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# Lecture03 - IE 505 MATHEMATICAL PROGRAMMING Lecture#3 Date...

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IE 505 MATHEMATICAL PROGRAMMING Lecture #3 Date: September 23 rd 2008 LP Examples 1

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Pala Textile Pala Textile produces five types of fabrics using five types of raw materials (wool, cotton, silk, flax, velvet) Production is carried in two stages: In stage 1,five types of raw materials are woven. In stage 2, each raw material is used to produce a specific fabric (raw material i is used to produce fabric i, i = 1, …, 5). Demand for fabric i is D i over a quarter year time horizon.
Pala Textile As well as weaving the raw materials in-house, the company can also outsource woven raw materials and in both cases use the woven raw materials for final operation to produce fabric. 3

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Pala Textile Fabric i is sold at the market for b i \$/meter. Woven raw material i can also be outsourced for c i \$/meter. In-house weaving of raw material i costs g i \$/meter. Stage 2 costs an additional g i \$/meter for woven raw material i .
Pala Textile There are 2 types of looms Dobbie (10 available) Regular (80 available). Production rate of fabric i at both types of looms is p i meters/hour for both stage 1 and stage 2. Dobbie looms can produce all five types of fabrics whereas regular ones can only produces types 3, 4, and 5.

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Pala Textile Assuming that the company operates seven days a week and 24 hours a day formulate the problem of maximizing total profit over a quarter year time horizon Note that a quarter year consists of 13 weeks.
Decision Variables For i = 1, …, 5 y i : the amount of fabric i produced. x i : amount of woven raw material i outsourced For i = 1, …, 5; j = 1, 2 z ij : the amount of fabric i produced at stage j with a Dobbie loom.

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Lecture03 - IE 505 MATHEMATICAL PROGRAMMING Lecture#3 Date...

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