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Roberta Russell & Bernard W. Taylor, III

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1 Roberta Russell & Bernard W. Taylor, III
Chapter 16 Scheduling Operations Management - 5th Edition Roberta Russell & Bernard W. Taylor, III

2 Lecture Outline Objectives in Scheduling Loading / Assignment
Sequencing Monitoring Theory of Constraints Employee Scheduling

3 What is Scheduling? Last stage of planning before production occurs
Specifies when labor, equipment, facilities are needed to produce a product or provide a service

4 Another Definition of Scheduling
Scheduling concerns the allocation of limited resources to tasks over time. It is a decision-making process that has as a goal the optimization of one or more objectives Michael Pinedo – Scheduling: Theory, Algorithms, and Systems I like this definition better.

5 Managers Must Schedule the Following
Scheduling Decisions Organization Managers Must Schedule the Following Arnold Palmer Hospital Operating room use Patient admissions Nursing, security, maintenance staffs Outpatient treatments University of Missouri Classrooms and audiovisual equipment Student and instructor schedules Graduate and undergraduate courses Lockheed-Martin factory Production of goods Purchases of materials Workers Hard Rock Cafe Chef, waiters, bartenders Delivery of fresh foods Entertainers Opening of dining areas Delta Airlines Maintenance of aircraft Departure timetables Flight crews, catering, gate, ticketing personnel

6 Objectives in Scheduling
Meet customer due dates Minimize job lateness Minimize response time Minimize completion time Minimize time in the system Minimize overtime Maximize machine or labor utilization Minimize idle time Minimize work-in-process inventory

7 Shop Floor Control Loading Sequencing Monitoring
Check availability of material, machines and labor Sequencing Release work orders to shop and issue dispatch lists for individual machines Monitoring Maintain progress reports on each job until it is complete

8 Loading Process of assigning work to limited resources
Perform work on most efficient resources Use assignment method of linear programming to determine allocation

9 Assignment Problem Example
WebStar, Inc. has 4 projects to complete They have 4 programmers, each with varying degrees of expertise On average, it costs $100 per hour Assign a single worker to a single project in order to minimize total cost Processing PROJECT Estimates (hr) Bryan Kari Noah Chris

10 Formulation Indices DATA Variables i = project index j = worker index
n = total number of projects (and workers) DATA COSTij = cost of having project i assigned to worker j Variables xij = indicates if project i assigned to worker j totcost = total cost of assignments

11 Formulation, cont’d. Objective Constraints min totcost =
for i = 1, …, n (assign only one worker to a project) for j = 1, …, n (assign only one project to a worker) xij binary

12 Another Example Spring Weekend is coming up and Joe has 3 commitments to keep: Go out one night with his girlfriend Go out one night with his UConn friends Go out one night with his HS friends He has estimated his costs for each commitment as shown on the next slide Help Joe decide which night he should spend with each group of friends

13 Joe’s Costs Girlfriend UConn Friends HS Friends Thursday $30 $50 $100
Friday $40 $60 $90 Saturday $80

14 Joe’s Dilemma Formulated
Let ??? Objective Function Subject to

15 Sequencing Prioritize jobs assigned to a resource
If no order specified use first-come first-served (FCFS) Many other sequencing rules exist Each attempts to achieve an objective

16 Sequencing Rules FCFS - first-come, first-served
LCFS - last come, first served DDATE - earliest due date CUSTPR - highest customer priority SETUP - similar required setups SLACK - smallest slack CR - critical ratio SPT - shortest processing time LPT - longest processing time

17 Critical Ratio Rule CR considers both time and work remaining CR = =
If CR > 1, job ahead of schedule If CR < 1, job behind schedule If CR = 1, job on schedule time remaining due date - today’s date work remaining remaining processing time

18 Sequencing Jobs Through One Process
Flowtime (completion time) Time for a job to flow through the system Makespan Time for a group of jobs to be completed Tardiness Difference between a late job’s due date and its completion time

19 Sequencing Jobs Through Two Serial Process
Johnson’s Rule List time required to process each job at each machine. Set up a one-dimensional matrix to represent desired sequence with # of slots equal to # of jobs. Select smallest processing time at either machine. If that time is on machine 1, put the job as near to beginning of sequence as possible. If smallest time occurs on machine 2, put the job as near to the end of the sequence as possible. Remove job from list. Repeat steps 2-4 until all slots in matrix are filled and all jobs are sequenced.

20 Johnson’s Rule A B C D E JOB PROCESS 1 PROCESS 2 A 6 8 B 11 6 C 7 3

21 Johnson’s Rule (cont.) E A D B C Completion time = 41
Process 1 (sanding) 5 11 20 31 38 Process 2 (painting) 15 23 30 37 41 Idle time Completion time = 41 Idle time = =10

22 Guidelines for Selecting a Sequencing Rule
SPT most useful when shop is highly congested Use SLACK for periods of normal activity Use DDATE when only small tardiness values can be tolerated Use LPT if subcontracting is anticipated Use FCFS when operating at low-capacity levels Do not use SPT to sequence jobs that have to be assembled with other jobs at a later date

23 Monitoring Work package Gantt Chart Input/Output Control
Shop paperwork that travels with a job Gantt Chart Shows both planned and completed activities against a time scale Input/Output Control Monitors the input and output from each work center

24 Theory of Constraints Not all resources are used evenly
Concentrate on the “bottleneck” resource Synchronize flow through the bottleneck Use process and transfer batch sizes to move product through facility

25 TOC Scheduling Procedure
Identify bottleneck Schedule job first whose lead time to the bottleneck is less than or equal bottleneck processing time Forward schedule the bottleneck machine Backward schedule the other machines to sustain the bottleneck schedule Transfer in batch sizes smaller than the process batch size

26 Drum, Buffer, Rope The drum is the beat of the system and provides the schedule or pace of production The buffer is the inventory necessary to keep constraints operating at capacity The rope provides the synchronization necessary to pull units through the system Another idea from TOC.

27 Employee Scheduling Labor is very flexible resource
Scheduling workforce is complicated repetitive task Assignment method can be used Heuristics are commonly used

28 Employee Scheduling Heuristic
Let N = no. of workers available Di = demand for workers on day i X = day working O = day off Assign the first N - D1 workers day 1 off. Assign the next N - D2 workers day 2 off. Continue in a similar manner until all days are have been scheduled If number of workdays for full time employee < 5, assign remaining workdays so consecutive days off are possible Assign any remaining work to part-time employees If consecutive days off are desired, consider switching schedules among days with the same demand requirements

29 Employee Scheduling DAY OF WEEK M T W TH F SA SU MIN NO. OF
WORKERS REQUIRED Homer Marge Bart Lisa Maggie

30 Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU MIN NO. OF WORKERS REQUIRED Homer O X X O X X X Marge O X X O X X X Bart X O X X O X X Lisa X O X X X X O Maggie X X O X X X O Completed schedule satisfies requirements but has no consecutive days off

31 Employee Scheduling (cont.)
DAY OF WEEK M T W TH F SA SU MIN NO. OF WORKERS REQUIRED Homer O O X X X X X Marge O O X X X X X Bart X X O O X X X Lisa X X X O X X O Maggie X X X X O X O Revised schedule satisfies requirements with consecutive days off for most employees

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