PRODUCTIONS/OPERATIONS MANAGEMENT

1
Operations Scheduling Chapter 8
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The Hierarchy of Production Decisions

• The logical sequence of operations in factory
  planning corresponds to the sequencing of
  chapters in a production management text book.
• All planning starts with the demand forecast.
• Demand forecasts are the basis for the top level
  (aggregate) planning.
• The Master Production Schedule (MPS) is the
  result of disaggregating aggregate plans down to
  the individual item level.
• Based on the MPS, MRP is used to determine the
  size and timing of component and subassembly
  production.
• Detailed shop floor schedules are required to
  meet production plans resulting from the MRP.

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Hierarchy of Production Decisions
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Detailed production schedule

• A detailed production schedule must include when
  and where each activity must take place in order
  to meet the master schedule.

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Scheduling Service Operations Vs Manufacturing
Operations

• Scheduling service systems presents certain
  problems not generally encountered in
  manufacturing systems. This is primarily due to
• The inability to store services
• The random nature of customer requests
• To avoid problems such as long delays,
  unsatisfied customers, service systems rely on
  appoinment systems and reservation systems.

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Goals of Production Scheduling

• High Customer Service on-time delivery
• Low Inventory Levels WIP and FGI
• High Utilization of machines and labor

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Measures to Evaluate Performance of a Scheduling
Method

• Service Level Fraction of orders filled on
  before their due dates (used in make-to-order
  systems)
• Fill Rate Fraction of demand that are met from
  inventory without backorder (used in
  make-to-stock systems)
• Job Flow Time Time elapsed from the release of a
  job until it is completed.

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Measures to Evaluate Performance of a Scheduling
Method

• Lateness Difference between completion time and
  due date of a job (may be negative).
• Tardiness The positive difference between the
  completion time and the due date of a job.
• Makespan The total length of the schedule (that
  is, when all the jobs have finished processing).

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Reducing WIP and Flow Time

• Shorter flow time means
• Less WIP
• Better responsiveness
• All of which reduce costs and improve sales
  revenue

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Measures to Evaluate Performance of a Scheduling
Method

• Production Rate
• Utilization
• Keep in mind that high utilization means high
  return on investment. This is good provided that
  the equipment is utilized to increase revenue.
  Otherwise, high utilization only helps to
  increase inventory, not profits.

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Types of Production Systems

• High Volume Systems (Mass Production)
• -Continous Production (petroleum
  refining, sugar refining)
• -Discrete Production (autos, personal
  computers, televisons)
• Intermediate-Volume Systems (Batch production)
• Low-Volume Systems (Job-Shops)

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High-Volume Systems

• Flow system High-volume system with Standardized
  equipment and activities

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High-Volume Systems

• High-volume systems are often referred to as flow
  systems scheduling in these systems is referred
  to as flow-shop scheduling. Major aspects of
  system design include line balancing and flow
  system design.

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High-Volume Systems

• Line balancing concerns allocating the required
  tasks to workstations so that they satisfy
  technical (sequencing) constraints and are
  balanced with respect to equal work times among
  stations.
• It results in the maximum utilization of
  equipment and personnel as well as the highest
  possible rate of output.

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Intermediate-Volume Systems

• Outputs are between standardized high-volume
  systems and made-to-order job shops
• The volume of output is not large enough to
  justify continuous production.
• Examples include canned foods, paint and
  cosmetics.

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Intermediate-Volume Systems

• The three basic issues in these systems are
• 1.Run size, 2.Timing, and 3.Sequence of jobs
• Economic run size

h is defined as h h(1- ?/P)
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Scheduling Low-Volume Systems

• Loading - assignment of jobs to process centers
• Sequencing - determining the order in which jobs
  will be processed
• Job-shop scheduling
• Scheduling for low-volume systems with many
  variations in requirements

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Gantt charts

• Gantt charts are used as visual aid for loading
  and scheduling purposes.
• The name was derived from Henry Gantt in the
  early 1900s.
• The purpose of Gantt charts is to organize the
  use of resources in a time framework.
• In most cases, a time scale is represented
  horizontally, and resources to be scheduled are
  listed vertically.

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Gantt Load Chart
Figure 15.2

• Gantt chart - used as a visual aid for loading
  and scheduling

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Loading
21
LOADING (The Assignment Problem)

• In many business situations, management needs to
  assign - personnel to jobs, - jobs to machines, -
  machines to job locations, or - salespersons to
  territories.
• Consider the situation of assigning n jobs to n
  machines.
• When a job i (1,2,....,n) is assigned to machine
  j (1,2, .....n) that incurs a cost Cij.
• The objective is to assign the jobs to machines
  at the least possible total cost.

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The Assignment Problem

• This situation is a special case of the
  Transportation Model and it is known as the
  assignment problem.
• Here, jobs represent sources and machines
  represent destinations.
• The supply available at each source is 1 unit and
  demand at each destination is 1 unit.

