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336 CHAPTER 7 TRANSPORTATION, ASSIGNMENT AND TRANSSHIPMENT PROBLEMS

a. Use the minimum cost method to find an initial feasible solution.
b. Use the transportation Simplex method to find an optimal solution.
c. Using your solution to part (b), identify an alternative optimal solution.
17 Use the per-unit cost changes for each unoccupied cell shown in Table 7.10 to do the
following:
a. Consider the arc connecting Brazil and Dubai as a candidate for the incoming arc.
Allocate 1 unit of flow, and make the necessary adjustments on the stepping-stone path
to maintain feasibility. Compute the value of the new solution, and show that the change
in value is exactly what has been indicated by the cost change per unit obtained using
the MODI method.
b. Repeat part (a) for the arc connecting China and London.
18 Refer again to the Contois Carpets problem for which the network representation is shown
in Figure 7.12. This problem can also be formulated and solved as a transportation
problem.
a. Develop a network representation of it as a transportation problem. (Hint: Eliminate the
inventory arcs, and add arcs showing that quarterly production can be used to satisfy
demand in the current quarter and all future quarters.)
b. Solve the problem using the transportation Simplex method.
19 Refer to Problem 9. Using the Hungarian method, obtain the optimal solution.
20 Use the Hungarian method to solve the Salisbury Discount, problem by using the profit
data in Table 7.27.

CASE PROBLEM 1 Distribution System Design

national charity organization operating through- for the German supplier to ship to Edinburgh. The
A out the UK provides support and advice to the Swedish supplier can supply a maximum of 30 000
elderly. One of their activities relates to home safety sets and the German supplier a maximum of 20 000.
for the elderly whereby the charity will supply and The charity operates on a regional basis with nine
install safety handles around the home. These han- regional zones across the UK. Table 7.35 shows the
dles are installed in bathrooms and by stairs and by estimated annual demand in each zone for sets of
other areas where the elderly person might need to handles over the next year (these are based on past
support themselves safely. The charity started out its demand and the workload capacity of the charity’s
activities a few years ago operating only in parts of staff in each zone). Each of the three distribution
Scotland. However, this initiative has proved so suc- centres supplies some of the zones when they require
cessful that it has since been expanded to cover the sets for installation. The Edinburgh distribution centre
whole of the UK. currently supplies the Northeast, Northwest, Northern
Currently the charity buys sets of handles from Ireland and Scotland; the Leeds centre supplies the
two suppliers: one based in Sweden, the other in Southeast, London and the Midlands; the Bristol
Germany and the handles are shipped to one of centre supplies Wales and the Southwest. The current
three regional distribution centres the charity has in shipping cost per set of handles from each centre to
Edinburgh, Leeds and Bristol. The cost of each set each zone is shown in Table 7.36. Note that some
of handles from Sweden is E10.50 and E10 from zones cannot be supplied by some of the centres
Germany. The cost of shipping a set of handles from because of transport logistics constraints.
each of the two suppliers to each of the charity’s To determine how many sets to ship from each
distribution centres is shown in Table 7.34. Note that centre to each zone, the demand forecasts are
because of transport restrictions, it is not possible aggregated and a transportation model is used to

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