Question 1

1) A company wishes to transport goods from four supply points to three demand points. The per unit costs, supply point capacities, and demand point requirements are given by the following table:

(a) Formulate in algebraic form a balanced transportation model whose solution will inform the company how to minimize total transportation cost 

(b) Find a basic feasible solution to the model formulated in part (a) by the minimum cost method

(c) Starting with the basic feasible solution formulated in part (b) Use the transportation simplex method to find the optimal solution to the model.

(d) Analyse the strengths and weaknesses of the solution found in part (c) from a perspective of the company.

The analysis should contain reflection on the advantages and disadvantages of the solution. For example, the solution may be preferred on the grounds of cost minimisation but may have other disadvantages that have not been considered under this solution. The analysis should be presented in a clear, unbiased style appropriate for reading by a general manager.

Question 2

Describe and discuss the issues faced by a company wishing to import, under normal market conditions, a fashionable range of high quality summer clothing from a South-East Asian country to the United Kingdom and then on through a logistic chain of warehouses, depots, and distribution centres until the company sells the goods directly to shops and boutiques. Include a diagrammatic illustration and a modelling of the company’s possible objectives in your answer.

The solution should contain a consideration of factors, such as the following, in the context of the given situation:

 Mode of shipping (ship, road, rail)

 Special requirements (appropriate storage for goods)

 Time related factors (seasonal factors, changes in fashion require fast transport)

 Access to ports

 Free trade zone agreements

 Customs considerations and laws

 Environmental and energy considerations

The transportation network (diagrammatic illustration) given should show a multiple number of each trans-shipment point.

Possible objectives include, but are not limited to:

 Minimization of total costs

 Minimization of total time of transportation

 Minimization of total distance travelled

 Minimization of energy used

The discussion should include comments about the degree of conflict amongst the objectives and recognition of the multi-objective nature of the situation, plus an explanation, for example, about the possible use of weights to produce different solutions.