Scheduling Chapter 16
How Scheduling fits the Operations Management Philosophy Operations As a Competitive Weapon Operations Strategy Project Management Process Strategy Process Analysis Process Performance and Quality Constraint Management Process Layout Lean Systems Supply Chain Strategy Location Inventory Management Forecasting Sales and Operations Planning Resource Planning Scheduling
Air New Zealand • Flight and crew scheduling is a complex process. • Scheduling begins with a five-year market plan. • This general plan is further refined to a three-year plan, and put into an annual budget in which flight segments have specific departure and arrival times. • Crew availability must be matched to the flight schedule. Two types of crews–pilots and attendants–each comes with its own set of constraints. • Sophisticated optimization models are used to design generic minimum-cost schedules.
Scheduling • Scheduling: The allocation of resources over time to accomplish specific tasks. • Demand scheduling: A type of scheduling whereby customers are assigned to a definite time for order fulfillment. • Workforce scheduling: A type of scheduling that determines when employees work. • Operations scheduling: A type of scheduling in which jobs are assigned to workstations or employees are assigned to jobs for specified time periods.
Performance Measures • Job flow time: The amount of time a job spends in the service or manufacturing system. Also referred to as throughput time or time spent in the system, including service. • Makespan: The total amount of time required to complete a group of jobs. • Past due (Tardiness): The amount of time by which a job missed its due date or the percentage of total jobs processed over some period of time that missed their due dates. • Work-in-process (WIP) inventory: Any job that is waiting in line, moving from one operation to the next, being delayed, being processed, or residing in a semi-finished state. • Total inventory: The sum of scheduled receipts and on-hand inventories. • Utilization: The percentage of work time that is productively spent by an employee or machine.
Gantt Charts • Gantt chart: Used as a tool to monitor the progress of work and to view the load on workstations. • The chart takes two basic forms: (1) the job or activity progress chart, and (2) the workstation chart. • The Gantt progress chart graphically displays the current status of each job or activity relative to its scheduled completion date. • The Gantt workstation chart shows the load on the workstations and the nonproductive time.
Start activity Scheduled activity time Current date Finish activity Actual progress Nonproductive time Job 4/17 4/18 4/19 4/20 4/21 4/22 4/23 4/24 4/25 4/26 Ford Plymouth Pontiac Gantt Progress Chart Gantt Progress Chart for an Auto Parts Company
Gantt Workstation Chart Gantt Workstation Chart for Hospital Operating Rooms
Scheduling Customer Demand • Three methods are commonly used to schedule customer demand: • Appointments assign specific times for service to customers. • Reservations are used when the customer actually occupies or uses facilities associated with the service. • Backlogs: • The customer is given a due date for the fulfillment a product order, or • Allow a backlog to develop as customers arrive at the system. Customers may never know exactly when their orders will be fulfilled
Scheduling Employees • Rotating schedule: A schedule that rotates employees through a series of workdays or hours. • Fixed schedule: A schedule that calls for each employee to work the same days and hours each week. • Constraints: The technical constraints imposed on the workforce schedule are the resources provided by the staffing plan and the requirements placed on the operating system. • Other constraints, including legal and behavioral considerations, also can be imposed.
Required employees Day M T W Th F S Su Number of employees 6 4 8 9 10 3 2 Workforce Scheduling Example 16.1 The Amalgamated Parcel Service is open 7 days a week. The schedule of requirements is: The manager needs a workforce schedule that provides two consecutive days off and minimizes the amount of total slack capacity. To break ties in the selection of off days, the scheduler gives preference to Saturday and Sunday if it is one of the tied pairs. If not, she selects one of the tied pairs arbitrarily.
Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Workforce Scheduling Example 16.1Steps 1 & 2 Required employees Step 1. Find all the pairs of consecutive days that exclude the maximum daily requirements. Select the unique pair that has the lowest total requirements for the 2 days. Friday contains the maximum requirements (10), and the pair S–Su has the lowest total requirements. Therefore, Employee 1 is scheduled to work Monday through Friday. Step 2. If a tie occurs, choose one of the tied pairs or ask the employee to make a choice.
Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirements 5 3 7 8 9* 3 2 Employee 2 X X X X X Workforce Scheduling Example 16.1Step 3 Required employees Step 3. Subtract the requirements satisfied by the Employee 1 from the net requirements for each day the employee is to work and repeat step one. Again the pair S–Su has the lowest total requirements. Therefore, Employee 2 is scheduled to work Monday through Friday.
Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirement 5 3 7 8 9* 3 2 Employee 2 X X X X X Requirement 4 2 6 7 8* 3 2 Employee 3 X X X X X Requirement 3 1 5 6 7* 3 2 Workforce Scheduling Example 16.1Step 4 Required employees Step 4. Repeat steps 1 through 3 until all the requirements have been satisfied. After Employees 1, 2, and 3 have reduced the requirements, the pair with the lowest requirements changes, and Employee 4 will be scheduled for Wednesday through Sunday.
