Construct the standard data table

Question

Problems:

Transportation Problem Set

1. Consider a transportation problem with 4 sources and 3 demand points.

(a) Write the min-cost model in full (without using ∑ notation).

(b) Draw the network.

(c) Construct the standard data table.

2. Consider a transportation problem for which c_ij = h_i + h_j , where is a handling cost at node i.  (This can be unloading/loading charge from/to a barge or railroad car.)  Prove that if total supply equals total demand, every feasible shipping policy is optimal.

3. Prove or give a counter-example to each of the following.

(a) If assignment costs are unique, the optimal assignment is unique.

(b) If there is excess supply and all shipping costs are positive, every optimal shipping policy ships only the amount of total demand (i.e., no demand is over-satisfied).

4. A 400-meter relay requires 4 different swimmers who each swim 100 meters of backstroke, breaststroke, butterfly, and freestyle.  A coach has 5 swimmers whose expected times (in seconds) are given in the following table.

	backstroke	breaststroke	butterfly	freestyle
Chris	65	73	63	57
Charlie	67	70	65	58
Francis	68	72	69	55
Jackie	67	75	70	59
Terry	71	69	75	57

(a) How should the coach assign swimmers to the relay so as to minimize their total time?

(b) Consider the swimmer not assignment to any event.  How much must each of the 4 event-times decrease for that swimmer to be assigned to an event?  Who is replaced?

(c) How valuable would a new swimmer be with the following times:

	backstroke	breaststroke	butterfly	freestyle
No Name	66	72	68	57

Attachment:- Transportation Problem Set Templates.rar