# EmptyCarrierTripsEstimation 180328 (1)

```ISyE 4024 Fund. of Materials Handling
5 May 99
Empty Carrier (Vehicle) Trip Analysis
some more typos fixed
The first table below represents the loaded trips to be moved in a network during a time period.
We wish to estimate the empty carrier (vehicle) trips. Three methods are presented.
1. Simple factoring
2. Transportation assignment problem
3. First-order approximation followed by factoring
Per Hour
11
12
13
14
15
16
From:
Inbound
Basic
Data:
0, 1, 2
1. Best
Case:
3, 4, 5
0.
1.
2.
3.
4.
5.
2. Worst 6.
Case: 7.
6, 7, 8
8.
3. First- 9.
Order
11
4
9
11
0
14
38
Station
Dual Operations,
min. of the two values
Excess, Empty
Deficit, Empty
Dual Operations
Excess, Empty
Deficit, Empty
Appxn. 10 Dual Operations,
opportunistic
9-12
11 Excess, Empty
12 Deficit, Empty
To:
13
12
20
2
0
7
41
12
13
7
6
0
3
29
11
38
32
32
12
29
44
29
6
14
5
11
10
0
22
48
15
2
9
1
0
5
17
16
0
0
0
0
0
-
13
41
27
27
14
48
19
19
15
17
0
0
14
29
17
Outbound
32
44
27
19
0
51
173
16
0
51
0
Total
173
173
107
51
0
0
51
66
66
0
173
173
N/A
0
38
32
15
0
29
44
0
41
27
0
48
19
0
17
0
38 x
0.2/60 =
0.127
0.127 x 32
= 4.1
29 x
0.2/60 =
0.097
0.097 x 44
= 4.3
41 x
0.2/60 =
0.137
0.137 x 27
= 3.7
48 x
0.2/60 =
0.160
0.160 x 19
= 3.0
17 x
0.2/60 =
0.057
0.057 x 0
=0
0 x 51
=0
15.1
33.9
27.9
24.7
39.7
37.3
23.3
45.0
16.0
17.0
0
0
51.0
157.9
157.9
0
Method 1. Best case: solve the transportation assignment problem with supplies as follows:
11:6, 13:14, 14:29, and 15:17; see line 4 in table above; and demands as follows: 12:15 and 16:51;
see line 5 in table above. This gives a theoretical lower bound for the empty travel trips
between stations, but it might not be achievable in practice.
Method 2. The table below illustrates simple factoring. Lines 7 and 8 give the excess and deficit of vehicles at
each station under the assumption that there are no “opportunistic” dual operations. Simple factoring is
equivalent to a first-come, first-serve (FCFS) dispatching rule where transport requests are assigned to the next
free carrier. It will assign a carrier that has just unloaded to another station if a request there has a higher time
stamp than a request at the same station. The sum of dual operations is 26.1. Outbound and Inbound Totals
do not include diagonal elements since we are focusing on empty trips. The diagonal elements (lightly shaded)
represent probabilistic dual operations (carrier unloads and then loads at the same station), as a result of the
FCFS dispatching.
EmptyCarrierTripsEstimation_180328
ISyE 4024 Fund. of Materials Handling
2. Factoring
after
worst case:
11
12
From:
13
14
15
16
Inbound
5 May 99
To:
11
12
13
14
15
16
Outbound
32x38/173
= 7.0
32x29/173
= 5.4
32x41/173
= 7.6
32x48/173
= 8.9
32x17/173
= 3.1
32x0/173 =
0
44x38/173
= 9.7
44x29/173
= 7.4
44x41/173
= 10.4
44x48/173
= 12.2
44x17/173
= 4.3
44x0/173 =
0
27x38/173
= 5.9
27x29/173
= 4.5
27x41/173
= 6.4
27x48/173
= 7.5
27x17/173
= 2.7
27x0/173
=0
19x38/173
= 4.2
19x29/173
= 3.2
19x41/173
= 4.5
19x48/173
= 5.3
19x17/173
= 1.9
19x0/173 =
0
0x38/173
=0
0x29/173
=0
0x41/173
=0
0x48/173
=0
0x17/173
=0
0x0/173 =
0
51x38/173
= 11.2
51x29/173
= 8.5
51x41/173
= 12.1
51x48/173
= 14.2
51x17/173
= 5.0
51x0/173
=0
31.0
25
36.6
20.6
13.8
0
51
147
21.6
34.6
42.8
17.0
0
The table below illustrates Method 3, factoring after first-order approximation. The data used are from lines
10 – 12 in the first table. Lines 9 – 10 present the results of “opportunistic dual operations”; these occur when a
carrier is unloading at a station and an outbound load arrives at that station (it would be foolish to send the
carrier away empty). The sum of these opportunistic dual operations is 15.1/period. The remaining outbound
requests are handled by the factoring (FCFS) method described earlier. The factoring method then results in an
additional, 22.3 probabilistic dual operations (shown lightly shaded), for a total of (15.1 + 22.3) = 37.4 dual
operations, involving no travel time. The Outbound and Inbound Totals in the table below ignore diagonal
elements, since they do not involve travel.
3. Factoring after
1st Order Appxn.
From:
12
14
15
0x33.9/
157.9 = 0
11
39.7x33.9/
27.9x33.9/
157.9 = 8.5
157.9 = 6.0
23.3x33.9/
157.9 = 5.0
16x33.9/
157.9 = 3.4
12
27.9x24.7/
157.9 =
4.4
27.9x37.3/
157.9 =
6.6
27.9x45.0/
157.9 =
8.0
27.9x17.0/
157.9 =
3.0
27.9x0/
157.9 = 0
39.7x24.7/
157.9 = 6.2
23.3x24.7/
157.9 = 3.6
16x24.7/
157.9 = 2.5
39.7x37.3/
157.9 = 9.4
23.3x37.3/
157.9 = 5.5
16x37.3/
157.9 = 3.8
39.7x45.0/
157.9= 11.3
23.3x45.0/
157.9 = 6.6
16x45.0/
157.9 = 4.6
39.7x17.0/
157.9 = 4.3
23.3x17.0/
157.9 = 2.5
16x17.0/
157.9 = 1.7
39.7x0/
157.9 = 0
23.3x0/
157.9 = 0
16x0/ 157.9
= 0
33.5
17.7
11.4
13
14
15
16
Inbound
11
To:
13
22
16
51x33.9/
157.9 =
10.9
0x24.7/
51x24.7/
157.9 = 0
157.9 =
8.0
0x37.3/
51x37.3/
157.9 = 0
157.9 =
12.0
0x45.0/
51x45.0/
157.9 = 0
157.9 =
14.5
0x17.0/
51x17.0/
157.9 = 0
157.9 =
5.5
0x0/ 157.9 51x0/ 157.9
= 0
= 0
0
50.9
Outbound
27.8
18.5
31.8
40.4
17.0
0
135.5