Operations Scheduling 14 Operations Scheduling For Operations Management, 9e by Krajewski/Ritzman/Malhotra © 2010 Pearson Education Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Stages in Planning and Scheduling (A review from Week 3) Aggregation Product families Workforce Time The relationship of operations plans and schedules to other plans A business plan An annual plan or financial plan Resource planning The lowest planning level is scheduling Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Stages in Planning and Scheduling Figure 14.1 – The Relationship of Sales and Operations Plans and Schedules to Other Plans Business or annual plan Operations strategy Sales Plan Operations Sales and Operations Plan Forecasting Constraint management Master production schedule Material requirements planning Resource Planning (manufacturing) Workforce schedule Materials and facility resources Resource Planning (services) Employee and equipment schedules Production order schedules Purchase order schedules Scheduling Employee schedules Facility schedules Customer schedules Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Scheduling Takes operations and scheduling process from planning to execution and requires gathering data from sources such as demand forecasts, resource availability from the sales and operations plan, and specific constraints from employees and customers. Generates a work schedule for employees or sequences of jobs or customers at workstations. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Strategic Importance of Short-Term Scheduling By scheduling effectively, companies use assets more effectively and create greater capacity per dollar invested lower cost This added capacity and related flexibility provides faster delivery better customer service Good scheduling and increased flexibility are competitive advantages dependable delivery You might stress to students that scheduling is what the end-customer actually sees. Ω

