Ch 6: Transportation I. Formulation II. Northwest Corner III. Production Smoothing

Formulation Application: Decision about how many units to ship from factory to warehouse, given several factories and several warehouses If planning new factory or new warehouse, can be used to decide location (ex: Pennsylvania Rite Aid built warehouse at Palmdale)

Linear Programming Objective: MINIMIZE transportation cost Constraints: Supply, demand Supply: Factory capacity Demand: Warehouse requirement

Example Three warehouses: Albuq, Boston, Cleve Three factories: Des Moines,Evansville, Ft Lauderdale Next slide: Data given

Transportation matrix To From A B C Supply D 100 E 300 F Demand 200 700

Northwest Corner Start at northwest corner Number of units = MIN (supply,demand) Ex: Row D,Col A: MIN(100,300)=100 After allocation, subtract units

Transportation matrix To From A B C Supply D 100 E 300 F Demand 200 700

Transportation matrix To From A B C Supply D 100 E 300 F Demand 300-100 =200 200 700

Transportation matrix To From A B C Supply D 100 E 200 300 F Demand 300-100 =200 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300 Demand 300-100 =200 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300 Demand 300-100 =200 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300 Demand 300-100 =200 200-100 =100 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300 Demand 300-100 =200 200-100 =100 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300-100 =200 Demand 200-100 =100 700

Transportation matrix To From A B C Supply D 100 E 200 300-200 =100 F 300-100 =200 Demand 200-100 =100 700

MIN Cost Would need unit cost between factory and warehouse Use Excel to minimize cost Northwest Corner is initial allocation

Production Smoothing Factory replaced by production period Warehouse repl by demand period

Two month example Month Feb Mar Supply 15 5=inventory end of Feb 20 Demand 25 40