1Introduction To Linear ProgrammingA. C. PandeyToday many of the resources needed as inputs to operations are in limited supply.Operations managers must understand the impact of this situation on meeting their objectives.Linear programming (LP) is one way that operations managers can determine how best to allocate their scarce resources.NOTE: Linear Programming is presented in Supplement I for Chapter 11. We will focus on formulation in this class.
2Linear Programming (LP) in OMThere are five common types of decisions in which LP may play a roleProduct mixProduction planIngredient mixTransportationAssignment
3LP Problems in OM: Product MixObjectiveTo select the mix of products or services that results in maximum profits for the planning periodDecision VariablesHow much to produce and market of each product or service for the planning periodConstraintsMaximum amount of each product or service demanded; Minimum amount of product or service policy will allow; Maximum amount of resources available
4LP Problems in OM: Production PlanObjectiveTo select the mix of products or services that results in maximum profits for the planning periodDecision VariablesHow much to produce on straight-time labor and overtime labor during each month of the yearConstraintsAmount of products demanded in each month; Maximum labor and machine capacity available in each month; Maximum inventory space available in each month
5Recognizing LP ProblemsCharacteristics of LP Problems in OMA well-defined single objective must be stated.There must be alternative courses of action.The total achievement of the objective must be constrained by scarce resources or other restraints.The objective and each of the constraints must be expressed as linear mathematical functions.
6Steps in Formulating LP Problems1.Define the objective. (min or max)2.Define the decision variables. (positive, binary)3.Write the mathematical function for the objective.4.Write a 1-or 2-word description of each constraint.5.Write the right-hand side (RHS) of each constraint.6.Write <, =, or >for each constraint.7.Write the decision variables on LHS of each constraint.8.Write the coefficient for each decision variable in each constraint.
7Cycle Trends is introducing two new lightweight bicycle frames, the Deluxe and the Professional, to be made from aluminum and steel alloys. The anticipated unit profits are $10 for the Deluxe and $15 for the Professional.The number of pounds of each alloy needed per frame is summarized on the next slide. A supplier delivers 100 pounds of the aluminum alloy and 80 pounds of the steel alloy weekly. How many Deluxe and Professional frames should Cycle Trends produce each week?
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