Chapter 16 – Scheduling
Enrichment Module: Runout Time Method
Make-to-stock companies produce different products on a common machine or work center. For example,
a paint manufacturing company may decide to mix different colors of paint using the same “mixer.” In
this scenario, the plant manager has to decide how much of different colors of paint to produce in each
batch and the sequence of production. This decision generally is made based on the current level of
inventory, the production rate associated with a particular product, and the rate of demand. The optimal
lot size can be determined using the economic production quantity (EPQ) model, which was covered in
the inventory management chapter and balances the trade-off between carrying cost and the setup cost.
However, when several products share a common machine or work center for production, the batch sizes
may need to be modified because the product sequencing may affect cost also. If the setups are sequence-
dependent, sequence of the items may be important in making the sequencing decision at the common
machine or work center. In addition, the EPQ model covered in the inventory chapter does not take into
account the level of inventory. Therefore, using the EPQ model may result in too much inventory for
some items and not enough inventory for other items. The EPQ model also is not designed for scheduling
specific work centers. Instead, the “runout time” method of scheduling can be utilized to determine
production runs for a group of items that share the same machine or work center. The basic objective of
this method is to balance the utilization of the machine or work center across all products that share this
machine or work center such that the demand is satisfied and the inventory is minimized. In other words,
production is balanced across all products using the common machine or work center rather than
concentrating on a few products while ignoring the other products.
There are two versions of the runout time method available:
1. Aggregate runout time method: This method is used if the lot size is variable.
2. Individual runout time method: This method is used if there are fixed lot sizes.
Aggregate Runout Time Method
First, we will illustrate the aggregate runout time method with the following example.
Kim Reuter starts her own company producing computer diskettes, CD-ROMs, DVDs, and cassette tapes.
All of these products are processed by the “Blue Monster,” an automated assembly line to produce these
schedule that would achieve her objective using the aggregate runout time method.
Item
Inventory
Production time (hours/unit)
Forecast in units (per week)
Diskettes
94
.10
85
CD–ROMs
50
.15
150
Cassettes
117
.30
60
DVDs
150
.60
120
16–81
To solve this problem, first we must convert all the inventory and forecasted demand into machine hours
by multiplying each by the production time/unit (hours). Once we have the inventory and the forecasted
demand stated in machine hour terms, then we need to sum the machine hours for inventory and
forecasted demand. After obtaining these totals, we must determine the aggregate runout time. The basic
principle behind the aggregate runout time formula is that we need to manufacture a sufficient quantity of
all products so that they will last until a future time period called the “runout time,” when theoretically we
would run out of all the parts at the same time. The aggregate runout time is based on the inventory and
To determine the aggregate runout time, we will utilize the following table:
Item
Production
time/unit
(hours)
Forecasted
demand
(units)
Inventory
(hours)
Forecasted
demand
(hours)
Runout
time
(in weeks)
Diskettes
.10
94
85
9.4
8.5
2
CD–ROMs
.15
150
7.5
22.5
2
Cassettes
.30
60
35.1
18.0
2
DVDs
.60
120
90.0
72.0
2
Totals
142.0
121.0
weeks 2
121
100142
erunout tim Aggregate
Because the aggregate runout time is 2 weeks, we need to have 2 weeks of supply of each item, given our
current inventory levels. The following table illustrates the calculation to determine the production
quantity by the production time per unit to determine the length of the production run for each item. The
sum of the hours in the last column must add up to the production capacity of the machine. Therefore, the
sum of the values in the last column can serve as a “check” value. If the sum does not equal the
production capacity specified, then we made a mistake and need to go back and correct it.
Chapter 16 – Scheduling
Item
Production
Time
(in hrs.)
(1)
Inventory
(in units)
(2)
Forecast
(in units)
(3)
ROT
(in
weeks)
(4)
# of items
needed
(5)=(3)x(4)
Production
schedule
(in units)
(6)=(5)–(2)
Production
schedule
(in machine
hrs.)
(7)=(1)x(6)
Diskettes
.10
94
85
2
170
76
7.6
CD–ROMs
.15
50
150
2
300
250
37.5
Cassettes
.30
117
60
2
120
3
0.9
DVDs
.60
150
120
2
240
90
54.0
Totals
100.0
Individual Runout Time Method
In many situations, the aggregate runout time method described above is inadequate because the company
produces products in fixed lot sizes. Note that in the table given above, we are scheduled to manufacture
only three cassettes. This may not be an acceptable lot size—especially if the setup cost is significant. If
the company has fixed lot sizes, we can utilize the individual runout time method. Instead of calculating
an aggregate runout time for all items, we will calculate a runout time for each item. The individual
runout time (ROT) is: ROT = inventory level /forecasted demand. In other words, the individual runout
CD-ROMs = 260 units
Cassettes = 150 units
DVDs = 60 units
Use the runout method to determine the production schedule. Remember that Kim has 100 machine hours
available per week.
Summing the lot-size hours (20 + 39 + 45 +36) = 140, we see that the production capacity (100 hours) is
less than the required hours for all four products. Therefore, because not all four products can be
manufactured within a week, we need to sequence the products in ascending order of their individual
runout times. This way, the product that we are running out of the fastest is scheduled to be manufactured
first. Using this logic, the runout times for the four products are:
Chapter 16 – Scheduling
Education.
weeksROTweeksROT
weeksROTweeksROT
DVDcassette 25.1
120
150
; 95.1
60
117
33.