Scheduling Service provider Front-office process Demand scheduling customers are assigned to a definite time for order fulfillment Workforce scheduling determines when employees work Operations scheduling jobs are assigned to workstations or employees are assigned to jobs for specified time periods Service provider Front-office process Service provider Back-office process Manufacturing company While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Demand Scheduling 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 of 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 While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Gantt Charts The job or activity progress chart The workstation chart Current date Nissan Ford Pontiac Job 4/20 4/22 4/23 4/24 4/25 4/26 4/21 4/17 4/18 4/19 Start activity Finish activity Scheduled activity time Actual progress Nonproductive time Figure 14.7 – Gantt Progress Chart for an Auto Parts Company Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Gantt Charts Operating Room A Workstation 7am Operating Room B Operating Room C 12 pm 8am 9am 10am 11am 1pm 2pm 3pm 4pm 5pm 6pm Time Dr. Jon Adams Dr. Aubrey Brothers Dr. Alaina Bright Dr. Gary Case Dr. Jeff Dow Dr. Madeline Easton Dr. Dan Gillespie Dr. Jordanne Flowers Figure 14.8 – Gantt Workstation Chart for Operating Rooms at a Hospital Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Scheduling Employees Translate the staffing plan into specific schedules of work for each employee Constraints Technical constraints Legal and behavioral considerations Psychological needs of workers Rotating schedule Fixed schedule Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Scheduling Employees Steps in developing a workforce schedule Step 1: Find all the pairs of consecutive days Step 2: If a tie occurs, choose one of the tied pairs, consistent with the provisions written into the labor agreement Step 3: Assign the employees for the selected pair of days off Step 4: Repeat steps 1 – 3 until all of the requirements have been satisfied Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Developing a Workforce Schedule EXAMPLE 14.2 The Amalgamated Parcel Service is open seven days a week. The schedule of requirements is Day M T W Th F S Su Required number of employees 6 4 8 9 10 3 2 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. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Developing a Workforce Schedule SOLUTION Friday contains the maximum requirements, and the pair S – Su has the lowest total requirements. Therefore, Employee 1 is scheduled to work Monday through Friday. Note that Friday still has the maximum requirements and that the requirements for the S – Su pair are carried forward because these are Employee 1’s days off. These updated requirements are the ones the scheduler uses for the next employee. The day-off assignments for the employees are shown in the following table. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Developing a Workforce Schedule Scheduling Days Off M T W Th F S Su Employee Comments 6 4 8 9 10 3 2 1 The S–Su pair has the lowest total requirements. Assign Employee 1 to a M-F schedule. 5 7 The S–Su pair has the lowest total requirements. Assign Employee 2 to a M-F schedule. The S–Su pair has the lowest total requirements. Assign Employee 3 to a M-F schedule. The M–T pair has the lowest total requirements. Assign Employee 4 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 5 to a M-F schedule. The M–T pair has the lowest total requirements. Assign Employee 6 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 7 to a M-F schedule. Four pairs have the minimum requirement and the lowest total. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 8 to a M-F schedule. Arbitrarily choose the Su–M pair to break ties because the S–Su pair does not have the lowest total requirements. Assign Employee 9 to a T-S schedule. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 10 to a M-F schedule. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Developing a Workforce Schedule Scheduling Days Off M T W Th F S Su Employee Comments 6 4 8 9 10 3 2 1 The S–Su pair has the lowest total requirements. Assign Employee 1 to a M-F schedule. 5 7 The S–Su pair has the lowest total requirements. Assign Employee 2 to a M-F schedule. The S–Su pair has the lowest total requirements. Assign Employee 3 to a M-F schedule. The M–T pair has the lowest total requirements. Assign Employee 4 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 5 to a M-F schedule. The M–T pair has the lowest total requirements. Assign Employee 6 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 7 to a M-F schedule. Four pairs have the minimum requirement and the lowest total. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 8 to a M-F schedule. Arbitrarily choose the Su–M pair to break ties because the S–Su pair does not have the lowest total requirements. Assign Employee 9 to a T-S schedule. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 10 to a M-F schedule. 6 4 8 9 10 3 2 1 The S–Su pair has the lowest total requirements. Assign Employee 1 to a M-F schedule. 5 3 7 8 9 2 The S–Su pair has the lowest total requirements. Assign Employee 2 to a M-F schedule. 4 2 6 7 8 3 The S–Su pair has the lowest total requirements. Assign Employee 3 to a M-F schedule. 3 1 5 6 7 2 4 The M–T pair has the lowest total requirements. Assign Employee 4 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 5 to a M-F schedule. The M–T pair has the lowest total requirements. Assign Employee 6 to a W-Su schedule. The S–Su pair has the lowest total requirements. Assign Employee 7 to a M-F schedule. 8 Four pairs have the minimum requirement and the lowest total. Choose the S–Su pair according to the tie-breaking rule. Assign Employee 8 to a M-F schedule. 9 Arbitrarily choose the Su–M pair to break ties because the S–Su pair does not have the lowest total requirements. Assign Employee 9 to a T-S schedule. 10 Choose the S–Su pair according to the tie-breaking rule. Assign Employee 10 to a M-F schedule. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Developing a Workforce Schedule In this example, Friday always has the maximum requirements and should be avoided as a day off. The final schedule for the employees is shown in the following table. Final Schedule Employee M T W Th F S Su Total 1 X off 2 3 4 5 6 7 8 9 10 Capacity, C 50 Requirements, R 42 Slack, C – R Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Forward and Backward Scheduling Forward scheduling: begins the schedule as soon as the requirements are known jobs performed to customer order (FCFS) schedule can be accomplished even if due date is missed often causes buildup of WIP Backward scheduling: begins with the due date for completion; schedules jobs in reverse order used in many manufacturing environments, catering, scheduling surgery Students should be asked to consider how, using either process, they would modify the schedule when (a) an order is cancelled, (b) a priority, rush order is accepted, or (c) a delay is encountered.

Short-Term Scheduling Deals with timing of operations Short run focus: Hourly, daily, weekly Types Today Due Date B E Forward Scheduling Backward Scheduling

Operations Scheduling Short-term plans designed to implement the master production schedule and subassembly manufacturing schedules Job shop dispatching Scheduling jobs for one workstation Scheduling jobs for multiple workstations Labor-limited environments While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Scheduling Methods Differ by Process Level Use Methods Repetitive-Focused Product-Focused Process-Focused Variety of Methods

Process-Focused Work Centers (Job Shop, Batch) High-variety, low-volume systems Products made to order Products require different materials and processing Complex production planning and control Production planning aspects Shop loading Job sequencing Assigning most effective resource

Requirements for Scheduling Process-Focused Work Centers Schedule incoming orders without violating capacity constraints of individual work centers Check availability of tools and materials before releasing an order to a department Establish due dates for each job and check progress against need dates and order lead times Check work-in-progress as jobs move through the shop Provide feedback (metrics) on plant and production activities Provide work-efficiency statistics and monitor operator times for payroll and labor distribution analyses

Sequencing Specifies the order that jobs will be worked on Sequencing rules First come, first served (FCFS) Shortest processing time (SPT) Earliest due date (EDD) Longest processing time (LPT) Critical ratio (CR) Johnson’s rule (for two operations in sequence) The next seven slides provide additional discussion of these rules.

