1. An Integrated Goods and Services Approach
OPERATIONS MANAGEMENT
An Integrated Goods and Services Approach
CHAPTER 14
Scheduling Models and Applications
JAMES R. EVANS
AND
DAVID A. COLLIER
Operations Management/Ch. 14 Scheduling Models and Applications
©2007 Thomson South-Western

2. Chapter 14 Learning Objectives
To identify characteristics of scheduling at different organizational planning levels, and describe the application of computers to scheduling problems.
To become acquainted with different types of scheduling approaches in MRP systems, staff assignments, and appointment systems.

3. Chapter 14 Learning Objectives
To apply basic sequencing rules to develop schedules that meet important operations performance criteria.
To learn and apply specific sequencing methods to specific problem structures.
To explain the need for monitoring and controlling schedules using a Gantt chart, and list reasons why planned schedules do not always achieve their intended results.

4. Chapter 14 Scheduling Models and Applications
This chapter addresses key issues and methods for
scheduling and sequencing in manufacturing and
service organizations.
Scheduling refers to the assignment of start and completion times to particular jobs, people, or equipment.
Sequencing refers to determining the order in which jobs or tasks are processed.

5. Chapter 14 Scheduling Models and Applications
Scheduling and sequencing are fundamental to all three levels of aggregation and disaggregation planning.
Level 3 decisions (explained in Chapter 13 and Exhibit 14.1) require detailed resource (trucks, labor, equipment, computers, and jobs) scheduling, sequencing, and day-to-day execution.

6. Exhibit 14.1
Scheduling in the Three levels of Aggregate and Disaggregate Planning

7. Exhibit 14.2
Portion of American League Umpire Schedule
One example of scheduling is telling umpires where to go in the American Baseball League. Critical factors in developing these schedules were to ensure that umpire crews were not assigned to consecutive series with the same team, that a team was balanced over the season, and that travel sequences were realistic. Samples of the schedule developed are shown below and in the next slide.

8. Exhibit 14.3
A Portion of a Typical Umpire Crew Schedule (Crew 6 in Exhibit “H” denotes an assignment with the team at home; the visiting team is denoted by “X”)

9. Chapter 14 Scheduling Models and Applications
Computer-Based Scheduling
The complexity of many business situations dictates that effective scheduling systems be computerized.
Computer-based scheduling systems can perform three major tasks: schedule generation, schedule evaluation, and automated scheduling.
Computer-generated schedules and the sharing of production, purchasing, inventory, delivery, and customer information among suppliers and buyers in the supply chain enables faster service at lower cost.

10. Chapter 14 Scheduling Models and Applications
Scheduling in Supply Chains
The complexity of many business situations dictates that effective scheduling systems be computerized.
Scheduling and information exchange are at the heart of managing an efficient and responsive supply chain because the network of processes need to be synchronized.
Computer-generated schedules and the sharing of production, purchasing, inventory, delivery, and customer information among suppliers and buyers in the supply chain enables faster service at lower cost.

11. Chapter 14 Scheduling Models and Applications
Scheduling in MRP Systems
Materials requirement planning and scheduling paves the way for sequencing decisions about specific job schedules and sequences.
Planned order releases create an important “forward looking” level 2 schedule for all subassemblies, component parts, and raw materials.
Schedule information is used by capacity requirements planning to determine workloads for key work centers and plays a critical role in purchasing materials and scheduling employees and work shifts.

12. Exhibit 14.4
Example MRP Record (Level 2 Planned Schedule)
Planned order releases (PORs) create an important “forward looking” level 2 schedule for all subassemblies, component parts, and raw materials. Also see Exhibit in next slide.

13. Exhibit 13.13
Disaggregation Framework for Manufacturing Plans and Schedules

14. Chapter 14 Scheduling Models and Applications
Staff Scheduling
Staff scheduling attempts to match available personnel with the needs of the organization (customer/client demand) by:
Accurately forecasting demand and translating it into the quantity and timing of work to be done,
Determining the staffing required to perform the work by time period,
Determining the personnel available and full- and part-time mix,
Matching capacity demand requirements and developing a work schedule that maximizes service and minimizes costs.

15. Scheduling Procedure for T.R. Accounting Service
Exhibit 14.5
Scheduling Procedure for T.R. Accounting Service
T. R. Accounting Service is developing a workforce schedule for three weeks from now and has forecast demand and translated them into the following minimum personnel requirements for the week.
Day Mon Tue Wed Thur Fri Sat Sun
Min Personnel

16. Exhibit 14.6
Final T. R. Accountant Schedule

17. Chapter 14 Scheduling Models and Applications
Appointment Systems
From an operations’ perspective, appointments can be viewed as a reservation for service time and capacity.
Four decisions to make regarding designing an appointment system are the following:
Determine the appointment time intervals,
Determine the length of each workday and time off-duty,
Decide how to handle overbooking, and
Develop customer appointment rules that maximize customer satisfaction.