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The Assignment Problem
The assignment model can be expressed
mathematically as follows Xij 0, if the job
j is not assigned to machine i 1, if the job j
is assigned to machine i
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The Assignment Problem
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The Assignment Problem Example

• Ballston Electronics manufactures small
  electrical devices.
• Products are manufactured on five different
  assembly lines (1,2,3,4,5).
• When manufacturing is finished, products are
  transported from the assembly lines to one of the
  five different inspection areas (A,B,C,D,E).
• Transporting products from five assembly lines to
  five inspection areas requires different times
  (in minutes)

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The Assignment Problem Example

• Ballston Electronics manufactures small
  electrical devices.
• Products are manufactured on five different
  assembly lines (1,2,3,4,5).
• When manufacturing is finished, products are
  transported from the assembly lines to one of the
  five different inspection areas (A,B,C,D,E).
• Transporting products from five assembly lines to
  five inspection areas requires different times
  (in minutes)

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The Assignment Problem Example
Under current arrangement, assignment of
inspection areas to the assembly lines are 1 to
A, 2 to B, 3 to C, 4 to D, and 5 to E. This
arrangement requires 107121719 65 man
minutes.
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The Assignment Problem Example

• Management would like to determine whether some
  other assignment of production lines to
  inspection areas may result in less cost.
• This is a typical assignment problem. n 5
  And each assembly line is assigned to each
  inspection area.
• It would be easy to solve such a problem when n
  is 5, but when n is large all possible
  alternative solutions are n!, this becomes a
  hard problem.

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The Assignment Problem Example

• Assignment problem can be either formulated as a
  linear programming model, or it can be
  formulated as a transportation model.
• However, An algorithm known as Hungarian Method
  has proven to be a quick and efficient way to
  solve such problems.
• This technique is programmed into many computer
  modules such as the one in WINQSB.

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The Assignment Problem Example
WINQSB solution for this problem is as follows
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Sequencing

• Sequencing Determine the order in which jobs at
  a work center will be processed.
• Workstation An area where one person works,
  usually with special equipment, on a specialized
  job.

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Common Sequencing Rules

• FCFS. First Come First Served. Jobs processed in
  the order they come to the shop.
• SPT. Shortest Processing Time. Jobs with the
  shortest processing time are scheduled first.
• EDD. Earliest Due Date. Jobs are sequenced
  according to their due dates.
• CR. Critical Ratio. Compute the ratio of
  processing time of the job and remaining time
  until the due date. Schedule the job with the
  largest CR value next.

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Sequencing n jobs on a Single Machine

• Priority rules
• Simple heuristics such as FCFS, SPT, DD, CR are
  used to select the order in which jobs will be
  processed.
• CR (Due Date Current Time)/ Processing Time

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Example Sequencing Rules

• Use the FCFS, SPT, and Critical Ratio rules to
  sequence the five jobs below. Evaluate the rules
  on the bases of average flow time, average number
  of jobs in the system, and average job lateness.
• 
  (Due Date)
• Job Processing Time Time to Promised
  Completion
• A 6 hours 10 hours
• B 12 16
• C 9 8
• D 14 14
• E 8 7

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Example Sequencing Rules

• FCFS Rule A gt B gt C gt D gt E
• Processing Due Flow
• Job Time Date Time
  Lateness
• A 6 10 6 0
• B 12 16 18 2
• C 9 8 27 19
• D 14 14 41 27
• E 8 7 49 42
• 49 141 90

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Example Sequencing Rules

• FCFS Rule Performance
• Average flow time
• 141/5 28.2 hours
• Average number of jobs in the system
• 141/49 2.88 jobs
• Average job lateness
• 90/5 18.0 hours

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Example Sequencing Rules

• SPT Rule A gt E gt C gt B gt D
• Processing Due Flow
• Job Time Date Time Lateness
• A 6 10 6 0
• E 8 7 14 7
• C 9 8 23 15
• B 12 16 35 19
• D 14 14 49 35
• 49 127 76

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Example Sequencing Rules

• SPT Rule Performance
• Average flow time
• 127/5 25.4 hours
• Average number of jobs in the system
• 127/49 2.59 jobs
• Average job lateness
• 76/5 15.2 hours

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Example Sequencing Rules

• Critical Ratio Rule E gt C gt D gt B gt A
• Processing Promised Flow
• Job Time Completion Time Lateness
• E (.875) 8 7 8 1
• C (.889) 9 8 17 9
• D (1.00) 14 14 31 17
• B (1.33) 12 16 43 27
• A (1.67) 6 10 49 39
• 49 148 93

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Example Sequencing Rules

• Critical Ratio Rule Performance
• Average flow time
• 148/5 29.6 hours
• Average number of jobs in the system
• 148/49 3.02 jobs
• Average job lateness
• 93/5 18.6 hours

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Example Sequencing Rules

• Comparison of Rule Performance
• Average Average Average
• Flow Number of Jobs Job
• Rule Time in System
  Lateness
• FCFS 28.2 2.88 18.0
• SPT 25.4 2.59
  15.2
• CR 29.6 3.02
  18.6
• SPT rule was superior for all 3 performance
  criteria.

