Introduction to Optimization Introduction to Optimization

ancmat02.qxd 11/16/06 3:26 PM Page B18B18 • SUPPLEMENT BINTRODUCTION TO OPTIMIZATIONFIGURE B-16Solver Results box indicating model notdetected as linearIf you are sure your problem is linear, make sure all spreadsheet formulas involvingvariables are linear. Solver’s check for a model being linear is not perfect, however, andsometimes simply solving the model again will cause a more normal completion message.Particular culprits for true nonlinearity are constraints involving percentages orratios (usually these can be put into a linear form) or the use of functions such as IF,MAX, MIN, and other functions in the model. These functions are nonlinear and cannotbe used to manipulate the decision variables in a LP.OPTIMIZATION WITHIN OM: PUTTING IT ALL TOGETHERSupplement Highlights234As we discussed in the opening paragraphs of this chapter, everyone uses informal optimizationthinking to make many routine decisions. However, formal optimization isused in all types of decisions in organizations. On a large scale, Continental Airlinesrecently developed an optimization-based system to better recover from unexpectedevents such as inclement weather, aircraft mechanical problems, and crew (pilots andflight attendants) availability. Disruptions in one part of the flight network cause rippleeffects throughout, because planes and crews do not get where they need to go.CALEB Technologies developed a system called CrewSaver that has already helpedContinental recover from major disruptions ranging from weather delays to the September11, 2001 terrorist attacks. Since 2000, CALEB estimates it has saved Continental$40 million due to more effective recovery procedures.On a smaller scale, but no less significant to the organization, Welch’s has developeda spreadsheet-based optimization tool to help it develop the optimal recipes forfruit juices. Since raw ingredient supplies and prices vary and demand also changes,management must have a tool that will provide the optimal allocation of the raw materialsto the products. The tool is used each month to aid management in the logisticsplan. The savings during the first year (1994) were between $130,000 and $170,000.1 People use informal “optimization” to make decisions5 Solver, an Excel add-in, is able to solve both linear andalmost every day.nonlinear problems. This supplement focuses on solvinglinear problems.Organizations use formal optimization methods to addressproblems across the organization, from optimal pricing tolocating a new facility.The algebraic formulation of an LP comprises the definitionsof the decision variables, an algebraic statement of theobjective function, and algebraic statements of the constraints.The spreadsheet model for an optimization problem shouldbe guided by the algebraic formulation.67After solving a LP, you must interpret the results to see ifthey make sense, fix problems with the model, and find theinsights useful for management.Solver can generate the Answer and Sensitivity Reports. TheSensitivity Report provides additional information aboutwhat happens to the solution when certain coefficients ofthe problem are changed.