IE 151
Chapter 5 – Understanding Short-Term Scheduling
Laboratory Notes and Practice Problems
Scheduling – refers to the establishment of timing of the use of equipment, facilities, and human
activities in an organization; involves timing of operations or assigning due dates to specific activities
• Forward scheduling – begins the schedule as soon as the requirements are known
• Backward scheduling – begins with the due date of final operation; schedules jobs in
reverse order
Process-Focused Work Centers
Loading – assigning jobs to work center; capacity control technique that highlights overloads and
underloads
1. Finite Loading – jobs are assigned to work centers considering the work center capacity and
job processing time
a. Gantt Chart – used to schedule resources and allocate time; shows relative workload
in facility which may help managers to make necessary adjustments
b. Assignment Method of Linear Programming – assigns tasks or jobs to resources; type
of linear programming model where the objective is usually to minimize total cost
and the constraint is you can only assign 1 job per resource and/or 1 resource per
job
i. 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
ii. Draw the minimum number of vertical and horizontal straight lines
necessary to cover all zeros in the table (If the number of lines equals either
the number of rows or the number of columns, then you can make an
optimal assignment, proceed to step iv)
iii. 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
iv. Optimal assignments will always be at the zero locations of the table
2. Infinite Loading – assigns jobs to work centers without regards to capacity of the work
center
Sequencing – specified the order in which the jobs should be done at each other; the
following are common priority rules for dispatching/sequencing jobs:
i. First come first served (FCFS)
vi. Last come first served (LCFS)
ii. Longest processing time (LPT)
vii. Slack time remaining (STR)
iii. Earliest due date (EDD)
viii. STR per operation (STR/OP)
iv. Shortest processing time (SPT)
ix. Critical ratio (CR)
v. Random order or whim
x. Johnson’s rule
Criteria to evaluate priority rules:
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑐𝑜𝑚𝑝𝑙𝑒𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 =
𝛴 𝑓𝑙𝑜𝑤 𝑡𝑖𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑜𝑏𝑠
𝑈𝑡𝑖𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 =
𝛴 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑡𝑖𝑚𝑒𝑠
𝛴 𝑓𝑙𝑜𝑤 𝑡𝑖𝑚𝑒𝑠
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑜𝑏𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑠𝑦𝑠𝑡𝑒𝑚 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑗𝑜𝑏 𝑙𝑎𝑡𝑒𝑛𝑒𝑠𝑠 =
𝛴 𝑓𝑙𝑜𝑤 𝑡𝑖𝑚𝑒𝑠
𝛴 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑡𝑖𝑚𝑒𝑠
𝛴 𝑙𝑎𝑡𝑒 𝑡𝑖𝑚𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑗𝑜𝑏𝑠
Product-Focused Manufacturing
1. Flow shop scheduling – scheduling of flow systems (medium to high volume system with
standardized products, equipment and activities).
2. Level material use – the use of frequent, high quality, small lot sizes that contribute to JIT
production; can shorten monthly cycles from large monthly batches to weekly, daily, or
hourly cycle
a. Determine the minimum lot size that will keep the production process moving
b. Modify the economic production order quantity (POQ) to determine the desired
setup time
Services
Scheduling in the service industry involves scheduling customers, workforce, and equipment
•
•
•
•
•
Scheduling customers is demand management (e.g. appointment system, reservations, FCFS,
most critical first, discount offers, etc.)
Scheduling workforce is capacity management (cyclical scheduling, scheduling daily and
hourly work times, etc.)
Scheduling equipment (reservation system, applicable priority sequencing rules, etc.)
Steps in cyclical scheduling
1. Determine the maximum staffing requirements.
2. Starting with the total number of workers required for each day of the week, create
a schedule by adding 1 worker at a time.
3. Assign the first worker to all the days that require staffing by simply recopying
requirements for each day. A positive number means that workers had been
assigned; zero means no assignment.
4. Circle the two consecutive days with the lowest numbers for the newly assigned
worker. These will be considered for days off.
5. In case of ties, choose the days off pair with the lowest requirement on an adjacent
day before or after the pair. If tie remain, choose arbitrarily.
6. Make a new row for the next employee by subtracting 1 from the preceding row
(because 1 day has been worked) – except for the circled days (which represents the
days not worked) and any day that has a zero (i.e. do not subtract from a circled day
or a day that has a value of zero.
7. In the new row, identify the two consecutive days that have the lowest total
requirements and circle them. Assign the next employee to the remaining days.
8. Repeat steps 6 and 7 until all staffing requirements are met.
Steps in First Hour Principle Procedure
1. Assume that each worker works continuously for 8 hours shift.
2. Assign a number equal to the requirement of that period
3. For each subsequent period, assign the exact number of additional workers to meet
requirements.
