Facility Location and Distribution System Planning Today’s Today’s Agenda Agenda �� Why Why study study facility facility location? location? Issues Issues to to be be modeled modeled Basic Basic models models � � Fixed Fixed charge charge problems problems � � Core Core uncapacitated uncapacitated and and capacitated capacitated facility facility location location models models �� Large-scale Large-scale application application (Hunt(HuntWesson Wesson Foods) Foods) Logistics Logistics Industry Industry �� U.S. U.S. logistics logistics industry: industry: $900 $900 billion billion -- almost almost double double the the size size of of the the high-tech high-tech industry: industry: >> 10 10 percent percent of of the the U.S. U.S. gross gross domestic domestic product product 11 11 per per cent cent of of Singapore's Singapore's GDP GDP with with aa growth growth of of 99 per per cent cent in in year year 2000 2000 Singapore Singapore Logistics Logistics Enhancement Enhancement & & Applications Applications Programme Programme (LEAP) (LEAP) 2001 2001 Global Global logistics: logistics: $3.43 $3.43 trillion trillion 1998, 1998, U.S. U.S. trucking trucking industry industry revenues revenues just just under under $200 $200 billion billion 7.7 7.7 million million trucks trucks carried carried over over 11 trillion trillion ton ton miles miles of of freight freight Singapore Singapore Retail Retail 21 21 Plan Plan Basic Basic Issue Issue �� Where Where to to locate locate and and how how to to size size facilities? facilities? How How to to meet meet customer customer demands demands from from the the facilities? facilities? � � Which Which facility facility (facilities) (facilities) serve serve each each customer? customer? � � How How much much customer customer demand demand is is met met by by each each facility? facility? Facilities might be warehouses, retail outlets, wireless bay stations, communication concentrators Some Some Elements Elements of of Cost Cost & & Service Service �� Transportation Transportation Costs Costs � � Vehicles, Vehicles, Drivers, Drivers, Fuel Fuel �� Warehousing Warehousing � � Facility Facility Construction/Rental, Construction/Rental, Handling Handling Costs, Costs, Inventory Inventory �� Customer Customer Service Service � � Service Service Time, Time, Single Single Sourcing Sourcing System System Trade-offs Trade-offs Transportation Costs - Fixed Costs + Effect of More Facilities System System Trade-offs Trade-offs Costs - Service + Effect of “Individualized” Service (e.g., Direct Shipments) Nature Nature of of Costs Costs �� Fixed Fixed Costs Costs � � Facility Facility construction/rental construction/rental � � Vehicle Vehicle purchases purchases & & rentals rentals � � Personnel Personnel (drivers, (drivers, managers) managers) � � Fixed Fixed overhead overhead �� Variable Variable Costs Costs � � Inventory, Inventory, handling, handling, fuel fuel Optimization Optimization Applications Applications �� Hunt-Wesson Hunt-Wesson Foods Foods saves saves over over $1 $1 million million per per year year Restructuring Restructuring North North America America operations, operations, Proctor Proctor and and Gamble Gamble reduces reduces plants plants by by 20%, 20%, saving saving $200 $200 million/year million/year Many, Many, many many others others (e.g., (e.g., supplying supplying parts parts to to plants) plants) Facility Facility Location Location Challenge Challenge 19 19 Modeling Modeling Issue Issue �� How How do do we we model model “lumpiness” “lumpiness” of of the the costs costs (e.g., (e.g., fixed fixed costs)? costs)? How How do do we we model model logical logical conditions conditions (e.g., (e.g., choice choice of of warehouse warehouse locations)? locations)? Modeling Modeling Fixed Fixed Costs Costs Flow x > 0 Flow z > 0 �� Incur Incur fixed fixed cost cost F F if if either either xx >> 00 or or zz >> 00 Suppose 3/2 (demand (demand limitation) limitation) Suppose xx ++ zz << 3/2 Model Minimize Fy + other terms subject to y = 1 if either x > 0 or z > 0 Three Three Models Models (LP (LP Relaxations) Relaxations) Model 1 x + z < 3/2 x < 1, z < 1 x + z < 2y x > 0, z > 0 0 0, z > 0 0 0, z > 0 0