Linear Programming Modeling Applications with Computer Analyses

Linear Programming Modeling Applications with Computer Analyses

1. Purpose

   • linear programming (LP) can be used to model real-world problems in several managerial decision-making areas such as product mix, make–buy decisions, media selection, marketing research, financial portfolio selection, labor planning, shipping and transportation, allocation decisions, ingredient blending, and multiperiod scheduling

2. Aplications

   • Manufacturing Applications
     • Product Mix Problem
       • A fertile field for the use of LP is in planning for the optimal mix of products that a company should produce. A company must meet a myriad of constraints, ranging from financial concerns to sales demands to material contracts to union labor demands. Its primary goal is either to generate the largest profit (or revenue) possible or to keep the total manufacturing costs as low as possible
     • Make-Buy Decision Problem
       • An extension of the product mix problem is the make-buy decision problem it can satisfy the demand for a product by making some of it in-house (“make”) and by subcontracting or outsourcing the remainder to another firm (“buy”)
   • Marketing Applications
     • Media Selection Problem
       • LP models have been used in the advertising field as a decision aid in selecting an effective media mix
     • Marketing Research Problem
       • to marketing research problems and the area of consumer research
   • Finance Applications
     • Portfolio Selection Problem
       • A problem encountered by managers of banks, mutual funds, investment services, and insurance companies is the selection of specific investments from among a wide variety of alternatives
     • Alternate Formulations of the Portfolio Selection Problem
   • Employee Staffing Applications
     • Labor Planning
       • Labor planning problems address staffing needs over a specific planning horizon, such as a day, week, month, or year
     • Assignment Problem
       • Determine the most efficient assignment of people to jobs, machines to tasks, police cars to city sectors, salespeople to territories, and so on
   • Transportation Applications
     • Vehicle Loading Problem
       • Vehicle loading problems involve deciding which items to load on a vehicle (e.g. truck, ship, aircraft) to maximize the total value of the load shipped.
     • Transportation Problem

3. Aplications

   • Blending Applications
     • Diet Problem
       • The diet problem involves specifying a food or feed ingredient combination that satisfies stated nutritional requirements at a minimum cost level
     • Blending Problem
   • Multiperiod Applications
     • Production Scheduling Problem
       • Setting a low-cost production schedule over a period of weeks or months is a difficult and important management problem in most plants. Because most companies produce more than one product, the scheduling process is often quite complex that PL can help to solve
     • Sinking Fund Problem
       • An investor or a firm seeks to establish an investment portfolio, using the least possible initial investment, that will generate specific amounts of capital at specific time periods in the future.