Question

Consider the transportation table below. The solution displayed was obtained by performing some iterations of the transportation method on this problem.

                                                                                                                                

Consider the transportation table below. The solution displayed was obtained by performing some iterations of the transportation method on this problem.                                                                                                                                  Copy to Clipboard + Destination Source DenverDenver YumaYuma MiamiMiami Supply HoustonHouston ​$22 ​$88 ​$11 2020 2020 St. LouisSt. Louis ​$44 ​$55 ​$66 3030 1010 2020 ChicagoChicago ​$66 ​$33 ​$22 4040 1010 3030 Demand 3030 3030 3030 The total cost of the current solution provided​ = ​$270 270. Using stepping stone​ method, to perform an improvement​ iteration, the improvement index for the unused cell will​ be: HoustonHoustonminus−YumaYumaequals= 5 5 HoustonHoustonminus−MiamiMiamiequals= negative 1−1 St. LouisSt. Louisminus−MiamiMiamiequals= nothing

	Destination
Source	Denver		Yuma		Miami		Supply
Houston		​$2		​$8		​$1	20
	20
St. Louis		​$4		​$5		​$6	30
	10		20
Chicago		​$6		​$3		​$2	40
			10		30
Demand	30		30		30

The total cost of the current solution provided​ =

​$270.

Using stepping stone​ method, to perform an improvement​ iteration, the improvement index for the unused cell will​ be:

Houston - Yuma = 5

Houston - Miami = -1

St. Louis - Miami= ????

Answer 1

The total cost of the current solution provided = 20*2+10*4+20*5+10*3+30*2 = $ 270

Improvement index of empty cells is calculated by alternatively adding and subtracting the cost of cells which form a closed loop the empty cell at one of its corner and non-empty cells at all the other corners.

Closed loop for empty cell Houston-Yuma is formed by cells (Houston-Yuma) - (St.Louis-Yume) + (St.Louis-Denver) - (Houston-Denver)

Houston-Yuma = 8-5+4-2 = 5

Closed loop for empty cell Houston-Miami is formed by cells (Houston-Yuma) - (Chicago-Miami) + (Chicago-Yuma) - (St.Louis-Yume) + (St.Louis-Denver) - (Houston-Denver)

Houston-Miami = 1-2+3-5+4-2 = -1

Closed loop for empty cell St.Louis-Miami is formed by cells (St.Louis-Miami) - (Chicago-Miami) + (Chicago-Yuma) - (St.Louis-Yuma)

St.Louis-Miami = 6-2+3-5 = 2

Houston - Yuma = 5

Houston - Miami = -1

St. Louis - Miami= 2