Required employees Day M T W Th F S Su Number of employees 6 4 8 9 10* 3 2 Employee 1 X X X X X Requirement 5 3 7 8 9* 3 2 Employee 2 X X X X X Requirement 4 2 6 7 8* 3 2 Employee 3 X X X X X Requirement 3 1 5 6 7* 3 2 Employee 4 X X X X X Requirement 3 1 4 5 6* 21 Employee 5 X X X X X Workforce Scheduling Example 16.1 Step 4continued
Required employees Day M T W Th F S Su Requirement 2 0 3 4 5* 2 1 Employee 6 X X X X X Requirement 2 0 2 3 4* 1 0 Employee 7 X X X X X Requirement 1 0 1 2 3* 1 0 Employee 8 X X X X X Requirement 0 0 0 1 2* 1 0 Employee 9 X X X X X Requirement 0 0 0 0 1* 0 0 Employee 10 X X X X X Workforce Scheduling Example 16.1Step 4continued
Final Schedule Day M T W Th F S Su Employee 1 X X X X X off off Employee 2 X X X X X off off Employee 3 X X X X X off off Employee 4 off off X X X X X Employee 5 X X X X X off off Employee 6 off off X X X X X Employee 7 X X X X X off off Employee 8 X X X X X off off Employee 9 off X X X X X off Employee 10 X X X X X off off Workforce Scheduling Example 16.1
Final Schedule Total Capacity, C 7 8 10 10 10 3 2 50 Requirements, R 6 4 8 9 10 3 2 42 Slack, C – R 1 4 2 1 0 0 0 8 Workforce Scheduling Example 16.1Final Schedule M T W Th F S Su Employee 1 X X X X X off off Employee 2 X X X X X off off Employee 3 X X X X X off off Employee 4 off off X X X X X Employee 5 X X X X X off off Employee 6 off off X X X X X Employee 7 X X X X X off off Employee 8 X X X X X off off Employee 9 off X X X X X off Employee 10 X X X X X off off
Operations Scheduling • Operations schedules are short-term plans designed to implement the master production schedule. • Operations scheduling focuses on how best to use existing capacity. • Often, several jobs must be processed at one or more workstations. Typically, a variety of tasks can be performed at each workstation. • Job shop: A firm that specializes in low- to medium-volume production and utilizes job or batch processes. • Flow shop: A firm that specializes in medium- to high-volume production and utilizes line or continuous processes.
Shipping Department Raw Materials Legend: Batch of parts Workstation Manufacturing Process
Job Shop Dispatching • Dispatching: A method of generating schedules in job shops whereby the decision about which job to process next is made using simple priority rules whenever the workstation becomes available for further processing. • Priority sequencing rules: The rules that specify the job processing sequence when several jobs are waiting in line at a workstation. • Critical ratio (CR): A ratio that is calculated by dividing the time remaining until a job’s due date by the total shop time remaining for the job. CR =(Due date – Today’s date)/Total shop time remaining • Total Shop Time = Setup, processing, move, and expected waiting times of all remaining operations, including the operation being scheduled.
Job Shop Dispatching • Earliest due date (EDD): A priority sequencing rule that specifies that the job with the earliest due date is the next job to be processed. • First-come, first-served (FCFS): A priority sequencing rule that specifies that the job arriving at the workstation first has the highest priority. • Shortest processing time (SPT): A priority sequencing rule that specifies that the job requiring the shortest processing time is the next job to be processed.
S/RO = ((Due date – Today’s date) – Total shop time remaining) Number of operations remaining Job Shop Dispatching • Slack per remaining operations (S/RO): A priority sequencing rule that determines priority by dividing the slack by the number of operations that remain, including the one being scheduled.
Scheduling Jobs for One Workstation • Single-dimension rules: A set of rules such as FCFS, EDD, and SPT, that bases the priority of a job on a single aspect of the job, such as arrival time at the workstation, the due date, or the processing time. • Priority rules, such as CR and S/RO, incorporate information about the remaining workstations at which the job must be processed. We call these rules multiple-dimension rules. • Multiple-dimension rules: A set of rules that apply to more than one aspect of a job.
Example 16.2 Single-Dimension Rule Sequencing Five engine blocks are waiting for processing. The processing times have been estimated. Expected completion times have been agreed. The table shows the situation as of Monday morning. Customer pickup times are measured in business hours from Monday morning. Determine the schedule by using the EDD rule and then the SPT rule. Calculate the average hours early, hours past due, WIP inventory, and total inventory for each method. If low job flow times and WIP inventories are critical, which rule should be chosen?
