9 9 2 12P–4P 1 0 1 0 1 6 1 4P–8P 1 2 2 0 8 8 1 12P–4P 0 0 1 0 0 5 0 4P–8P 0 1 2 0 7 7 0

* _{From Exhibit TN.2 last row of 12}_P_._M_.–4_P_._M_. **_{From Exhibit TN.3 last row of 4}_P_._M_.–8_P_._M_.

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EXHIBIT TN.6 Remaining Part-Time Employee Requirements

M T W Th F S Su 8A–12P 2 0 1 1 0 7 0 12P–4P 0 0 1 0 0 5 0 4P–8P 0 1 2 0 7 7 0 8P–12A 1 0 1 0 2 0 0 12A–4A 0 0 0 0 0 1 1 4A–8A 2 0 0 3 0 1 1

Note: This matrix represents the requirements that remain after the full-time employees were scheduled. They are

transcribed from the last row of requirements from Exhibits TN.2, TN.3, TN.4, and TN.5.

EXHIBIT TN.7 Part-Time Employee Work Schedule

M T W TH F S SU

PT–1 (20 hr) 8A–12P 8A–12P 8A–12P 8A–4P

PT–2 (20 hr) 4P–8p 4P–8P 4P–12A 4P–8P

PT–3 (20 hr) 8p–12A 8P–12A 4P–12A 4P–8P

PT–4 (20 hr) 4A–8A 12A–8A 12A–8A

PT–5 (20 hr) 4A–12P 4P–8P 8A–4P

PT–6 (20 hr) 4A–8A 4A–8A 4P–8A 8A–4P

PT–7 (20 hr) 12P–4P 4A–8A 4P–8P 12P–8P PT–8 (16 hrs) 4P–8P 4P–8P 8A–4P PT–9 (12 hrs) 4P–8P 8A–12P 4P–8P PT–10 (8 hrs) 8A–12P 4P–8P PT–11 (8 hrs) 8A–12P 4P–8P PT–12 (4 hrs) _____ _____ _____ _____ _____ 4P–8P _____ Total 5 1 5 4 9 21 2 number of four-hour shifts

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APPENDIX A Student Solutions

A. Food King—Scheduling

Two methods were used to determine the schedule. Both methods required the full-time employees to be given two consecutive days off. In addition, standard start times with 8-hour shifts were used whenever possible.

Method 1 results are provided as Attachment 1. For this method, workers were

assigned in a way that emphasized three standard shifts: (Tue-Sat at 8 A.M., 4 P.M., and 12 A.M.). Other shifts were used as required to balance workers.

Method 2 results are provided as Attachment 2. For this method, workers were assigned in a way that minimized slack, as defined in the text. Days off were selected one worker at a time, based on the minimum capacity (employee) requirements. The pair of 4-hour blocks selected was based on the maximum number of workers required for two consecutive blocks. These rules were modified as required to balance the number of workers.

Additional information concerning trade-offs and priorities:

Excess full-time workers were not used with either method. With this restriction, the

fraction of part-time employees slightly exceeded 50 percent for Method 1.

Food King likely requires additional full-time workers because the part-time worker

head count was based on 20-hour workweeks.

Method 2 does a better job of minimizing part-time workers during peak stocking

hours. For both methods, the use of part-time workers is maximized during peak bagging hours as much as possible.

Options to allow more fairness in the schedule:

Food King should cycle individual worker schedules once a month or so. Workers should be allowed to swap 4-hour schedule blocks.

A method should be developed to allow weekends off on a rotating basis.

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ATTACHMENT 1: FOOD KING

Stocking/bagging personnel required

Mon Tue Wed Thur Fri Sat Sun Total

8:00 A.M. 6 8 5 5 8 15 4 51 12:00 P.M. 6 8 5 5 10 15 6 55 4:00 P.M. 5 6 5 5 15 15 6 57 8:00 P.M. 4 4 4 4 8 6 4 34 12:00 A.M. 4 4 4 4 5 4 4 29 4:00 A.M. 8 4 4 8 5 4 4 37 33 34 27 31 51 59 28 263 Full-time personnel

8:00 A.M. 4 5 4 5 6 7 4 35 12:00 P.M. 5 7 4 5 9 9 6 45 4:00 P.M. 4 6 4 5 8 8 5 40 8:00 P.M. 3 4 3 4 6 6 3 29 12:00 A.M. 3 4 3 4 4 4 3 25 FT 4:00 A.M. 3 4 4 5 3 4 3 26 emps 22 30 22 28 36 38 24 200 20 Part-time personnel

8:00 A.M. 2 3 1 0 2 8 0 16 12:00 P.M. 1 1 1 0 1 6 0 10 4:00 P.M. 1 0 1 0 7 7 1 17 8:00 P.M. 1 0 1 0 2 0 1 5 12:00 A.M. 1 0 1 0 1 0 1 4 PT 4:00 A.M. 5 0 0 3 2 0 1 11 emps 11 4 5 3 15 21 4 63 12.6

Hours\Days Tu–Sa We–Su Th–Mo Fr–Tu Sa–We Su–Th

8:00 A.M.–4:00 P.M. 3 1 1 12:00 P.M.–8:00 P.M. 1 3 4:00 P.M.–12:00 A.M. 3 1 8:00 P.M.–4:00 A.M. 1 1 Full–time 12:00 A.M.–8:00 A.M. 2 1 employees 4:00 A.M.–12:00 A.M. 1 1 20

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ATTACHMENT 2: FOOD KING

Stocking/bagging personnel required

8:00 A.M. 6 8 5 5 8 15 4 51 12:00 P.M. 6 8 5 5 10 15 6 55 4:00 P.M. 5 6 5 5 15 15 6 57 8:00 P.M. 4 4 4 4 8 6 4 34 12:00 A.M. 4 4 4 4 5 4 4 29 4:00 A.M. 8 4 4 8 5 4 4 37 33 34 27 31 51 59 28 263 Full-time personnel

Mon Tue Wed Thur Fri Sat Sun Total

8:00 A.M. 4 8 4 5 8 8 4 41 12:00 P.M. 5 8 4 5 9 10 5 46 4:00 P.M. 5 6 3 5 8 8 5 40 8:00 P.M. 4 4 2 4 6 6 4 30 12:00 A.M. 4 4 2 3 4 4 4 25 FT 4:00 A.M. 4 4 3 4 5 4 4 28 emps 26 34 18 26 40 40 26 210 21 Part-time personnel

8:00 A.M. 2 0 1 0 0 7 0 10 12:00 P.M. 1 0 1 0 1 5 1 9 4:00 P.M. 0 0 2 0 7 7 1 17 8:00 P.M. 0 0 2 0 2 0 0 4 12:00 A.M. 0 0 2 1 1 0 0 4 PT 4:00 A.M. 4 0 1 4 0 0 0 9 emps 7 0 9 5 11 19 2 53 10.6

Hours/Days Mo–Fr Tu–Sa We–Su Th–Mo Fr–Tu Sa–We Su–Th

8:00 A.M.–4:00 P.M. 2 1 12:00 P.M.–8:00 P.M 2 1 3 4:00 P.M.–12:00 A.M. 1 1 8:00 P.M.–4:00 A.M. 1 1 2 Full-time employees 12:00 A.M.–8:00 A.M. 1 21 4:00 A.M.–12:00 A.M. 2 1 2