The port of Lajitas has three loading docks. The distance (in meters) between the loading docks is given in the following table. 23 Tanker 2 Tanker 3 Three tankers currently at sea are coming into Lajitas. It is necessary to assign a dock for each tanker. Also, only one tanker can anchor in a given dock. Currently, ships 2 and 3 are empty and have no cargo. However, ship 1 has cargo that must be loaded onto the other two ships. The number of tons that must be transferred are as follows. 1 Dock 1 10 100 150 100 0 50 3 150 50 0 Formulate and solve an optimization problem with binary decision variables (where 1 means an assignment and 0 means no assignment) that will assign ships to docks so that the product of tonnage moved times distance is minimized. There are 12 nonzero terms in the objective function. (Hints: This problem is an extension of the assignment problem introduced in Chapter 6. Also, be careful with the objective function. Only include the nonzero terms. Each of the 12 nonzero terms in the objective function is a quadratic term, or the product of two variables.) Let X-1 if tanker / is assigned loading dock / and 0 if not. First consider the constraints. Every tanker must be assigned to a loading dock. These constraints are as follows. Tanker 1 Dock 2 Dock 3 2 100 To 1 2 3 From 1 070 90 -1 Since there are three tankers and three loading docks each loading dock must be assigned to a tanker. These constraints are as follows. -1 -1 1 -1 -1
The port of Lajitas has three loading docks. The distance (in meters) between the loading docks is given in the following table. 23 Tanker 2 Tanker 3 Three tankers currently at sea are coming into Lajitas. It is necessary to assign a dock for each tanker. Also, only one tanker can anchor in a given dock. Currently, ships 2 and 3 are empty and have no cargo. However, ship 1 has cargo that must be loaded onto the other two ships. The number of tons that must be transferred are as follows. 1 Dock 1 10 100 150 100 0 50 3 150 50 0 Formulate and solve an optimization problem with binary decision variables (where 1 means an assignment and 0 means no assignment) that will assign ships to docks so that the product of tonnage moved times distance is minimized. There are 12 nonzero terms in the objective function. (Hints: This problem is an extension of the assignment problem introduced in Chapter 6. Also, be careful with the objective function. Only include the nonzero terms. Each of the 12 nonzero terms in the objective function is a quadratic term, or the product of two variables.) Let X-1 if tanker / is assigned loading dock / and 0 if not. First consider the constraints. Every tanker must be assigned to a loading dock. These constraints are as follows. Tanker 1 Dock 2 Dock 3 2 100 To 1 2 3 From 1 070 90 -1 Since there are three tankers and three loading docks each loading dock must be assigned to a tanker. These constraints are as follows. -1 -1 1 -1 -1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The complete objective function is found by considering the result of assigning tankers to docks and the product of distance and tonnage moved.
] )·X₁1*X32 + ( [
·X₁1X22 + ( [
]).X13X21+
X₁1X23+ ([
]).X13X22 + (
X₁1X33+ ([
X13*X32
Complete the solution to the model. Let X;;= 1 if tanker / is assigned loading dock j and 0 if not.
X11 =
X12 =
X13 =
X21 =
MIN =
X22 =
X23 =
X31 =
X32 =
X33 =
Objective value
Thus tanker 1 should be assigned to dock -?--, tanker 2 to dock --?-- and tanker 3 to dock --?--✓.
·X₁2²X21 + ([
X₁2²X₂23 + ([
·X₁2²X31 + ( [
]).X12*X33](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F862c5bc2-e09a-4feb-bd28-f7638a835094%2F0c3fd139-8af4-4c84-b6c4-04cbcd6d3884%2Fogqpyhq_processed.png&w=3840&q=75)
Transcribed Image Text:The complete objective function is found by considering the result of assigning tankers to docks and the product of distance and tonnage moved.
] )·X₁1*X32 + ( [
·X₁1X22 + ( [
]).X13X21+
X₁1X23+ ([
]).X13X22 + (
X₁1X33+ ([
X13*X32
Complete the solution to the model. Let X;;= 1 if tanker / is assigned loading dock j and 0 if not.
X11 =
X12 =
X13 =
X21 =
MIN =
X22 =
X23 =
X31 =
X32 =
X33 =
Objective value
Thus tanker 1 should be assigned to dock -?--, tanker 2 to dock --?-- and tanker 3 to dock --?--✓.
·X₁2²X21 + ([
X₁2²X₂23 + ([
·X₁2²X31 + ( [
]).X12*X33
Transcribed Image Text:The port of Lajitas has three loading docks. The distance (in meters) between the loading docks is given in the following table.
Tanker 1
Three tankers currently at sea are coming into Lajitas. It is necessary to assign a dock for each tanker. Also, only one tanker can anchor in a given dock. Currently, ships 2 and 3 are empty and have no cargo. However, ship 1 has cargo that must be loaded onto the other two ships. The number of tons
that must be transferred are as follows.
Tanker 2
Tanker 3
2 3
10 100 150
100 0 50
3 150 50 0
Dock 1
1
2
Dock 2
Dock 3
Formulate and solve an optimization problem with binary decision variables (where 1 means an assignment and 0 means no assignment) that will assign ships to docks so that the product of tonnage moved times distance is minimized. There are 12 nonzero terms in the objective function. (Hints: This
problem is an extension of the assignment problem introduced in Chapter 6. Also, be careful with the objective function. Only include the nonzero terms. Each of the 12 nonzero terms in the objective function is a quadratic term, or the product of two variables.)
Let X;;= 1 if tanker i is assigned loading dock j and 0 if not.
First consider the constraints. Every tanker must be assigned to a loading dock. These constraints are as follows.
1
To
From 1 0 70 90
2
= 1
= 1
Since there are three tankers and three loading docks each loading dock must be assigned to a tanker. These constraints are as follows.
= 1
= 1
= 1
3
= 1
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