18. Chapter 14 Scheduling Models and Applications
Appointment Systems
From an operations’ perspective, appointments can be viewed as a reservation for service time and capacity.
Given the perishable nature of professional service-provider time and the potential loss of revenue, most service providers overbook.
Example: If you book a dentist appointment and do not reschedule and do not show up, the dentist may lose the revenue he/she could make forever.
Appointment systems are critical to maximizing revenue and minimizing idle time.

19. Chapter 14 Scheduling Models and Applications
Sequencing
Sequencing is required when several activities must be processed using a common resource.
Example: An insurance claims analyst needs to process 25 customer medical claims on a computer (the resource). What claims should be processed first, second, -- last to maximize customer satisfaction or minimize average claim lateness?

20. Chapter 14 Scheduling Models and Applications
Sequencing
Flow time is the amount of time a job spent in the shop or factory. Flow time is computed as follows:
Fi = ∑pij + ∑wij = Ci - Ri

21. Chapter 14 Scheduling Models and Applications
Sequencing
Makespan is the time needed to process a given set of jobs; a short makespan aims to achieve high equipment utilization.
M = C - S [14.2]
where
M = makespan of a group of jobs,
C = completion time of last job i in the group,
S = start time of first job i in the group.

22. Chapter 14 Scheduling Models and Applications
Sequencing
Lateness and tardiness measure performance related to customer-focused due-date criteria.
Lateness is the difference between the completion time and the due date (either positive or negative).
Tardiness is the amount of time by which the completion time exceeds the due date. (Tardiness is defined as zero if the job is completed before the due date, and therefore no credit is given for completing a job early).
Li = Ci - Di [14.3]
Ti = Max (0, Li) [14.4]
where Li = lateness of job i
Ti = tardiness of job i
Di = due date of job i.

23. Chapter 14 Scheduling Models and Applications
Sequencing
The two most popular sequencing rules for prioritizing jobs are:
Shortest Processing Time (SPT)
With different processing times, SPT sequencing maximizes workstation utilization and minimizes average job flow time.
Earliest Due Date (EDD)
Using Earliest Due Date (EDD), the maximum job tardiness and lateness are minimized.

24. Chapter 14 Scheduling Models and Applications
Sequencing
The critical ratio is the time remaining until the due date divided by the number of days required to complete the job.
Critical Ratio (CR) = Due Date - Current Date [13.5]
Total Processing Time Remaining
The total processing time remaining includes run, changeover/setup, transport, and waiting times.
CR uses two criteria--the customer's due date, and external performance measure, and the total processing time remaining, an internal measure.
One could think of the numerator as a marketing driven performance metric and the denominator as an operation focused metric.

25. Computing Critical Ratios
Exhibit 7.7
Exhibit 14.7
Valuation Client Information for VMPE, Inc.
Computing Critical Ratios

26. Chapter 14 Scheduling Models and Applications
Single-Resource Sequencing Problem
In a serial manufacturing process, a bottleneck workstation controls the output of the entire process. Therefore, it is critical to schedule it efficiently.
With different processing times, SPT sequencing maximizes workstation utilization and minimizes average job flow time.
When processing times are relatively equal, first-come-first-serve sequencing is applied.
Using Earliest Due Date (EDD), the maximum job tardiness and lateness are minimized.

27. Exhibit 14.8
Comparison of Three Ways (By-the Numbers, SPT & EDD) to Sequence the Five Jobs

28. Chapter 14 Scheduling Models and Applications
Sequencing
The two most popular sequencing rules for prioritizing jobs are:
Shortest Processing Time (SPT)
With different processing times, SPT sequencing maximizes workstation utilization and minimizes average job flow time.
Earliest Due Date (EDD)
Using Earliest Due Date (EDD), the maximum job tardiness and lateness are minimized.

29. Chapter 14 Scheduling Models and Applications
Two-Resource Sequencing Problem (often called Johnson’s Rule)
In the following example, we assume that each job must be processed first on Resource #1 and then on Resource #2.
Hirsch Products manufactures custom parts that first require a shearing operation and then a punch-press operation. Order information is provided below.
Job
Shear (days)
Punch (days) 1 4 5 2 3 10 6

30. Exhibit 14.9
Gantt Two-Resource Job Sequence Chart for Hirsch Product Sequence By-the-Numbers Rule
If jobs are completed by order number, the punch press oftentimes experiences idle time awaiting the next job as shown below (Exhibit 14.9). The makespan is 37 days.

