Presentation on theme: "Transshipment Problem"— Presentation transcript:
1 Transshipment Problem STRATEGICRESOURCEALLOCATIONandPLANNINGMGMT E-5050Bamm Mining CompanyTransshipment Problem
2 Bamm Mining Company Bamm Mining Company is currently extracting rock from two mines. Once it is taken from theground and loaded on a truck, it is sent to oneof two plants for processing.The processed rock is then shipped to one ofthree builders’ supply stores, where it is soldfor landscaping purposes.The cost of transportation, the supply availableat each mine, and the processing capacity of eachplant are given on the following table:
3 Daily Process Capacity Bamm Mining CompanyCost per Ton for ShippingTo PlantFrom Mine#1#2Daily SupplyA$6.00$8.00320 tonsB$7.00$10.00450 tonsDaily Process Capacity500 tons
4 Bamm Mining Company To From Plant #1 $13.00 $17.00 $20.00 #2 $19.00 The cost of shipping from each processing plant to eachstore and the daily demand are as follows:Cost per Ton for ShippingToFrom PlantSupply Store ASupply Store BSupply Store C#1$13.00$17.00$20.00#2$19.00$22.00$21.00Daily Demand200240330
5 Bamm Mining Company REQUIREMENT: Formulate a linear program that can be used todetermine how to meet the demands of the 3supply stores at the least cost.Solve this by computer. How many tons shouldbe shipped from each mine to each plant?How many tons should go from each plant toeach store?
6 Bamm Mining Company Assume that the cost of processing the rock is $22.00 per ton at Plant 1 and $18.00 per ton atPlant 2.REQUIREMENT:Formulate a linear program to minimize thetotal processing and transportation cost.Solve this by computer. What is the optimalsolution?
7 Solution Let : A1 = tons of ore from mine A to plant 1 B1 = tons of ore from mine B to plant 1B2 = tons of ore from mine B to plant 2
8 Solution Let : X1 = tons shipped to Builder’s Home from plant 1 Y1 = tons shipped to Homeowners’ Hdqtrs from plant 1Y2 = tons shipped to Homeowners’ Hdqtrs from plant 2Z1 = tons shipped to Hardware City from plant 1Z2 = tons shipped to Hardware City from plant 2
9 Solution Minimize cost = 6A1 + 8A2 + 7B1 + 10B2 + 13X1 + 19X2 + 17Y1 + 22Y2 + 20Z1 + 21Z2subject to :A1 + A2 = 320 ( supply at mine A )B1 + B2 = 450 ( supply at mine B )A1 + B1 =< 500 ( capacity at plant 1 )A2 + B2 =< 500 ( capacity at plant 2 )
10 Solution X1 + X2 = 200 ( demand at Builder’s Home ) Y1 + Y2 = 240 ( demand at Homeowners’ Hdqtrs )Z1 + Z2 = 330 ( demand at Hardware City )A1 + B1 = X1 + Y1 + Z1Units shipped into plant 1 must equal units shipped out of plant 1A2 + B2 = X2 + Y2 + Z2Units shipped into plant 2 must equal units shipped out of plant 2All variables => 0
11 Solution A1 = 50 tons of ore from mine A to plant 1 B1 = 450 tons of ore from mine B to plant 1X1 = 200 tons shipped to Builder’s Home from plant 1Y1 = 240 tons shipped to Homeowners’ Hdqtrs from plant 1Z1 = 60 tons shipped to Hardware City from plant 1Z2 = 270 tons shipped to Hardware City from plant 2All other variables = 0Minimum total cost = $19,160.00