Criteria to Evaluate Priority Rules Process time: Time required to do job once it is started. This is often called cycle time. Flow time: Time a job spends in the system. This is the sum of the job’s process time plus the amount of time the job waits before work on it actually starts. Past Due: The length of time beyond the due date until a job is completed. If a job is completed before the due date, this value is zero. Makespan: The total amount of time to complete a group of jobs. You might point out (even though you have probably noted it before) that ratings or rankings of the different scheduling rules will differ depending upon the criteria used.

Job Shop Dispatching Critical ratio (CR) Earliest due date (EDD) 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 Shipping Raw Materials Critical ratio (CR) Earliest due date (EDD) First-come, first-served (FCFS) Shortest processing time (SPT) Slack per remaining operations (S/RO) Johnson’s rule (for two operations in sequence) While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

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. While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Comparing EDD and SPT Rules Earliest Due Date (EDD) Shortest Processing Time (SPT) Engine Block Sequence Ranger Explorer Econoline Bronco T-Bird Begin Work 0 8 14 17 32 Processing Time (hr) 8 6 3 15 12 Job Flow Time 8 14 17 32 44 Engine Block Sequence Econoline Explorer Ranger T-Bird Bronco Begin Work 0 3 9 17 29 Processing Time (hr) 3 6 8 12 15 Job Flow Time 3 9 17 29 44 + + + + + = = = = = + + + + + = = = = = While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later. Average job flow time = 23 hr Average past due = 7.2 hr Average WIP = 2.6 eng. Average job flow time = 20.4 hr Average past due = 7.6 hr Average WIP = 2.3 eng.

Critical Ratio (CR) and Slack per Remaining Operations (S/RO) Operation Time Time at Remaining Number of Engine to Due Date Operations Shop Time Job Lathe (hr) (Days) Remaining Remaining CR 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 0.89 1.10 0.46 – 0.44 While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later. CR = Time remaining to due date Shop time remaining S/RO = Time remaining to due date – Shop time remaining Number of operations remaining

Advantages of the Critical Ratio Scheduling Rule Use of the critical ratio can help to: determine the status of a specific job establish a relative priority among jobs on a common basis relate both stock and make-to-order jobs on a common basis adjust priorities and revise schedules automatically for changes in both demand and job progress dynamically track job progress and location

Critical Ratio (CR) Example Current Day = 0 Job Job Work Processing time in days Job Due Date (days from now) Critical Ratio __Due Date__ Process Time A 6 8 1.33 B 2 3.0 C 18 2.25 D 3 15 5.0 E 9 23 2.56 CR Sequence A C E B D

Scheduling Jobs for One Workstation Earliest Due Date + performs well on past due – does not do well on flow time, WIP, or utilization Shortest Processing Time + performs well on mean flow time, WIP, past due, and utilization – Can increase total inventory, large variance on past due, unresponsive to date changes First-Come, First-Served + Considered fair to jobs/customers – Performs poorly on all performance measures Critical Ratio Slack per Remaining Operations While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later. Multiple-dimension rules – no choice is clearly best

Priority Rule Metrics You might point out (even though you have probably noted it before) that ratings or rankings of the different scheduling rules will differ depending upon the criteria used.

Johnson’s Rule Used to sequence N jobs through 2 machines in the same order © 1995 Corel Corp. Saw Drill Job A Job B Job C Jobs (N = 3)

Johnson's Rule - Scheduling N Jobs on Two Consecutive Machines All jobs are to be listed, and the time each requires on each machine shown. Select the job with the shortest processing time on either machine. If the shortest time lies with the first machine, the job is scheduled first on the first machine. If the shortest time lies with the second machine, the job is scheduled last on the second machine. Once a job is scheduled, eliminate it from the list. Apply steps 2-3 to the remaining jobs, working toward the center of the scheduling sequence until all jobs are scheduled.