31. Exhibit 14.10
Gantt Two-Resource Job Sequence Chart for Hirsch Product Sequence Using Johnson’s Rule
Johnson’s Rule results in a reduction in makespan from 37 days to 27 days, as shown in the Gantt chart below in Exhibit So, smart scheduling is important for customer service and process efficiency!

32. Chapter 14 Scheduling Models and Applications
Dispatching and Simulation-Based Sequencing
Real-life sequencing problems in job shops are often too large and complex to find optimal solutions, except for some special cases like the single- or two-resource problems previously described.
Simulation-based approaches apply one or more dispatching rules to rank the order of jobs waiting to be processed at a machine in order to use available capacity effectively.
Dispatching is the process of selecting jobs for processing and authorizing the work to be done.

33. Exhibit 14.11
Job Data for Lynwood Manufacturing
In the example of Lynwood Manufacturing, the characteristics of four jobs are specified through analysis of historical data. The data of these four jobs is used as the basis for the simulation.

34. This illustrates the status of the shop at any point in time.
Exhibit 14.12
Status of Lynwood Job Shop at Any Point in Time
This illustrates the status of the shop at any point in time.

35. Exhibit 14.13
Flowchart for Simulating Lynwood Manufacturing Job Shop
The flowchart helps to simulate the behavior of the Lynwood Manufacturing job shop over time.

36. Exhibit 14.14
Status of Lynwood Job Shop at Time 0
The simulation begins at T = 0 and the least-work-remaining rule is used to schedule jobs. At time 0, Jobs 1 and 2 arrive. Job 1 is assigned to the lathe and Job 2 is assigned to the drill press.

37. Exhibit 14.15
Status of Lynwood Job Shop of Time 10
At T = 10, Job 1 is finished on the lathe and Job 2 is still on the drill press. Therefore, Job 1 must wait.

38. Exhibit 14.16
Status of Lynwood Job Shop at Time 20
Nothing happens at T = 20. Job 1 is still waiting for the completion of Job 2 on the drill press. Job 3 arrives and joins the queue at the drill press.

39. Exhibit 14.17
Status of Lynwood Job Shop at Time 25
At T = 25, Job 2 is completed at the drill press. Job 3 is scheduled next because it has a smaller total remaining processing time.

40. Exhibit 14.18
Simulation of Lynwood Job Shop over Time
This is the final simulation of the shop over time, until all four jobs are completed.

41. Exhibit 14.19
Gantt Chart for Lynwood Job Shop Using Least-Remaining-Work Rule
The Gantt Chart shows the results of the scheduling process.

42. Exhibit 14.20
Simulation Results for Lynwood Job Shop Using Least-Remaining-Work Rule
A summary of machine utilization and job waiting time are used as measures for comparing various dispatching rules. Simulations give the user an idea of where bottlenecks might occur or where more capacity is needed.

43. Chapter 14 Scheduling Models and Applications
Batch Production Sequencing and Scheduling
This problem structure highlights the issues involved in sequencing different manufactured goods on common facilities.
The decisions faced by managers of such production systems are (1) how much to produce in each batch and (2) the sequence, or order, in which the batches are to be produced.
The batch quantity and frequency of production affect inventory levels and setup costs.
One technique commonly used is scheduling by run out time. This is illustrated with the following example.

44. Exhibit 14.21
Lot Size and Demand Data for Five Manufactured Product Sizes
The lot sizes and demand data for a consumer-products company that produces five sizes of a laundry soap at one plant are detailed below. Let’s use the run out time method to do the scheduling/sequencing.

45. Exhibit 14.22
Run Out Time for Five Manufactured Product Sizes
The run out time (R) for a product is defined as:
R = Inventory Level/Demand Rate
Run out times in the laundry soap example are calculated for each product size. The smallest run out time is produced first, that is, the medium size with a run out time of 2.4 weeks.

46. Exhibit 14.23
Updated Inventory for Five Manufactured Product Sizes

47. Exhibit 14.24
New Run Out Times Based on Updated Inventory
With the new inventory levels, updated run out times are computed and the next product size to run is selected based on the smallest run time, in this case, the giant size.
Using smallest run out time, scheduling is planned in response to current inventory levels and anticipated demand—a more dynamic approach.

