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# Class_2a - EMSE 154 254 Applied Optimization Modeling Class...

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EMSE 154 – 254 Applied Optimization Modeling Class 2 Instructor: Hernan Abeledo Source: Applications Modeling with Xpress-MP 1 EMSE 154-254 Applied Optimization Modeling Hernán Abeledo Department of Engineering Management and Systems Engineering The George Washington University Fall 2008

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EMSE 154 – 254 Applied Optimization Modeling Class 2 Instructor: Hernan Abeledo Source: Applications Modeling with Xpress-MP 2 Today This handout: Mosel examples Graphical solution of LPs with two variables Possible outcomes of an LP Introduction to sensitivity analysis PPT handout: LP modeling Typical LP constraints Network models (if we have enough time)
EMSE 154 – 254 Applied Optimization Modeling Class 2 Instructor: Hernan Abeledo Source: Applications Modeling with Xpress-MP 3 The chess set problem: description A small joinery makes two different sizes of boxwood chess sets. The small set requires 3 hours of machining on a lathe, and the large set requires 2 hours. There are four lathes with skilled operators who each work a 40 hour week, so we have 160 lathe-hours per week. The small chess set requires 1 kg of boxwood, and the large set requires 3 kg. Unfortunately, boxwood is scarce and only 200 kg per week can be obtained. When sold, each of the large chess sets yields a profit of \$20, and one of the small chess set has a profit of \$5. The problem is to decide how many sets of each kind should be made each week so as to maximize profit. Let xs : the number of small chess sets to make xl : the number of large chess sets to make Then, an LP model of this decision problem is:

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EMSE 154 – 254 Applied Optimization Modeling Class 2 Instructor: Hernan Abeledo Source: Applications Modeling with Xpress-MP 4 Some modeling assumptions made above: Linearity assumptions: o For each size of chess set, manufacturing time is proportional to the number of sets made. o No down-time (or set-up costs) because of change in production between types of sets. o Revenue from sales is linear (e.g., no discount pricing) Deterministic assumptions: o Available supply of raw material (wood) is known with certainty. o All wood is usable (quality of raw material known). o All workers show up for work (labor availability assumed certain) o All sales at the same known price (prices are assumed known with certainty) Other modeling assumptions: o We can sell all the chess sets we made. o No expected breakdowns in production process. o
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Class_2a - EMSE 154 254 Applied Optimization Modeling Class...

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