4. When in period 1 or more workers come to the end of their shifts, add more
workers only if they are needed to meet the requirements
Practice Problems
1. An excavation company uses both Gantt scheduling chart and Gantt load charts. Today,
which is the end of day 7, the production analyst is reviewing the Gantt chart with the
schedules presented below. Draw the Gantt scheduling chart for the activities specified.
•
•
•
•
•
Job A was scheduled to begin on day 3 and to take 6 days. As of now, it is 1 day ahead of
schedule.
Job B was scheduled to begin on day 1 and take 4 days. It is currently on time.
Job C was scheduled to start on day 7 and take 2 days. It actually got started on day 6
and is progressing according to plan.
Job D was scheduled to begin on day 5, but missing equipment delayed it until day 6. It is
progressing as expected and should take 3 days.
Job E was scheduled to begin on day 4 and take 5 days. It got started on time but has
since fallen behind 2 days.
2. A manufacturer of electronic components is putting out four new products. Each of the four
plants has the capacity to add one more product to its current line of electronic parts. The
unit-manufacturing costs, in USD, for producing the different parts at the four plants are
shown in the table. How should the manufacturer assign the new products to the plants to
minimize manufacturing costs?
Electronic Component
C53
C81
D5
D44
Plant
1
0.10
0.05
0.32
0.17
2
0.12
0.06
0.40
0.14
3
0.13
0.04
0.31
0.19
4
0.11
0.08
0.30
0.15
3. A medical testing company wishes to assign a set of jobs to a set of machines. The following
table provides the production data for each machine when performing the specific job:
Machine
Job
A
7
10
11
9
1
2
3
4
B
9
9
5
11
C
8
7
9
5
D
10
6
6
8
Determine the assignment of jobs to machines that will maximize total production. What is
the total production of your assignment?
4. The following jobs are waiting to be processed at the same machine center. Jobs are logged
as they arrive:
Job
A
B
C
D
Due Date
313
312
325
314
Duration (Days)
8
16
40
5
E
314
3
In what sequence would the jobs be ranked according to the following decision rules: (a)
FCFS, (b) EDD, (c) SPT, (d) LPT, and (e) STR? All dates are specified as manufacturing planning
calendar days. Assume that all jobs arrive on day 275. Which decision is best and why?
5. The following jobs are waiting to be processed. These jobs were logged as they arrived. All
dates are specified as planning calendar days. Assume all jobs arrived on day 180 and
today’s date is 200. Using the critical ratio scheduling rule, in what sequence would the jobs
be processed?
Job
Due Date
103
205
309
412
517
214
223
217
219
217
Remaining Times
(Days)
10
7
11
5
15
6. A lumberyard has four jobs on order, as shown in the following table. Today is day 205 on
the yard’s schedule. In what sequence would the jobs be ranked according to the following
decision rules: (a) FCFS, (b) SPT, (c), LPT, (d), EDD, (e) STR, and (f) critical ratio? Which is best
and why? Which has the minimum lateness?
Job
Due Date
A
B
C
D
212
209
208
210
Remaining Times
(Days)
6
3
3
8
7. Six jobs are to be processed through a two-step operation. The first operation involves
sanding, and the second involves painting. Processing time, in hours, are presented in the
table below. Determine a sequence that will minimize the total completion time for these
jobs. Illustrate graphically.
Job
A
B
C
D
E
F
Operation 1
10
7
5
3
2
4
Operation 2
5
4
7
8
6
3
8. The following jobs are to be processed through two work centers at a printing company. The
sequence is first printing, then binding. Processing time at each work center is shown in the
table below. What is the optimal sequence for these jobs to be scheduled? Chart these jobs
through the two work centers.
Job
A
B
C
D
E
F
Operation 1
10
7
5
3
2
4
Operation 2
5
4
7
8
6
3
9. A barbershop is open seven days a week but has fluctuating demand. The manager analyzed
the staffing needs and resulted in the following plan presented in the table below. Develop a
staff schedule for the barbershop with the minimum number of barbers.
Barbers Needed
Mon.
6
Tue.
5
Wed.
5
Thu.
5
Fri.
6
Sat.
4
Sun.
3
10. Given the following demand for waiters and waitresses at a restaurant, determine the
minimum staff needed with a policy of 2 consecutive days off.
Staff Needed
Mon.
3
Tue.
4
Wed.
4
Thu.
5
Fri.
6
Sat.
7
Sun.
4
References:
Heizer, J., & Render, B. (2011). Operations management (10th ed.). New Jersey, USA: Prentice-Hall
Inc.