Job Scheduled Actual Engine Processing Flow Customer Customer Hours Block Begin Time Time Pickup Pickup Hours Past Sequence Work (hr) (hr) Time Time Early Due Ranger 8 10 Explorer 6 12 Econoline 150 3 18 Bronco 15 20 Thunderbird 12 22 0 + = 8 10 2 8 + = 14 14 2 14 + = 17 18 1 17 + = 32 32 12 32 + = 44 44 22 8 + 14 + 17 + 32 + 44 44 10 + 14 + 18 + 32 + 44 44 Average total inventory = Example 16.2 Single-Dimension Rule – EDD Average job flow time = 23 hours Average hours early = 0.6 hour Average hours past due = 7.2 hours Average WIP = 2.61 blocks Average total inventory = 2.68 engine blocks
Job Scheduled Actual Engine Processing Flow Customer Customer Hours Block Begin Time Time Pickup Pickup Hours Past Sequence Work (hr) (hr) Time Time Early Due Ranger 8 10 Explorer 6 12 Econoline 150 3 18 Bronco 15 20 Thunderbird 12 22 0 + = 31815 8 + = 912 14 + = 171737 17 + = 29297 29 + = 444424 3 + 9 + 17 + 29 + 44 44 18 + 12 + 17 + 20 + 44 44 Average total inventory = Example 16.2 Single-Dimension Rule – SPT 3 6 8 12 15 0 3 9 17 29 18 12 10 22 20 Econoline 150 Explorer Ranger Thunderbird Bronco Average job flow time =20.4 hours Average hours early = 3.6 hour Average hours past due = 7.6 hours Average WIP = 2.32 blocks Average total inventory = 2.73 engine blocks
EDD SPT Average job flow time 23.00 20.40 Average hours early 0.60 3.60 Average hours past due 7.20 7.60 Average WIP 2.61 2.32 Average total inventory 2.68 2.73 Comparing the EDD and SPT Rules Using the previous example, a comparison of the EDD and SPT sequencing is shown below. • The SPT schedule has a lower average job flow time and lower WIP inventory. • The EDD schedule has better customer service, (average hours past due) and lower maximum hours past due. • EDD also has a lower total inventory because fewer hours were spent waiting for customers to pick up their engine blocks after they had been completed.
Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining RemainingCR S/RO 1 2.3 15 10 6.1 2.46 2 10.5 10 2 7.8 1.28 3 6.2 20 12 14.5 1.38 4 15.6 8 5 10.2 .78 Time remaining to due date Shop time remaining CR= Example 16.3 Multiple-Dimension Rule – CR
Operation Time Time at RemainingNumber of Engine to Due DateOperationsShop Time Job Lathe (hr) (Days)RemainingRemaining CR S/RO 1 2.3 15 10 6.1 2.46 0.89 2 10.5 10 2 7.8 1.28 1.10 3 6.2 20 12 14.5 1.38 0.46 4 15.6 8 5 10.2 .78 – 0.44 Time remaining to due date – Shop time remaining Number of operations remaining S/RO = Example 16.3 Multiple-Dimension Rule – S/RO
Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining Remaining CRS/RO 1 2.3 15 10 6.1 2.46 0.89 2 10.5 10 2 7.8 1.28 1.10 3 6.2 20 12 14.5 1.38 0.46 4 15.6 8 5 10.2 .78 – 0.44 CR Sequence = CR Sequence = 4 – 2 – 3 – 1 S/RO Sequence = 4 – 3 – 1 – 2 Comparing the CR and S/RO Rules
Shortest Slack per Processing Earliest Critical Remaining FCFS Time Due Date Ratio Operation Avg Flow Time 17.175 16.100 26.175 27.150 24.025 Avg Early Time 3.425 6.050 0 0 0 Avg Past Due7.350 8.900 12.925 13.900 10.775 Avg WIP 1.986 1.861 3.026 3.129 2.777 Avg Total Inv2.382 2.561 3.026 3.129 2.777 © 2007 Pearson Education Priority Rule Summary • The S/RO rule is better than the EDD rule and the CR rule but it is much worse than the SPT rule and the FCFS rule for this example. • S/RO has the advantage of allowing schedule changes when due dates change. These results cannot be generalized to other situations because only four jobs are being processed. FCFS = 1 – 2 – 3 – 4 SPT = 1 – 3 – 2 – 4 EDD = 4 – 2 – 1 – 3 CR = 4 – 2 – 3 – 1 S/RO = 4 – 3 – 1 – 2
Scheduling Jobs for Multiple Workstations • Priority sequencing rules can be used to schedule more than one operation. Each operation is treated independently. • Identifying the best priority rule to use at a particular operation in a process is a complex problem because the output from one process becomes the input for another. • Computer simulation models are effective tools to determine which priority rules work best in a given situation. • When a workstation becomes idle, the priority rule is applied to the jobs waiting for that operation, and the job with the highest priority is selected. • When that operation is finished, the job is moved to the next operation in its routing, where it waits until it again has the highest priority.
