Transportation Problem, Integer and Binary Programming, and Goal Programming

ADM2302 M, N, P and Q Assignment # 3

Winter 2020 Page 1

Assignment # 3

Transportation Problem, Integer and Binary Programming, and Goal Programming

ADM2302 students are reminded that submitted assignments must be typed (i.e. can NOT be hand

written), neat, readable, and well-organized. Assignment marks will be adjusted for sloppiness, poor

grammar, spelling, for technical errors as well as if you submit a PDF file.

The assignment is to be submitted electronically as a single Word Document file via Brightspace by

the NEW DATE on Tuesday March 24th prior to 23:59. Front page of the Word document has to

include title of the assignment, course code and section, student name and student number. Second

page is the individual statement of integrity that must be signed.

Note: Each student must provide an individual original submission of completed Assignment #3. Please

also note: Assignment #3 copies that are submitted jointly (i.e., by more than one author) will not be

graded.

E-mail questions related to the assignment should be sent to the Teaching Assistant or posted on the

Brightspace course website “Discussion page” (viewed by all).

Section M: Parisa Keshavarz (pkesh064@uottawa.ca)

Section N: : Niki Khorasanizadeh (mkhor084@uottawa.ca)

Section P: Makbule Kandakoglu (mkand098@uottawa.ca)

Section Q: Ghazaleh Hassanzadeh Kamalabadi (ghass052@uottawa.ca)

Problem 1: Transportation problem (25 points)

The J. Mehta Company’s production manager is planning a series of one-month production periods for

stainless steel sinks. The forecasted demand for the next four months is as follows:

Month Demand for Stainless Steel Sinks

1 90

2 100

3 250

4 150

The Mehta firm can normally produce 75 stainless steel sinks in a month. This is done during regular

production hours at a cost of $100 per sink. If demand in any one month cannot be satisfied by regular

production, the production manager has three other choices:

(1) he can produce up to 40 more sinks per month in overtime but at a cost of $150 per sink; (2) he can purchase a limited number of sinks from a friendly competitor for resale (the maximum

number of outside purchases over the four-month period COMBINED is 200 sinks (NOT 200

units each month), at a cost of $200 each;

(3) Or, he can fill the demand from his on-hand inventory. The ending inventory cost is $20 per sink per month.

A constant workforce level is expected. Back orders are NOT permitted (e.g. order taken in period

3 to satisfy demand in later period 2 is not permitted). Inventory on hand at the beginning of month

1 is 40 sinks.

ADM2302 M, N, P and Q Assignment # 3

Winter 2020 Page 2

a. Formulate algebraically the above problem as a TRANSPORTATION Linear Programming model. Define the decision variables, objective function, and constraints. (16 points)

Hint: Draw the transportation network model that corresponds to the problem, to figure out how to

formulate.

b. Formulate this same problem on a spreadsheet and SOLVE using Excel Solver (Provide the corresponding “Excel Spreadsheet” and the “Answer Report”). Include “managerial

statements” that communicate the results of the analyses. (9 points)

Hint: Use the Excel spreadsheet formulation of a transportation problem (refer to the problem

discussed in class).

Problem 2 (20 points)

The manager of a stamping department is getting ready to begin a new operation. A single product is to

be produced. It can be produced on any of three machines.

Information concerning the machines is contained in the following table:

Machine Setup Cost Profit per Unit Daily Capacity A $300 $10 500

B 250 12 450

C 325 13 450

Each machine requires an operator, and two operators are available. The profit per unit excludes setup

cost, and setups must be done at the start of each new day.

a. Formulate algebraically this profit maximization problem for the optimal quantities to produce

per day on each machine. Define the decision variables, objective function, and constraints.

(13 points)

b. Formulate this same problem on a spreadsheet and SOLVE using Excel solver (Provide the

corresponding “Excel Spreadsheet” and the “Answer Report”). Describe clearly and completely

the optimal solution to this problem using a managerial statement. (7 points)

Problem 3 (20 points)

The board of directors of a large manufacturing firm is considering a set of investments shown in the

following table. Let Ri be the total revenue from investment i and Ci be the cost to make investment i.

The board wishes to maximize the total revenue and invest no more than a total of M dollars.

Formulate this model as a Binary Integer Programming Problem (BIP). Define your decision variables,

and write down the algebraic formulation of the model.

Investment Condition

1 None 2 Only if 1 3 Only if 2 4 Must if 1 and 2 5 Not if 1 or 2 6 Not if 2 and 3 7 Only if 2 and Not 3

ADM2302 M, N, P and Q Assignment # 3

Winter 2020 Page 3

Problem 4: Goal Programming (35 points)

Major Bill Bligh, director of the Army War College’s new six-month attaché training program, is

concerned about how the 20 officers taking the course spend their precious time while in his charge.

Major Bligh recognizes that there are 168 hours per week and thinks his students have been using them

rather inefficiently. Bligh lets

X1 = number of hours of sleep needed per week

X2 = number of personal hours per week (eating, personal hygiene, handling laundry, and so on)

X3 = number of hours of class and studying per week

X4 = number of hours of social time off base per week (dating, sports, family visits, and so on)

He thinks that students should go to class and study exactly 30 hours a week to have time to absorb

materials. This is the most important goal. Bligh feels that students need at most 7 hours of sleep per

night on average and that this goal is number 2 in term of priority. He believes that goal number 3

(least important goal) is to provide at least 20 hours per week of social time.

a. Formulate this as a preemptive goal programming problem. Define the decision variables,

objective function, and constraints. (20 points)

b. Formulate this same problem on a spreadsheet and SOLVE using Excel solver (Provide the corresponding “Excel Spreadsheet” and the “Answer Report”). (11 points)

c. Describe clearly and completely the solution to this problem using a managerial statement.

(4 points)