Transshipment Problem:-
MAC Transport is trying to minimize their shipping costs for next week. The company has been contracted to ship drums of 3 different chemicals. The transshipment network is shown below:
The table below gives the capacity of each product for each source:
|
|
Source A
|
Source B
|
Source C
|
Source D
|
|
Product 1
|
90
|
65
|
95
|
40
|
|
Product 2
|
70
|
60
|
80
|
75
|
|
Product 3
|
55
|
80
|
65
|
55
|
The table below gives the demand of each product for each source:
|
|
Destination G
|
Destination H
|
Destination I
|
Destination J
|
|
Product 1
|
80
|
60
|
85
|
40
|
|
Product 2
|
85
|
70
|
70
|
60
|
|
Product 3
|
55
|
65
|
50
|
80
|
The tables below give the shipping costs between nodes for each product:
|
Product 1
|
Source A
|
Source B
|
Source C
|
Source D
|
|
Warehouse E
|
$7
|
$3
|
$4
|
$8
|
|
Warehouse F
|
$5
|
$4
|
$6
|
$5
|
|
Product 1
|
Destination G
|
Destination H
|
Destination I
|
Destination J
|
|
Warehouse E
|
$6
|
$7
|
$9
|
$6
|
|
Warehouse F
|
$8
|
$6
|
$7
|
$4
|
|
Product 2
|
Source A
|
Source B
|
Source C
|
Source D
|
|
Warehouse E
|
$14
|
$7
|
$3
|
$7
|
|
Warehouse F
|
$20
|
$7
|
$12
|
$6
|
|
Product 2
|
Destination G
|
Destination H
|
Destination I
|
Destination J
|
|
Warehouse E
|
$10
|
$3
|
$4
|
$5
|
|
Warehouse F
|
$8
|
$12
|
$7
|
$12
|
|
Product 3
|
Source A
|
Source B
|
Source C
|
Source D
|
|
Warehouse E
|
$10
|
$14
|
$16
|
$13
|
|
Warehouse F
|
$12
|
$13
|
$15
|
$13
|
|
Product 3
|
Destination G
|
Destination H
|
Destination I
|
Destination J
|
|
Warehouse E
|
$9
|
$12
|
$12
|
$11
|
|
Warehouse F
|
$14
|
$16
|
$18
|
$16
|
The total capacity for each warehouse (total of the three products) is 420.
Federal regulations prohibit the shipping of product 2 from warehouse E to destination H and from warehouse E to destination J.
Formulate a linear program to optimize total cost. Use the EXCEL template provided on Carmen.
Attachment:- Transshipment-Problem--.xlsx
Maximal Flow Problem:-
Nick Nugent (an OSU alumni) is employed as a shipping supervisor for ASC Corporation. He has just received a panic phone call from the company's facility in Boston that the scheduled shipment of parts is delayed and that additional parts have to be sent from Los Angeles overnight. Nick contacts LCC Express which is an overnight shipping service that serves Atlanta (ATL), Boston (BOS), Chicago (ORD), Dallas (DFW), Denver (DEN), Los Angeles (LAX), Philadelphia (PHL), and San Francisco (SFO). Since the company's Boston facility can use as many parts as can be shipped, LCC needs to calculate the maximum number that it can ship for Nick. LCC collects information on the remaining available capacity on tonight's flights; the possible shipping lanes are shown on the network below and the capacity on each shipping lane is shown in the table below. Assume that there is adequate time at each airport to unload the parts from the arriving plane and load the parts on the next plane. Formulate as a linear program and determine the maximum number of parts that can be shipped from Los Angeles to Boston using LCC?
The table below gives the maximum shipments for each of the shipping lanes.
|
From
|
To
|
Maximum
|
|
From
|
To
|
Maximum
|
|
From
|
To
|
Maximum
|
|
ATL
|
BOS
|
50
|
|
DFW
|
ORD
|
20
|
|
ORD
|
BOS
|
60
|
|
ATL
|
PHL
|
10
|
|
DFW
|
PHL
|
20
|
|
ORD
|
PHL
|
30
|
|
DEN
|
ATL
|
40
|
|
LAX
|
DEN
|
30
|
|
PHL
|
BOS
|
80
|
|
DEN
|
ORD
|
40
|
|
LAX
|
DFW
|
20
|
|
SFO
|
DEN
|
70
|
|
DEN
|
PHL
|
30
|
|
LAX
|
ORD
|
10
|
|
SFO
|
DFW
|
40
|
|
DFW
|
ATL
|
10
|
|
LAX
|
SFO
|
40
|
|
SFO
|
ORD
|
30
|
Use the EXCEL template provided on Carmen.
Attachment:- Maximal-Flow-Problem--.xlsx
Shortest Path Problem:-
Mike Mangold (another OSU alumni) is anxious about leaving work and driving to see his "significant other" for the weekend. He also took Dr. Mark's BusMgt 2321 class and wants to use what he learned in class to solve the problem. He has analyzed the roads from his office (Node "L") and this destination (Node "A"). The network is shown below. Formulate as a linear program to determine the shortest distance between nodes "L" and "A" and what path yields that shortest distance?
Use the EXCEL template provided on Carmen.
Attachment:- Shortest-Path-Problem--.xlsx