Problem 1

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

1 120

2 160

3 240

4 100

The Mehta firm can normally produce 100 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 50 more sinks per month in overtime but at a cost of $130 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 is 450 sinks, at a cost of $150 each);

(3) Or, he can fill the demand from his on-hand inventory. The inventory carrying cost is $10 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.

a. Set up and formulate algebraically the above “production scheduling” problem as a TRANSPORTATION Model to minimize cost.

b. SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”).

Problem 2

Bradford Electronics produces a variety of DVD drives for installation into home-use DVD players. Bradford can assemble DVD drives on any or all five production stations, some of which are more automated than others, and thus, have lower variable costs of assembly but require higher one-time setup costs to convert to assembling a particular model of DVD drive. Bradford has received an order for assembling 2,500 DVD drives of a particular model.

Assembly Variable Assembly Capacity In Setup Cost

Station Cost/DVD Drive DVD Drives

1 $62 500 $12,000

2 $68 600 $ 6,000

3 $72 700 $ 3,000

4 $78 450 $ 1,500

5 $85 1000 $ 500

Given the setup costs, capacities and variables assembly costs at each of the five production stations in the above table:

(a) Formulate this problem algebraically as an integer/binary programming model.

(b) Use Excel Solver to determine how many DVD drives should be assembled at each of the five production stations to minimize total costs?

Problem 3

Harris Segal, Marketing director for the Upper Canada Power Corporation is about to begin an advertising campaign promoting energy conversation. In trying to budget between television and newspaper advertisements, he sets the following goals and assigns the weights shown.

1. The total advertising budget of $120,000 should not be exceeded. Weight = 100

2. There should be a mix of TV and newspaper ads, with at least 10 TV spots (costing $5,000 each) and at least 20 newspaper ads (costing $2,000 each). Weight = 75 each.

3. The total number of people to read or hear the advertisements should be at least 9 million. Weight = 40 per 100,000

Each television spot reaches approximately 300,000 people. A newspaper advertisement is read by about 150,000 persons.

(a) Formulate Segal’s goal programming problem to find out how many of each type of ad to place.

(b) Solve using Excel to find out how many of each type of ad to place. How many people, in total, will read or hear the advertisements?

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

1 120

2 160

3 240

4 100

The Mehta firm can normally produce 100 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 50 more sinks per month in overtime but at a cost of $130 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 is 450 sinks, at a cost of $150 each);

(3) Or, he can fill the demand from his on-hand inventory. The inventory carrying cost is $10 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.

a. Set up and formulate algebraically the above “production scheduling” problem as a TRANSPORTATION Model to minimize cost.

b. SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”).

Problem 2

Bradford Electronics produces a variety of DVD drives for installation into home-use DVD players. Bradford can assemble DVD drives on any or all five production stations, some of which are more automated than others, and thus, have lower variable costs of assembly but require higher one-time setup costs to convert to assembling a particular model of DVD drive. Bradford has received an order for assembling 2,500 DVD drives of a particular model.

Assembly Variable Assembly Capacity In Setup Cost

Station Cost/DVD Drive DVD Drives

1 $62 500 $12,000

2 $68 600 $ 6,000

3 $72 700 $ 3,000

4 $78 450 $ 1,500

5 $85 1000 $ 500

Given the setup costs, capacities and variables assembly costs at each of the five production stations in the above table:

(a) Formulate this problem algebraically as an integer/binary programming model.

(b) Use Excel Solver to determine how many DVD drives should be assembled at each of the five production stations to minimize total costs?

Problem 3

Harris Segal, Marketing director for the Upper Canada Power Corporation is about to begin an advertising campaign promoting energy conversation. In trying to budget between television and newspaper advertisements, he sets the following goals and assigns the weights shown.

1. The total advertising budget of $120,000 should not be exceeded. Weight = 100

2. There should be a mix of TV and newspaper ads, with at least 10 TV spots (costing $5,000 each) and at least 20 newspaper ads (costing $2,000 each). Weight = 75 each.

3. The total number of people to read or hear the advertisements should be at least 9 million. Weight = 40 per 100,000

Each television spot reaches approximately 300,000 people. A newspaper advertisement is read by about 150,000 persons.

(a) Formulate Segal’s goal programming problem to find out how many of each type of ad to place.

(b) Solve using Excel to find out how many of each type of ad to place. How many people, in total, will read or hear the advertisements?

## This question was asked on Mar 16, 2010.

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