Consider the transportation problem having the following parameter table:

(a) Notice that this problem has three special characteristics:

(1) number of sources number of destinations, (2) each supply 1, and (3) each demand 1. Transportation problems with these characteristics are of a special type called the assignment problem (as described in Sec. 8.3). Use the integer solutions property to explain why this type of transportation problem can be interpreted as assigning sources to destinations as a one-to-one basis.

(b) How many basic variables are there in every BF solution? How many of these are degenerate basic variables ( 0)?

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(c) Use the northwest corner rule to obtain an initial BF solution.

I

(d) Construct an initial BF solution by applying the general procedure for the initialization step of the transportation simplex method. However, rather than using one of the three criteria for step 1 presented in Sec. 8.2, use the minimum cost criterion given next for selecting the next basic variable.

(With the corresponding interactive routine in your OR Courseware, choose the Northwest Corner Rule, since this choice actually allows the use of any criterion.)

Minimum cost criterion: From among the rows and columns still under consideration, select the variable xij having the smallest unit cost cij to be the next basic variable. (Ties may be broken arbitrarily.)

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(e) Starting with the initial BF solution from part (c), interactively apply the transportation simplex method to obtain an optimal solution.