Johnson’s Rule • Johnson’s rule: A procedure that minimizes makespan when scheduling a group of jobs on two workstations. • Step 1. Find the shortest processing time among the jobs not yet scheduled. If two or more jobs are tied, choose one job arbitrarily. • Step 2. If the shortest processing time is on workstation 1, schedule the corresponding job as early as possible. If the shortest processing time is on workstation 2, schedule the corresponding job as late as possible. • Step 3. Eliminate the last job scheduled from further consideration. Repeat steps 1 and 2 until all jobs have been scheduled.
Time (hr) Motor Workstation 1 Workstation 2 M1 12 22 M2 4 5 M3 5 3 M4 15 16 M5 10 8 Eliminate M3 from consideration. The next shortest time is M2 at Workstation 1, so schedule M2 first. Shortest time is 3 hours at workstation 2, so schedule job M3 last. Eliminate M2 from consideration. The next shortest time is M5 at workstation #2, so schedule M5 next to last. Eliminate M1 and the only job remaining to be scheduled is M4. Eliminate M5 from consideration. The next shortest time is M1 at workstation #1, so schedule M1 next. Example 16.5Johnson’s Ruleat the Morris Machine Co. Sequence = M2 M1 M4 M5 M3
Workstation M2 M1 M4 M5 M3 Idle—available 1 Gantt Chart for the Morris Machine Company Repair Schedule (4) (12) (15) (10) (5) for further work M2 M1 M4 M5 M3 2 Idle Idle (5) (22) (16) (8) (3) 0 5 10 15 20 25 30 35 40 45 50 55 60 65 Day Example 16.5Johnson’s Ruleat the Morris Machine Co. The schedule minimizes the idle time of workstation 2 and gives the fastest repair time for all five motors. No other sequence will produce a lower makespan.
Labor-limited Environments • The limiting resource thus far has been the number of machines or workstations available. A more typical constraint is the amount of labor available. • Labor-limited environment: An environment in which the resource constraint is the amount of labor available, not the number of machines or workstations. • Assign personnel to the workstation with the job that has been in the system longest. • Assign personnel to the workstation with the most jobs waiting for processing. • Assign personnel to the workstation with the largest standard work content. • Assign personnel to the workstation with the job that has the earliest due date.
Linking Operations Scheduling to the Supply Chain • Advanced planning and scheduling (APS) systems: Systems that seek to optimize resources across the supply chain and align daily operations with strategic goals. Four characteristics of these systems are: • Demand Planning. This capability enables companies in a supply chain to share demand forecasts. • Supply Network Planning. Optimization models based on linear programming can be used to make long-term decisions. • Available-to-Promise. Firms can use this capability to promise delivery to customers by checking the availability of components and materials at its suppliers. • Manufacturing Scheduling. This module attempts to determine an optimal grouping and sequencing of manufacturing orders based on detailed product attributes, production line capacities, and material flows.
Solved Problem 1 • The Food Bin grocery store operates 24 hours per day, 7 days per week. At the end of the month, they calculated the average number of checkout registers that should be open during the first shift each day. Results showed peak needs on Saturdays and Sundays. Develop a schedule that covers all requirements while giving two consecutive days off to each clerk. How many clerks are needed? Plans can be made to use the clerks for other duties if slack or idle time resulting from this schedule can be determined. How much idle time will result from this schedule, and on what days?
© 2007 Pearson Education Solved Problem 1
© 2007 Pearson Education Solved Problem 1
Solved Problem 2 • The Neptune’s Den Machine Shop specializes in overhauling outboard marine engines. Currently, five engines with varying problems are awaiting service. The best estimates for the labor times involved and the promise dates (in number of days from today) are shown in the following table. Customers usually do not pick up their engines early. Develop separate schedules using SPT and then EDD rules. Compare them using average job flow time, % of past due jobs, and maximum past due days. Calculate average WIP inventory (in engines) and average total inventory.
© 2007 Pearson Education Solved Problem 2 SPT EDD
© 2007 Pearson Education Solved Problem 2
Solved Problem 4 Cleanup of chemical waste storage basins involves two operations. Operation 1: Drain and dredge basin. Operation 2: Incinerate materials. Management estimates that each operation will require the following amounts of time (in days): Find a schedule that minimizes the makespan. Calculate the average job flow time of a storage basin through the two operations. What is the total elapsed time for cleaning all 10 basins?
E H G F B J I C D A Solved Problem 4 Four jobs are tied for the shortest process time: A, D, E, and H. (E and H are tied for first place, while A and D are tied for last place.) We arbitrarily choose to start with basin E
Dredge E H G F B J I C D A Incinerate E H G F B J I C D A E H G F B J I C D A Solved Problem 4 The Gantt machine chart for this schedule Storage basin