Johnson’s Rule Steps List jobs & activity times per machine Pick job with least time at a machine Machine? Schedule FIRST on #1 LAST on #2 Eliminate job from list Jobs left? Break arbitrarily Ties? Yes #1 #2 Stop No

Johnson’s Rule - Example Times per Machine for Each Job Job Work Center 1 (Drill Press) Work Center 2 (Lathe) A 5 2 B 3 6 C 8 4 D 10 7 E 12 Selected shortest step time and its associated machine for each job

Johnson’s Rule - Example Step 1 A Step 2 B A Step 3 B C A Step 4 B E C A Step 5 B E D C A

Graphical Depiction of Job Flow Work center 1 Work center 2 0 3 10 20 28 33 0 3 9 10 22 29 33 35 Time => B E D C A B E D C A = Idle = Job completed

Using the FCFS Rule EXAMPLE 14.3 Currently a consulting company has five jobs in its backlog. The time since the order was placed, processing time, and promised due dates are given in the following table. Determine the schedule by using the FCFS rule, and calculate the average days past due and flow time. How can the schedule be improved, if average flow time is the most critical? Customer Time Since Order Arrived (days ago) Processing Time (days) Due Date (days from now) A 15 25 29 B 12 16 27 C 5 14 68 D 10 48 E 80 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Processing Time (days) Days Ago Since Order Arrived Using the FCFS Rule SOLUTION a. The FCFS rule states that Customer A should be the first one in the sequence, because that order arrived earliest—15 days ago. Customer E’s order arrived today, so it is processed last. The sequence is shown in the following table, along with the days past due and flow times. Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) A B C D E Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Processing Time (days) Days Ago Since Order Arrived Using the FCFS Rule SOLUTION a. The FCFS rule states that Customer A should be the first one in the sequence, because that order arrived earliest—15 days ago. Customer E’s order arrived today, so it is processed last. The sequence is shown in the following table, along with the days past due and flow times. Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) A B C D E + 25 = 29 15 40 25 + 16 = 41 27 14 12 53 41 + 10 = 51 48 3 61 14 65 68 5 70 12 77 80 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Using the FCFS Rule The finish time for a job is its start time plus the processing time. Its finish time becomes the start time for the next job in the sequence, assuming that the next job is available for immediate processing. The days past due for a job is zero (0) if its due date is equal to or exceeds the finish time. Otherwise it equals the shortfall. The flow time for each job equals its finish time plus the number of days ago since the order first arrived at the workstation. The days past due and average flow time performance measures for the FCFS schedule are 0 + 14 + 3 + 0 + 0 5 Average days past due = = 3.4 days 40 + 53 + 61 + 70 + 77 5 Average flow time = = 60.2 days Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Processing Time (days) Days Ago Since Order Arrived Using the FCFS Rule b. The average flow time can be reduced. One possibility is the sequence shown in the following table. Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) D E C B A Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Processing Time (days) Days Ago Since Order Arrived Using the FCFS Rule b. The average flow time can be reduced. One possibility is the sequence shown in the following table. Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) D E C B A + 10 = 48 10 20 10 + 12 = 22 80 22 22 + 14 = 36 68 5 41 16 52 27 25 12 64 77 29 48 15 92 0 + 0 + 0 + 25 + 48 5 Average days past due = = 14.6 days 20 + 22 + 41 + 64 + 92 5 Average flow time = = 47.8 days This schedule reduces the average flow time from to 60.2 to 47.8 days—a 21 percent improvement. However, the past due times for jobs A and B have increased. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Labor-limited Environments An environment in which the resource constraint is the amount of labor available, not machines or workstations Labor assignment rules: 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 While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Linking Operations Scheduling to the Supply Chain Advanced planning and scheduling (APS) systems seek to optimize resources across the supply chain and align daily operations with strategic goals. System components: Demand Planning – Share demand forecasts among companies in a supply chain Supply Network Planning – Optimization models for long-term decisions Available-to-Promise – Promise delivery to customers by checking the availability of components and materials at suppliers Manufacturing Scheduling – Determine optimal grouping and sequencing of manufacturing orders based on detailed product attributes, production line capacities, and material flows While we would like to minimize customer wait time, an alternate goal might be to make customer wait time consistent - we could always ask them to come later.

