Question

Two factories in Memphis and Denver, with supplies 150 per day, and 200 per day. Customers in Los Angeles and Boston, with a demand 130 per day each.

Widgetco believes that it may be cheaper to first ship some widgets to New York or Chicago and then ship them to their final destinations. The costs of shipping a widget are given.

Widgetco wants to minimize the total cost of shipping the required widgets to its customers.

Cost	New York	Chicago	Los Angeles	Boston
Memphis	8	13	25	28
Denver	15	12	26	25
New York	-	6	16	17
Chicago	6	-	14	16

	New York	Chicago	Los Angeles	Boston	Available Supply	Used Supply
Memphis
Denver
New York
Chicago
Demand

What the Minimum Transportation Cost ?

Answer 1

In this problem, his problem, Memphis & Denver are supply points, with supply at 150f 200 widgets per day respectivly New York & chicago are trans-shipment points. los Angeles & Bostan are demand points, each with Add dummy supply point it neccessary Now each supply point will have supply equal to it's origenal supply of each demand point will have demand equal to it's Origenal demand. While each transshipment point will have supply is equal to it's origenal supply + (S) & demand equal to it's origenal demand tis) This ensure that each transshipment point het inpul= net output. By adding some amount to demand of supply We ensure net output at any shipment point will be currect. Memphis New York Los Angeles) ns Sinuni endu Siwali Chicago Boston Denver Total supply = (s) = 150+200=350 Total demand= = 130+ 130 =260 350-260= got The dummy point have demand of go The other supply demand in the below are obtain by adding = shipment point supply & demand. bly demand in the transportation table obtain by adding s=350 to each trans-

e2 supply Dummy tot 20 150 Demand N.Y. Chicago LOA Memphis 1308 13 25 15 12 126 To 1616 No York | 220 Boston 28 25 17 25 200 Denver 130 16 350 130 350 chicago Demand 350 120 go 350 130 The optimal solution to widgetco Memphis 130, New York 130 [L. Angeles [ Denver ] [chicago ] [ Boston en 130

In interpreting the Interpreting the solution to transportation problem at we simply ignore shipment to dummy of from porn to itself. We find that Widgetco should produce 130 widget at Memphis, ship them to New York & transship them from new York to los Angeles The 130 widget produce at Denver should directly shipp. to Boston The net out flow of each city is Memphis = 130+20 = 150 Denver = 130+70 = 200 Chicago = 350-350 = 0 N. York = 220+130-130-2200 L. Angeles. = - 130 =-130 Boston = -130 = -130 Dummy = -20-70 = -90 A net negative outflow represent an inflow. Observe that each shipment point has het out flow zero; Whatever flow in transshipment point must leave transshipment point. suppose we allow shipment between Memphis & Denver then we will have supply = 150+350=500 & Denver row will have supply of = 2004 2350 = 550. The new Memphis column would have demand of of 350=850 3 & new Denver have demand of of 850 = 350 Finnaly suppose the shipment between demand point I. & Boston allowed. This would make Lo A & Boston ut point of rows for L.A & Boston. The supply of both the LoA & Boston rows would 750. The demand for both LoA & Boston coloumns would be 130+350=480 B5 Sijwali • Indu Sijwali