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Sequencing n jobs on two machines

• Johnsons Rule technique for minimizing
  completion time for a group of n jobs to be
  processed on two machines or at two work centers.
• Minimizes total idle time
• Johnsons Rule requires satisfying the following
  conditions

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Johnsons Rule Conditions

• Job time must be known and constant
• Job times must be independent of sequence
• Jobs must follow same two-step sequence
• Job priorities cannot be used
• All units must be completed at the first work
  center before moving to second

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Johnsons Rule Optimum Sequence

1. List the jobs and their times at each work center
2. Find the smallest processing time. If it belongs
   to the first operation of a job schedule that job
   next, otherwise schedule that job last.
3. Eliminate the job from further consideration
4. Repeat steps 2 and 3 until all jobs have been
   scheduled

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Johnsons Algorithm Example

• Data
• Iteration 1 min time is 4 (job 1 on M1) place
  this job first and remove from lists

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Johnsons Algorithm Example (cont.)

• Iteration 2 min time is 5 (job 3 on M2) place
  this job last and remove from lists
• Iteration 3 only job left is job 2 place in
  remaining position (middle).
• Final Sequence 1-2-3
• Makespan 28

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Gantt Chart for Johnsons Algorithm Example
Short task on M2 to clear out quickly.
Short task on M1 to load up quickly.
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Example

• A group of six jobs is to be processed
  through a two-machine flow shop. The first
  operation involves cleaning and the second
  involves painting. Determine a sequence that will
  minimize the total completion time for this group
  of jobs. Processing times are as follows

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• Select the job with the shortest processing time.
  It is job D, with a time of two hours.
• Since the time is at the first center, schedule
  job D first. Eliminate job D from further
  consideration.
• Job B has the next shortest time. Since it is at
  the second work center, schedule it last and
  eliminate job B from further consideration. We
  now have
• The remaining jobs and their times are

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• The shortest remaining time is six hours for job
  E at work center 1. Thus, schedule that job
  toward the beginning of the sequence (after job
  D). Thus,
• Job C has the shortest time of the remaining two
  jobs. Since it is for the first work center,
  place it third in the sequence. Finally, assign
  the remaining job (F) to the fourth position and
  the result is

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Scheduling Difficulties

• Randomness in job arrival times
• Variability in
• Setup times
• Processing times
• Interruptions
• Changes in the set of jobs
• No method for identifying optimal schedule
• Scheduling is not an exact science
• Ongoing task for a manager

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Classic Dispatching Results

• Optimal Schedules Impossible to find for most
  real problems.
• Dispatching sorts jobs as they arrive at a
  machine.
• Dispatching rules
• FIFO simplest, seems fair.
• SPT Actually works quite well with tight due
  dates.
• EDD Works well when jobs are mostly the same
  size.
• Many (100?) others.
• Problems with Dispatching
• Cannot be optimal (can be bad).
• Tends to be myopic.

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The Difficulty of Scheduling Problems

• Dilemma
• Too hard for optimal solutions.
• Need something anyway.
• Classifying Hardness
• Class P has a polynomial solution.
• Class NP has no polynomial solution.
• Example Sequencing problems grow as n!.
• Compare en/10000 and 10000n10.
• At n 40, en/10000 2.4 ? 1013, 10000n10 1.0
  ? 1020
• At n 80, en/10000 5.5 ? 1030, 10000n10 1.1
  ? 1023
• 3! 6, 4! 24, 5! 120, 6! 720, 10!
  3,628,800, while
• 13! 6,227,020,800
• 25! 15,511,210,043,330,985,984,000,000

en/10000
10000n10
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The Difficulty of Scheduling Problems

• NP stands for non polynomial, meaning that the
  time required to solve such problems is an
  exponential function of the number of jobs rather
  than a polynomial function.
• The problems for which total enumeration is
  hopeless are known in mathematics as NP hard.

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Computation Times

• Current situation Suppose computer can examine
  1,000,000 sequences per second and we wish to
  build a scheduling system that has response time
  of no longer than one minute. How many jobs can
  we sequence optimally?

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Effect of Faster Computers

• Future Situation New computer is 1,000 times
  faster, i.e. it can do 1 billion comparisons per
  second. How many jobs can we sequence optimally
  now?

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Implications for Real Problems

• Violation of Assumptions Most real-world
  scheduling problems violate the assumptions made
  in the classic literature
• There are always more than two machines.
• Process times are not deterministic.
• All jobs are not ready at the beginning of the
  problem.
• Process time are sequence dependent.
• Problem Difficulty Most real-world production
  scheduling problems are NP-hard.
• We cannot hope to find optimal solutions of
  realistic sized scheduling problems.
• Polynomial approaches, like dispatching, may not
  work well.

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Implications for Real Problems (cont.)

• Heuristic Approaches can be used to obtain good
  solutions for real-world problems.
• Examples of most commonly used meta-heuristics
  include
• Simulated Annealing
• Tabu Search
• Genetic Algorithms