Scheduling for Services Appointment systems - doctor’s office Reservations systems - restaurant, car rental First come, first served - deli Most critical first - hospital trauma room Must account for time off Regulated (e.g., airline pilots, truck drivers) Vacation, holidays Training Should have plans for unpredictable events Illness Breakdowns Weather and other delay causes Students should be asked to consider what special problems arise in scheduling services.

Assignment Scheduling Method Assigns tasks or jobs to most efficient resources Type of linear programming model Objectives Reduce total cost, time required, etc. Increase profit, total output rate Constraints 1 job per resource (e.g., machine, person, site, etc.) 1 resource per job Equal number of jobs and resources (add either dummy jobs or resources to achieve this) Students should be asked to consider what other assumptions must be made when using the assignment model for job scheduling.

Assignment Method – Type Setter Example Table of Costs for Each Typesetter to Do Each Job $11 $14 $ 6 S-66 $ 8 $10 T-50 $9 $12 $7 Initial set-up Goal is to assign the three jobs among the three typesetters for the minimum total cost.

Assignment Method - Four Steps Subtract the smallest number in each row from every number in that row; then subtract the smallest number in every column from every number in that column Draw the minimum number of vertical and horizontal straight lines necessary to cover all zeros in the table If the minimum number of lines required equals either the number of rows or the number of columns, then you can make an optimal assignment (Step 4) Otherwise (Step 3) Subtract the smallest number not covered by a line from every other uncovered number. Add the same number to any number(s) lying at the intersection of any two lines. Return to Step 2 Optimal assignments for each resource will always be at the zero locations of the table. Assign jobs first to those resources that have only one zero. It should be noted to students that there are other methodologies available for solving the assignment problem (branch-and-bound, etc.)

Steps 1a and 1b Typesetter A B C R-34 $11 $14 $ 6 S-66 $ 8 $10 T-50 $9 $12 $7 Typesetter Job A B C R-34 5 8 S-66 2 3 T-50 Typesetter Job A B C R-34 5 6 S-66 3 T-50 2 Step 1a (Subtracting minimum in each row) Step 1b (Subtracting minimum in each column)

Steps 2a and 2b Typesetter Job A B C R-34 5 6 S-66 3 T-50 2 Typesetter S-66 3 T-50 2 Typesetter Job A B C R-34 3 4 S-66 5 T-50 1 Smallest uncovered number After subtracting smallest uncovered number from all uncovered numbers

Steps 3 and 4 Typesetter Job A B C R-34 3 4 S-66 5 T-50 1 S-66 5 T-50 1 Make assignments >>> A= T-50, B = S-66, C= R-34 Total cost is $9 + $10 + $6 = $25 Note: Since R-34 has only one zero, it is assigned first to C. Then T-50 has only one zero for the remaining jobs, so it is assigned to A. This leaves S-66 to be assigned to B

