Week 4 BUSN 312 Homework
docx
School
American Military University *
*We aren’t endorsed by this school
Course
312
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
docx
Pages
5
Uploaded by AdmiralBear2937
Week 4 Assignment: Transportation Problem
John DOe
American Military University COURSE BUSN312: Operations Research
DR. Matasha Murrell Murrell Jones
28 May 2023
1. Find the minimum cost solution for the following transportation problem which has cost structure as:
To/From
P
Q
R
Availabili
ty
A
16
19
12
14
B
22
13
19
16
C
14
28
18
12
Requirem
ent
10
15
17
The first step is to find the cell with the lowest cost, which in this case is the cell (A, R) with a cost of 12. Next, we allocate the maximum possible quantity to the cell (A, R) based on the minimum value of availability and requirement (14 availability/17 requirement), in this case
is 14. The next step is to update the availability and requirement values based on the allocation made. Finally, since the availability of 14 has been exhausted, the rest of row A can be
eliminated as shown below:
To/From
P
Q
R
Availabili
ty
A
16
19
12 14
14
0
B
22
13
19
16
C
14
28
18
12
Requirem
ent
10
15
17 3
The above steps are repeated choosing the following available lowest cost, which in this case is cell (B, Q) with a value of 13. The updated table is shown below:
To/From
P
Q
R
Availabili
ty
A
16
19
12
14
14
0
B
22
13
15
19
16 1
C
14
28
18
12
Requirem
ent
10
15
0
17 3
After all the supply and demand values have been exhausted, the table is completed as follows:
To/From
P
Q
R
Availabili
ty
A
16
19
12
14
14,
0
B
22
13
15
19
1
16, 1
, 0
C
14
10
28
18
2
12, 2
, 0
Requirem
ent
10
0
15
0
17
3, 1
, 0
The transportation cost is then calculated by performing a multiplication of the individual combinations and adding all values:
TC= (14x12) + (15 x 13) + (10 x 14) + (2 x 18) + (1 x 19)
TC= 168 + 195 + 140 + 36 + 19, that equals 558.
2. Briefly describe the Simplex method, Goal Programming, and Integer Programming.
The Simplex method is an algorithm used to solve linear programming problems. An approach that improves the solution until an optimal solution is reached. The method starts with an initial feasible solution and then iteratively moves to adjacent feasible solutions that improve the objective function value. The algorithm continues until no further improvement is possible, indicating the optimal solution. The Simplex method is popular due to its efficiency and effectiveness in solving linear programming problems.
Goal Programming is an optimization technique to solve problems with conflicting objectives or goals. Unlike traditional linear programming, where there is a single objective to
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
maximize or minimize, goal programming allows for the consideration of multiple objectives simultaneously. Each objective is assigned a range of acceptable values, and the goal programming algorithm finds the best compromise solution that minimizes deviations from the target values. It provides flexibility to balance different objectives and is commonly used when trade-offs exist between conflicting goals.
Integer Programming is an optimization technique for solving problems where decision variables must take on integer values rather than continuous ones. This integer requirement often arises in real-world scenarios where decisions must be made in whole units or discrete quantities. These types of problems are generally more challenging to solve compared to linear programming due to the combinatorial nature of integer solutions.
In summary, the Simplex method solves linear programming problems, Goal Programming handles multiple conflicting objectives, and Integer Programming addresses optimization problems with discrete decision variables. Each technique provides a framework to find optimal or near-optimal solutions based on specific problem requirements and constraints.
In conclusion, the simplex method is efficient and solves complex mathematical problems and tells us if the solutions is optimal. Goal programming is used to deal with conflicting and different goals and prioritizes between them
Resources
Sharma, A. (n.d.). ProQuest Ebook Central. https://ebookcentral.proquest.com/lib/fjpw/home.action