Question

MG Auto, Produces four car models: M1, M2, M3, and M4. the Detroit plant produces models M1, M2, and M4. Models M1 and M2 are also Produced in New Orleans. The Los Angeles plants manufactures models M3 and M4. The capacities of the various plants and the demands at the distributions centers are given in the table.

the mileage chart is the same as given and the transportation rate remains at 8 cents per car mile for all models. Additionally, it is possible to satisfy a percentage of the demand for some models. Additionally, it is possible to satisfy a percentage of the demand for some models from the supply of others according to thespecifications below.

a) Formulate the corresponding transportation model.

b) Determine the optimum shipping schedule. Hint add four new destination corresponding to the new combinations [M1,M2] [M3,M4] [M1,M2] and [M2 M4] the demands at the new destination are determined from the given percentages.

Model

M1 M2 M3 M4 Total

Plant

Los Angeles ---- ---- 700 300 1000

Detroit 500 600 ------ 400 1500

New Orleans 800 400 ----- ----- 1200

Distribution Center

Denver 700 500 500 600 2300

Miami 600 500 200 100 1400

Distribution Center Percentage of demand Interchangeable models

Denver 10 M1,M2

20 M3, M4

Miami 10 M1,M2

5 M2, M4

Answer 1

Step-1 understand the problem:- here in the question, it is given that 4 different car models are produced and four new destinations corresponding to the new combinations [M1, M2] [M3, M4] [M1, M2] and [M2 M4] will be added.

So the initial Matrix would look like:-

Note :- All the combinations have been mentioned above. Capacity is given in the question and demand has been adjusted based on information given.

example :- for Denver :- Car M1 and M2 ---- demand = 700 and 500 and new segment [M1,M2] is 10% of that given demand

therefore adjusted demand for M1 = 700 - 10%of 700 = 700-70 = 630

M2 = 500 - 10%of 500 = 500-50 = 450

[M1,M2] = 10%of 700 + 10% of 500 = 120 and so on.

Step-2 Analyse the cost Matrix:- Reference has been taken from Book TAHA, which 8 cents based on the mileage chart, Example 5.1-1

Step-3 Objective Function :- Minimise the Shipping cost = =SUMPRODUCT(C4:N10,C17:N23) = cost* Shipping capacity with respect to demand and supply

Step-4 Optimise the solution through Excel

Optimum Shipping cost is $ 313,200

Shipping Schedule will be