Bài giảng Operations Management - Supplement 8 The Transportation Model

The Transportation ModelSupplement 8Copyright © 2015 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.Supplement 8: Learning ObjectivesYou should be able to:LO 8s.1 Describe the nature of a transportation problemLO 8s.2 Solve transportation problems manually and interpret the resultsLO 8s.3 Set up transportation problems in the general linear programming formatLO 8s.4 Interpret computer solutionsInvolves finding the lowest-cost plan for distributing a stock of goods or supplies from multiple points of origin to multiple destinations that demand the goodsTransportation ProblemLO 8s.1Model: Information RequirementsInformation requirementsA list of the origins and each one’s capacity or supply quantity per periodA list of the destinations and each one’s demand per periodThe unit cost of shipping items from each origin to each destinationLO 8s.2Model: AssumptionsTransportation model assumptionsThe items to be shipped are homogeneousShipping cost per unit is the same regardless of the number of units shippedThere is only one route or mode of transportation being used between each origin and destinationLO 8s.24771100123882008101651508090120160ABCDSupplyDemand123WarehouseFactory450450Factory 1 can supply 100 units per period Total capacity per periodCost to ship one unit from factory 1 to warehouse ATotal Demand per periodWarehouse B can use 90 units per periodLO 8s.2Intuitive Lowest-Cost ApproachIdentify the cell with the lowest costAllocate as many units as possible to that cell, and cross out the row or column (or both)Find the cells with the next lowest cost from among the feasible cellsRepeat steps (2) and (3) until all units have been allocatedInitial Solution LO 8s.2Table 6 – Initial Solution477100110012903110882008081010166051508090120160ABCDSupplyDemand123WarehouseFactory450450LO 8s.2Evaluating Stepping Stone Paths:Start by placing a + sign in the cell you wish to evaluate.Move horizontally (or vertically) to a cell that has units assigned to it. Assign a minus sign (-) to it.It is OK to pass through an empty cell or a completed cell without stopping. Choose a cell that will permit your next move to another completed cell. Change direction and move to another completed cell. Assign a plus sign (+) to the cell.Continue the process until a closed path back to the original cell can be completed. Stepping Stone MethodLO 8s.2Table 7 – Stepping Stone Method477100110012903110882008081010166051508090120160ABCDSupplyDemand123WarehouseFactory450450(+)(-)(+)(-)4 – 1 + 5 – 8 = 0LO 8s.2Improved Solution47107901100129031108820080810167051508090120160ABCDSupplyDemand123WarehouseFactory450450LO 8s.2Testing the Solution47107901100129031108820080810167051508090120160ABCDSupplyDemand123WarehouseFactory4504500+5+7+6+4+5LO 8s.2Transportation Problem: FormulationLO 8s.3Transportation: Computer SolutionTransportation problems can be solved manually in a straightforward mannerExcept for very small problems, solving the problem manually can be very time consumingFor medium to large problems, computer solution techniques are more practicalA variety of software packages are available for solving the transportation modelSome require formulating the problem as a general LP modelOthers allow data entry in a more simple, tabular formatLO 8s.4Transportation Problem: Excel TemplateLO 8s.4