Processing Time (days) Days Ago Since Order Arrived Application 14.4 Revisit Example 14.3, where the consulting company has five jobs in its backlog. Create a schedule using the EDD rule, calculating the average days past due and flow time. In this case, does EDD outperform the FCFS rule? SOLUTION Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) B A D C E + 16 = 27 12 28 16 + 25 = 41 29 12 15 56 41 + 10 = 51 48 3 61 14 65 68 5 70 12 77 80 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Processing Time (days) Days Ago Since Order Arrived Application 14.4 Customer Sequence Start Time (days) Processing Time (days) Finish Time (days) Due Date Days Past Due Days Ago Since Order Arrived Flow Time (days) B A D C E + 16 = 27 12 28 16 + 25 = 41 29 12 15 56 41 + 10 = 51 48 3 61 14 65 68 5 70 12 77 80 The days past due and average flow time performance measures for the EDD schedule are 0 + 12 + 3 + 0 + 0 5 Average days past due = = 3.0 days 28 + 56 + 61 + 70 + 71 5 Average flow time = = 58.4 days By both measures, EDD outperforms the FCFS. However, the solution found in part (b) of Example 14.3 still has the best average flow time of only 47.8 days. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 The Cranston Telephone Company employs workers who lay telephone cables and perform various other construction tasks. The company prides itself on good service and strives to complete all service orders within the planning period in which they are received. Each worker puts in 600 hours of regular time per planning period and can work as many as an additional 100 hours of overtime. The operations department has estimated the following workforce requirements for such services over the next four planning periods: Planning Period 1 2 3 4 Demand (hours) 21,000 18,000 30,000 12,000 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 Cranston pays regular-time wages of $6,000 per employee per period for any time worked up to 600 hours (including undertime). The overtime pay rate is $15 per hour over 600 hours. Hiring, training, and outfitting a new employee costs $8,000. Layoff costs are $2,000 per employee. Currently, 40 employees work for Cranston in this capacity. No delays in service, or backorders, are allowed. Use the spreadsheet approach to answer the following questions: a. Prepare a chase strategy using only hiring and layoffs. What are the total numbers of employees hired and laid off? b. Develop a workforce plan that uses the level strategy, relaying only on overtime and undertime. Maximize the use of overtime during the peak period so as to minimize the workforce level and amount of undertime. c. Propose an effective mixed-strategy plan. d. Compare the total costs of the three plans. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 a. The chase strategy workforce is calculated by dividing the demand for each period by 600 hours, or the amount or regular-time work for one employee during one period. This strategy calls for a total of 20 workers to be hired and 40 to be laid off during the four-period plan. Figure 14.9 shows the “chase strategy” solution that OM Explorer’s Sales and Operations Planning with Spreadsheets solver produces. We simply hide any unneeded columns and rows in this general-purpose solver. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 Figure 14.9 – Spreadsheet for Chase Strategy Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 b. The peak demand is 30,000 hours in period 3. As each employee can work 700 hours per period (600 on regular time and 100 on overtime), the workforce level of the level strategy that minimizes undertime is 30,000/700 = 42.86, or 43 employees. This strategy calls for three employees to be hired in the first quarter and for none to be laid off. To convert the demand requirements into employee-period equivalents, divide the demand in hours by 600. For example, the demand of 21,000 hours in period 1 translates into 35 employee-period equivalents (21,000/600) and demand in period 3 translates into 50 employee-period equivalents (30,000/600). Figure 14.10 shows OM Explorer’s spreadsheet for this level strategy that minimizes undertime. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 Figure 14.10 – Spreadsheet for Level Strategy Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 c. The mixed-strategy plan that we propose uses a combination of hires, layoffs, and overtime to reduce total costs. The workforce is reduced by 5 at the beginning of the first period, increased by 8 in the third period, and reduced by 13 in the fourth period. Figure 14.11 shows the results. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 Figure 14.11 – Spreadsheet for Mixed Strategy Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 1 d. The total cost of the chase strategy is $1,050,000. The level strategy results in a total cost of $1,119,000. The mixed-strategy plan was developed by trial and error and results in a total cost of $1,021,000. Further improvements are possible. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 2 The Food Bin grocery store operates 24 hours per day, 7 days per week. Fred Bulger, the store manager, has been analyzing the efficiency and productivity of store operations recently. Bulger decided to observe the need for checkout clerks on the first shift for a one-month period. At the end of the month, he calculated the average number of checkout registers that should be open during the first shift each day. His results showed peak needs on Saturdays and Sundays. Day M T W Th F S Su Number of Clerks Required 3 4 5 7 8 Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 2 Bulger now has to come up with a workforce schedule that guarantees each checkout clerk two consecutive days off but still covers all requirements. a. Develop a workforce schedule that covers all requirements while giving two consecutive days off to each clerk. How many clerks are needed? Assume that the clerks have no preference regarding which days they have off. b. 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? Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 2 SOLUTION a. We use the method demonstrated in Example 14.2 to determine the number of clerks needed. The minimum number of clerks is eight. Day M T W Th F S Su Requirements Clerk 1 Clerk 2 Clerk 3 Clerk 4 3 4 5 7 8 off X 3 4 6 7 off X 3 4 2 5 6 X off 2 3 4 5 X off Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall. Solved Problem 2 Day M T W Th F S Su Requirements Clerk 5 Clerk 6 Clerk 7 Clerk 8 1 2 3 4 X off The minimum number of clerks is eight. Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.

Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall.