University:
Massachusetts Institute of Technology
Course:
15.501/516 | Accounting
Academic year:

2023
Views:

286

Pages:

4
Author:

Winston Mercado

Guidelines on Formulating a Management Problem as a Linear Programming Model – Prof. Stephen Graves General Rules of Thumb • There is usually more than one correct formulation of a problem. • Sometimes it is unclear whether to use inequality or equality constraints. • Sometimes our intuition tells us that a constraint is irrelevant (i.e., it is never binding). Try to find such constraints. But when in doubt, leave the constraint in. Identifying Decision Variables • Start by using decision variables that agree with your intuition. Ask yourself, "What decision must I make in order to determine the outcome?" Identifying Constraints • Some constraints are resource-related: can't use more than available 2G2 + G3 + W1 + W2 <= 16000 (256K memory) • Other constraints are capacity limits Coal production from Consol mine • <= mine capacity Requirements Must satisfy demand • Quality Constraints Must have at least 19 % average volatility in coking coal • Policy Constraints At least 50% union mines Must satisfy workstation demand from key customer • Balance Constraints Conservation of Flow: Flow In equals Flow Out Inventory @ t+1 equals Inventory @ t plus production minus demand Identifying Objective Function • maximize revenue minus cost minimize cost minus revenue minimize number of people hired • Be careful to make sure all costs and profits are properly accounted for, appearing once and only once. • net out any sunk or fixed costs Classes of LP Models 1. Product Mix (e.g., Digital Short Term Planning) 2. Blending 3. Multi Period Planning 4. Multi Stage Coordination 5. Covering and Cutting Stock Problems 6. Design Parameter Optimization 7. Network Planning 8. Network Design 9. Capital Budgeting 10. Process Design and Layout Example - Logistics Planning Problem One Product Planning Period Planning Horizon Bulk Road Salt Month 12 Months: April ---- March Production Locations: 4 Mines Stockage Locations: 4 Mines 50 Stockpiles 100's of Customer Sites Transportation: Mines to Stockpiles by Rail ( Barges) Stockpiles to Customers by Truck Issues: Production Plan for Seasonal Demand Transportation and Inventory Plan Decision Support for Bidding Process Indices: i---mines; j--stockpiles; k--customers; t--time periods Data Requirements: demand forecasts capacities cost coefficients Decision Variables Production at i in time period t Inventory at i at end of time period t Inventory at j at end of time period t Inventory at k at end of time period t Rail shipments from i to j in t Truck shipments from j to k in t Constraints • Inventory Flow Balance • Limits on Production/Transportation Activities mine production rail cars inbound at stockpiles outbound link limit inventory storage • Objective MIN Cost = production costs + inventory holding costs + mine to stockpile shipment costs + stockpile to customer shipment costs