48. Chapter 14 Scheduling Models and Applications
Schedule Monitoring and Control
The scheduling process must be monitored on a continuing basis to track changes in the status of orders, input materials, inventory changes, labor turnover, and sales commitments. Reschedules are a normal part of scheduling and sequencing.
Short-term capacity fluctuations also necessitate changes in schedules and sequences.
Gantt charts are useful tools for monitoring schedules. Exhibit (next slide) shows a Gantt chart for a variety of jobs. This helps to track jobs that are behind, on, or ahead of schedule.

49. Exhibit 14.25
Gantt Chart Example for Monitoring Schedule Progress

50. Exhibit 14.26
Chapter 14 Solved Problem # 1
Five tax analysis jobs are waiting to be processed by Martha at T.R. Accounting Service. Use the shortest processing time (SPT) and earliest due date (EDD) sequencing rules to sequence the jobs. Compute the flow time, tardiness, and lateness for each job, and the average flow time, average tardiness, and average lateness for all jobs. Which rule do you recommend? Why?
Job Processing Time (days) Due Date

51. Exhibit 14.26
Chapter 14 Solved Problem # 1
Solution
The SPT sequence is
Due Lateness Tardiness
Job Flow (Fi) Date (Di) (Li) (Max (0, Li) =
5 + 5 = = =
Average

52. Chapter 14 Solved Problem # 1
Exhibit 14.26
Chapter 14 Solved Problem # 1
Solution
The EDD sequence is
Due Date Lateness Tardiness
Job Flow (Fi) (Di) (Li = Ci - Di) (Max (0, Li) = = = =
Average
Given the nature of the data this is not an easy decision. The SPT rule minimizes average flow time and average lateness but Job 5 is extremely late by 12 days. The EDD rule minimizes the maximum job tardiness and lateness. Jobs 1 and 5 are tardy by 6 days. If Job 5 is a big client with significant revenue potential then the EDD rule is probably best.

53. Chapter 14 Solved Problem # 2
Exhibit 14.26
Chapter 14 Solved Problem # 2
A manufacturing process involving machined components consists of two operations done on two different machines. The status of the queue the beginning of a particular week is as follows.
Scheduled Schedule
Time on Time on
Machine 1 Machine 2
Job Number of (min. per (min. per
Number Components piece) piece) J J J J J J
The processing on Machine 2 must follow processing on Machine 1. Schedule these jobs to minimize the makespan. Illustrate the schedule you arrive at with a bar chart.

54. Exhibit 14.26
Chapter 14 Solved Problem # 2
Solution
Because this is a two-machine flowshop problem, Johnson’s rule is applicable.
Total time in minutes on each machine is the product of the number of components and the unit times as shown below.
Job Machine Machine 2 J J J J J J

55. Chapter 14 Solved Problem # 2
Exhibit 14.26
Chapter 14 Solved Problem # 2
176
185
101
184
213
201
Machine 1
Machine 2
Minutes

56. Exhibit 14.26
Chapter 14 Solved Problem # 3
A detergent manufacturer uses a single facility for filling and packaging all four of its products. If the run out time method is used for scheduling this activity, how would the activity be scheduled in the first 2 weeks?

57. Chapter 14 Solved Problem #3
Solution
The initial solution is as follows:
Product Inventory Demand Run out Time
1 10,000 5, Schedule first
2 12,000 4, weeks
3 15,000 3,
4 6,000 1,
Since the economic lot size for item 1 (brand A, size A) is 10,000, that is, half of one week’s run, the next decision arises after one-half week. Thus, at time = 0.5 week, we have:
1 17,500 5, weeks
2 10,000 4,
3 13,500 3,
4 5,500 1,
Schedule product 2, which takes one week. Note that the inventory for product 1, 17,500, is computed as 10,000 = .5(5000) + 10,000. Schedule the next product at time = 1.5 weeks.

58. Chapter 14 Solved Problem #3
Solution
Product Inventory Demand Run out Time
1 12,500 5, weeks
2 11,000 4,
3 10,500 3,
4 4, ,
Schedule product 1, which takes 0.5 week. This takes us through the first two weeks.

59. Exhibit 14.26
Chapter 14 Solved Problem # 3
A detergent manufacturer uses a single facility for filling and packaging all four of its products. If the run out time method is used for scheduling this activity, how would the activity be scheduled in the first 2 weeks?
Solution: Product 1 has the smallest run out time, so it should be scheduled first (1/2 week). Next, Product 2 is scheduled (1 week). Product 1 should be scheduled again, as it has the smallest run out time after production of Product 2.

60. Exhibit 14.27
Case: Hickory Bank Actual Number of Customer Arrivals for Paris Branch Bank

61. Exhibit 14.28
Product Routing, Stephens Industries Case