**Order Instructions/Description**

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

Business Management 2321

Practical Exercise #5

(Individual / Groups of 2, 3, or 4 from same recitation)

Refer to Class Schedule for Due Date

Transshipment Problem (Continued)

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 toal cost.

Business Management 2321

Practical Exercise #5

(Individual / Groups of 2, 3, or 4 from same recitation)

Refer to Class Schedule for Due Date

Goal Programming Problem

A small financial company is considering 12 projects (A through L) and it trying to determine which of the projects it should implement in an effort to attain 7 management goals. The ratings for each of the projects are given in the table below.

Projects

A B C D E F G H I J K L

Goal 1 4 10 6 4 6 6 2 8 8 4 8 16

Goal 2 4 5 2 6 1 3 5 1 7 2 2 5

Goal 3 63 65 37 39 48 42 28 56 58 32 68 55

Goal 4 600 350 50 100 600 400 150 700 200 300 500 100

Goal 5 600 800 1600 4400 2000 3000 1200 1600 1600 1200 800 2200

Goal 6 1 3 2 7 8 4 6 1 2 4 3 6

Goal 7 5 3 4 2 3 3 2 5 4 1 4 1

The company has set the following eight goals:

Goal 1 (weight of 60) total should be less than or equal to 12

Goal 2 (weight of 80) total should be less than or equal to 50

Goal 3 (weight of 10) total should be greater than or equal to 400

Goal 4 (weight of 70) total should be greater than or equal to 5550

Goal 5 (weight of 50) total should be equal to 10,000

Goal 6 (weight of 20) total should be equal to 24

Goal 7 (weight of 40) total should be greater than or equal to 70

Goal 8 (weight of 30) total number of projects should be equal to 12

1. Formulate the problem as a binary integer program with 12 decision variables and 8 constraints. Maximize the number of projects.

Note: The problem will be INFEASIBLE!

2. Formulate the goal program to minimize weighted deviations. The model has 12 decision variables, 16 deviation variables, and 8 constraints.

3. Formulate the goal program to minimize percent deviations. The model has 12 decision variables, 16 deviation variables, and 8 constraints.Business Management 2321

Practical Exercise #5

(Individual / Groups of 2, 3, or 4 from same recitation)

Refer to Class Schedule for Due Date

Exercise Procedure (Transshipment Problem)

Download the EXCEL templates for Practical Exercise #5 from Carmen.

Do not modify the labels, column widths, or column heights on the template.

Using the “Transshipment” tab, input the objective function coefficients, constraint coefficients, and constraint RHS values.

Determine the optimal solution using Solver.

Exercise Procedure (Goal Program Problem)

Download the EXCEL templates for Practical Exercise #5 from Carmen.

Do not modify the labels, column widths, or column heights on the template.

Using the “Hard Constraint” tab, input the objective function coefficients, constraint coefficients, and constraint RHS values.

The decision variables for the projects should be binary.

Determine the optimal solution using Solver. The formulation will give you an infeasible solution.

Using the “Weighted Deviation” tab, convert the hard constraints into soft constraints by adding an underachieving deviation variable, subtracting an overachieving deviation variable, and setting the sign of the constraint to “=”.

The objective function values for the undesirable deviation variables should be the weights as specified in the problem.

The decision variable for the projects should be binary; the deviation variables should remain as continuous.

Determine the optimal solution using Solver.

Using the “Percent Deviation” tab, convert the hard constraints into soft constraints by adding an underachieving deviation variable, subtracting an overachieving deviation variable, and setting the sign of the constraint to “=”.

The objective function values for the undesirable deviation variables should be the 1/RHS

The decision variable for the projects should be binary; the deviation variables should remain as continuous.

Determine the optimal solution using Solver.

Business Management 2321

Practical Exercise #5

(Individual / Groups of 2, 3, or 4 from same recitation)

Refer to Class Schedule for Due Date

Exercise Requirements

(a) Cover sheet will all team member names in alphabetical order [1 page portrait].

(b) Transshipment Problem – Using Print Setup, print the worksheet 1 page high and 2 pages wide, landscape, and centered with margins set to 0.25”. [2 pages landscape].

(c) Goal Program (Hard Constraints) – Using Print Setup, print the worksheet 1 page high and 1 pages wide, landscape, and centered with margins set to 0.25”. [1 pages landscape].

(d) Goal Program (Weighted Deviation) – Using Print Setup, print the worksheet 1 page high and 1 pages wide, landscape, and centered with margins set to 0.25”. [1 pages landscape].

(e) Goal Program (Weighted Deviation) – Using Print Setup, print the worksheet 1 page high and 1 pages wide, landscape, and centered with margins set to 0.25”. [1 pages landscape].

Points will be deducted for professionalism!

The exercise cover page and all decision analysis must be typed!

The exercise cover page should have the student’s last name and first name as specified on Carmen (your last name is the name on your OSU e-mail account).

The exercise cover page should have the brackets removed around the last name, first name, and student number.

The exercise must be printed in black/white with no color, shading, or highlighting

The format of the spreadsheets (cell widths, cell heights, and fonts) should not be modified.

The exercise output cannot extend off the side or bottom of page

The exercise should not include excess output (this individual practical exercise is 6 pages)

The exercise should not be printed on both sides of the sheet of paper (duplex printed).

The exercise should not be stapled incorrectly (see file regarding stapling on Carmen)

The exercise should not be printed on “used” paper (excess printing on the front and/or back of the report)

The exercise must be stapled and should not have a physical (i.e. plastic) report cover or be bound.

No late submissions will be accepted!

Individual practical exercise can be submitted early to Dr. Mark, Professor Klinker, or to the Management Sciences office (600 Fisher). The individual practical exercises submitted to the Management Sciences office will be date/time stamped upon receipt. No individual practical exercises will be accepted by the TAs.

No electronic submissions via e-mail.

Have your individual practical exercise completed and printed the day before it is due to allow for “unforeseen” problems (i.e. printer breakdown, loss of computer file, etc.)

DO NOT PROCRATINATE IN WORKING ON YOUR INDIVIDUAL PRACTICAL EXERCISE!

No unsigned individual practical exercises will be accepted!

Do not type your name on the signature line or the date line of the cover sheet.

Business Management 2321

Practical Exercise #5

(Groups of up to 4 from same recitation or Individual)

Due Per Syllabus Schedule

This cover sheet must be filled in completely and signed to be accepted

Do not modify this cover sheet by erasing text or by changing the font.

Names must appear in alphabetical order sorted on last name.

All material must be stapled to the cover page.

By signing below, I/we attest that I/we have performed this analysis. I understand that any violation of this statement by handing in another student’s work as my/our own will result in a suspected case of academic misconduct.