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Decision Modeling. Special Applications of Linear Programming. Some General LP Applications. Archetypical LP models can serve as templates for large, real-life models Blending problem Transportation problem Inventory problem (multi-period). Transportation Problem.
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Decision Modeling Special Applications ofLinear Programming
Some General LP Applications • Archetypical LP models can serve as templates for large, real-life models • Blending problem • Transportation problem • Inventory problem (multi-period)
Transportation Problem • Management must decide how to send products from various sources to various destinations to satisfy requirements while minimizing cost • Known parameters: • Inventory at each source location • Demand at each destination location • Cost of transportation between each source-destination pair
Example • AutoPower Company makes a variety of battery and motorized uninterruptible power supplies (UPSs) • AutoPower has 4 final assembly plants in Europe and the diesel motors used by the UPSs are produced in the US, shipped to 3 harbors and then sent to the assembly plants • Production plans for the third quarter have been set. The requirements (demand at the destinations) and the available number of motors at the harbors (supply at the origins) are shown on the next slide
Demand • Assembly PlantNo. of Motors Required • Leipzig 12,000 • (2) Nancy 15,000 • (3) Liege 23,000 • (4) Tilburg 18,000 • 68,000 Sufficient Capacity Supply Harbor Production Capacity (A) Amsterdam 27,000 (B) Antwerp 30,000 (C) Le Havre 23,000 80,000
TO DESTINATION Leipzig Nancy Liege Tilburg FROM ORIGIN(1) (2) (3) (4) (A) Amsterdam 9.20 10.40 11.20 12.80 (B) Antwerp 9.60 10.80 13.60 10.00 (C) Le Havre 14.00 8.00 8.80 10.80 Example • AutoPower must decide how many motors to send from each harbor (origin) to each plant (destination) • The cost ($/motor) of shipping is given in the following table
Model Formulation • See board • See Excel solution • See Sensitivity report
Variations • Add manufacturing cost • Update transportation cost to include manufacturing cost • Maximize contribution margins instead of minimizing cost • Define different products as origins and contribution margin in destination markets as transportation cost • Demand exceeds supply • Add a dummy origin and let transportation cost equal opportunity cost of not meeting demand at a destination
Dynamic Models • Single time period models (such as the previous ones) are called static because time is not an important model factor • In many cases, decisions are made over a time horizon divided into time periods • These multi-period models are called dynamic models since the decision for one time period influences the decision in other time periods • In dynamic models, the timing of events must be very well defined
Dynamic Inventory Models • In dynamic inventory models, demand is manifested in each of several discrete time periods • Goods are acquired (e.g., manufactured) in different time periods • Inventory can be carried from one time period to another • Only goods that are available during a time period can be delivered to the customers
The Inventory Equation • Flows into and out of the inventory must balance in any given time period. Let • It denote the inventory on hand at the end of week t • xt production in week t • dt demand (filled) in week t • For any week t, the inventory equation is: It-1 + xt= It+ dt
Jan. Feb. Mar. Apr. Delivery Requirements58 36 34 59 Production Capacity60 62 64 66 Unit Production Costs (000s)$28 $27 $27.8 $29 Unit Inventory Holding Cost$300 $300 $300 $300 Dynamic Inventory Model Example • AutoPower generators are assembled in Singapore from imported parts, tested in Singapore, and exported to AutoPower’s Asian customers needing uninterrupted electric power. The following monthly data are available:
Model Formulation • See board • See Excel solution
