Two production facilities at denver and atlanta components

Question

Supply Chain Design at Ryan Electronics Co.

Ryan is an electronics company whose supply chain is presently as follows:

• Two production facilities at Denver and Atlanta. Components from these are shipped to warehouses. Production Capacities at each: 600 units at Denver and 400 units at Atlanta
• Two warehouses: Kansas City and Louisville. These warehouses are supplied by the production centers and in turn, supply the retail centers. Storage Capacity at each warehouse is more than sufficient to store the entire production of Ryan.
• Four Retail Centers: Detroit, Miami, Dallas, New Orleans. Expected Demands at these retails centers are: Detroit (200 units); Miami (150 units); Dallas (350 units); New Orleans (300 units)

Assuming that Transportation Costs are linear w.r.t. distance, the unit transportation costs are as follows:

(a) Find the distribution plan (from production centers to warehouses and thereafter, to retail centers) that minimizes total transportation cost for Ryan Electronics.  in MS-Excel and solve it therein using MS-Excel's Solver module.  Your answer must consist of

(i) Formulate the above as a linear program.  Indicate clearly the decision variables, constraints and the objective function.

(ii) Solve the linear program in (i) by using MS Excel.   Submit a printed copy of the spreadsheet you used to model the program showing the optimal solution you obtained

(iii) State your results as a table which summarizes the optimal distribution plan and presents the results in the following format.

From	To	Units Shipped	Transportation Cost per unit	Total Cost of Transportation
Denver	Kansas City
Denver	Louisville
Atlanta	Louisville
Kansas City	Detroit
Kansas City	Dallas
Louisville	Miami
Louisville	New Orleans
Total Transportation Cost Across The Entire Supply Chain

(b) Suppose that Ryan is contemplating the following modification to its current supply chain: shipping directly from Atlanta to New Orleans at $4/unit and from Dallas to New Orleans at $1/unit.  What is the new optimal distribution plan from production centers to warehouses and thereafter, to retail centers?  Your answer must consist of

(i) Formulate the above as a linear program.  Indicate clearly the decision variables, constraints and the objective function and how this formulation differs from the one in (a).

(ii) Solve the linear program in (i) by using MS Excel.   Submit a printed copy of the spreadsheet you used to model the program showing the optimal solution you obtained

(iii) State your results as a table which summarizes the optimal distribution plan and presents the results in the following format.

From	To	Units Shipped	Transportation Cost per unit	Total Cost of Transportation
Denver	Kansas City
Denver	Louisville
Atlanta	Louisville
Atlanta	New Orleans
Kansas City	Detroit
Kansas City	Dallas
Louisville	Miami
Louisville	New Orleans
Dallas	New Orleans
Total Transportation Cost Across The Entire Supply Chain

(c) Ryan is now considering the possibility of consolidating its retail markets to minimize transportation costs.  Suppose that there are no restrictions which retail center Ryan can supply to and each of the existing retail centers is capable of absorbing the entire 1000 units that Ryan produces.  What is the best selection of retail centers to supply and how much should be supplied from production centers to warehouses and thereafter, to retail centers?  Your answer must consist of

(i) Formulate the above as a linear program.  Indicate clearly the decision variables, constraints and the objective function and how this formulation differs from the one in (a).

(ii) Solve the linear program in (i) by using MS Excel.   Submit a printed copy of the spreadsheet you used to model the program showing the optimal solution you obtained

(iii) State your results as a table which summarizes the optimal distribution plan and presents the results in the following format.

From	To	Units Shipped	Transportation Cost per unit	Total Cost of Transportation
Denver	Kansas City
Denver	Louisville
Atlanta	Louisville
Kansas City	Detroit
Kansas City	Dallas
Louisville	Miami
Louisville	New Orleans
Total Transportation Cost Across The Entire Supply Chain

(d) Ryan is now considering consolidating its production.  It still wishes to keep up the supply of 1000 units but wants to investigate if it is optimal for Ryan to consolidate production at only one of its production facilities.  Assume that capacity at each plant can be increased to absorb the entire demand of 100 units and that the cost of production at both Denver and Atlanta are identical.  What is the optimal production and transportation plan (from production centers to warehouses and thereafter, to retail centers) for Ryan under this scenario that minimizes total transportation costs? Your answer must consist of

(i) Formulate the above as a linear program.  Indicate clearly the decision variables, constraints and the objective function and how this formulation differs from the one in (a).

(ii) Solve the linear program in (i) by using MS Excel.   Submit a printed copy of the spreadsheet you used to model the program showing the optimal solution you obtained

(iii) State your results as a table which summarizes the optimal distribution plan and presents the results in the following format.

From	To	Units Shipped	Transportation Cost per unit	Total Cost of Transportation
Denver	Kansas City
Denver	Louisville
Atlanta	Louisville
Kansas City	Detroit
Kansas City	Dallas
Louisville	Miami
Louisville	New Orleans
Total Transportation Cost Across The Entire Supply Chain

Question 2: Survey Sciences Inc (SSI).  SSI is a marketing research firm that does market surveys on behalf of its clients.  It has been recently contacted by a client to perform a survey for a new product line that will be targeted to the US population overall, but with a special niche market for Hispanic Americans.  The client has agreed to compensate SSI in full for the actual costs of the survey but has specified the following requirements for the survey. 

At least 2,300 U.S. households must be surveyed.

At least 1,000 households whose heads are ≤ 30 years old must be surveyed.

At least 600 households whose heads are between 31 and 50 must be surveyed.

Ensure that at least 15% of those surveyed live in a state that borders Mexico

Ensure that no more than 20% of those surveyed who are 51 years of age or over live in a state that borders Mexico

Because SSI conducts all its surveys in person, survey costs are high.  The cost accountants at SSI estimate of the costs of reaching people in each age and region category are as follows:

COST PER PERSON SURVEYED ($)
REGION	AGE ≤ 30	AGE 31-50	AGE ≥ 51
State bordering Mexico	$7.50	$6.80	$5.50
State not bordering Mexico	$6.90	$7.25	$6.10

Since SSI would like to get this surveying project from this client, its goal is to design a survey plan that minimizes the total cost of conducting the survey.  Formulate this decision problem for SSI as a linear program. Your answer must consist of

(i) Formulate the above as a linear program.  Indicate clearly the decision variables, constraints and the objective function.

(ii) Solve the linear program in (i) by using MS Excel.   Submit a printed copy of the spreadsheet you used to model the program showing the optimal solution you obtained

(iii) State your results as a table which summarizes the optimal survey plan and presents the results in the following format.

Survey Demographic Group	Number Surveyed In Optimal Survey Plan	Cost Of Surveying The Demographic Group
30 or younger and in a border state
31-50 and in a border state
51 or older and in a border state
30 or younger and in a non-border state
31-50 and in a non-border state
51 or older and in a non-border state
Totals