150
50
; 11.1
85
94
ROMCDdiskette
Based on the above calculations, the sequence of production in ascending order of runout times is:
1. CD–ROMs, 2. Diskettes, 3. DVDs, and 4. Cassettes. Based on this order, the week’s production
schedule is summarized in the following table:
Sequence
Machine hours
required
Cumulative machine
hours
Week’s production
schedule in units
CD–ROMs
39
39
260 units
Diskettes
20
59
200 units
DVDs
36
95
60 units
Cassettes
45
140
150 units
Totals
140
(40 hours over)
Note that we will exceed the weekly capacity after scheduling DVDs for production. The question is,
“How many cassettes can we manufacture within the remaining time of the week?” After producing
DVDs, we have 5 hours left (100 – 95) to manufacture the cassettes. Because each cassette takes .30
hours to manufacture, the estimated number of cassettes that we can manufacture during this week = 5 /
.30 = 16.67 = 16 units (round down). The revised production schedule is shown below:
Sequence
Machine hours
required
Cumulative machine
hours
Week’s production
schedule in units
CD–ROMs
39.0
39.0
260 units
Diskettes
20.0
59.0
200 units
DVDs
36.0
95.0
60 units
Cassettes
4.8
99.8
16 units
Totals
99.8
We would like to demonstrate the continuous nature of this process by showing the transition from one
week to another. We will assume that time has passed, and the week has gone by. Kim checks the
company records and determines that the company has sold the following quantities of each item:
Diskettes = 100 units
Chapter 16 – Scheduling
Update the inventory records for the next week and determine the new runout time for each product:
Using the following formula, we can update the inventory records.
Beginning inventory (current week) = Beginning inventory (prior week) + production (prior week) –
actual demand (prior week).
Beginning inventory for Diskettes (current week) = 94 + 200 – 100 = 194 units
Beginning inventory for CD-ROMs (current week) = 50 + 260 – 170 = 140 units
Beginning inventory for Cassettes (current week) = 117 + 16 – 50 = 83 units
Beginning inventory for DVDs (current week) = 150 + 60 – 140 = 70 units
Item
Production
time per unit
Lot size in
units
Inventory in
units
Forecasted
demand in units
Runout time
in weeks
Diskettes
.10
200
194
85
2.28 weeks
CD–ROMs
.15
260
140
150
0.93 weeks
Cassettes
.30
150
83
60
1.38 weeks
DVDs
.60
60
70
120
0.58 weeks
Based on these updated runout times, the new sequence is as follows:
1. Cassettes: Even though cassettes do not have the lowest ROT, we have to finish the lot that was
2. DVDs
3. CD–ROMs
4. Cassettes
5. Diskettes
Sequence
Machine hours
required
Cumulative
Machine hours
Week’s production
schedule in units
Cassettes
40.2
40.2
134
DVDs
36.0
76.2
60
CD–ROMs
39.0
115.2
260
Totals
115.2
(15.2 hours over)
Note: We run out of time when producing CD-ROMs. We have 100 – 76.2 = 23.8 hours available for CD-
ROMs. Therefore, the number to schedule = 23.8 / .15 = 158.67 = 158 units (round down). The revised
schedule is shown below:
Sequence
Machine hours
required
Cumulative
Machine hours
Week’s production
schedule in units
Cassettes
40.2
40.2
134
DVDs
36.0
76.2
60
CD–ROMs
23.7
99.9
158
Totals
99.9
16–85
Education.
Problems
1. Given the following data and 95 hours available per week for production, use the individual
runout time method of scheduling and determine the runout time sequence, batch production
times, and scheduled production quantity for each product.
Product
Production
time/unit (hours)
Lot size
Inventory
(units)
Forecasted
demand
(units/week)
A
.25
160
120
100
B
.10
120
140
120
C
.40
100
150
80
D
.30
80
100
70
2. Given the following data and 91 hours available per week for production, use the aggregate
runout time method of scheduling and determine the aggregate runout time, batch production
times, and scheduled production quantity for each product.
Product
Production
time/unit (hours)
Inventory
(units)
Forecasted
demand
(units/week)
A
.25
120
100
B
.10
140
120
C
.40
150
80
D
.30
100
70
Chapter 16 – Scheduling
16–86
Education.
Solutions to problems
1.
weeksROTweeksROT
weeksROTweeksROT
DC
BA
43.1
70
100
; 88.1
80
150
17.1
120
140
; 20.1
100
120
Sequence
Machine hours
required
Cumulative
Machine hours
Week’s production
schedule in units
B
12.0
12
120 units
A
40.0
52
160 units
D
24.0
76
80 units
C
18.8
94.8
47* units
Totals
94.8
*
units 475.47
40
7695
C sizeLot
.
(round down)
2.
Item
Production
time/unit
(hours)
Inventory
(units)
Forecasted
demand
(units)
Inventory
(hours)
Forecasted
demand
(hours)
Runout
time
(in weeks)
A
.25
120
100
30
25
2.5
B
.10
140
120
14
12
2.5
C
.40
150
80
60
32
2.5
D
.30
100
70
30
21
2.5
Totals
134
90
weeks 5.2
90
91134
erunout tim Aggregate
Chapter 16 – Scheduling
Solutions to problems
2. continued
Item
Production
Time
(in hrs.)
(1)
Inventory
(in units)
(2)
Forecast
(in units)
(3)
ROT
(in weeks)
(4)
# of items
needed
(5)=(3)x(4)
Production
schedule
(in units)
(6)=(5)–(2)
Production
schedule
(in machine
hrs.)
(7)=(1)x(6)
A
.25
120
100
2.5
250
130
32.5
B
.10
140
120
2.5
300
160
16.0
C
.40
150
80
2.5
200
50
20.0
D
.30
100
70
2.5
175
75
22.5
Totals
91.0