# Linear Programming and Capacity

**Topics:**Linear programming, Optimization, Operations research

**Pages:**4 (898 words)

**Published:**February 5, 2011

Prepared by

Team 7

Anupam Priyadarshi,

Ben Durwood,

Chung-Hsuan Tung,

Karen Boyd,

Matt Beaumont.

Executive Summary:

Filatoi Riuniti is expanding to meet growing demand, and we have used outsourcing to keep up. Currently, we outsource only coarse and medium-sized yarn, but we believe that it would be more efficient to look at outsourcing all types. There are so many potential suppliers and constraints to consider that we constructed a linear programming model to identify our best option and check our solution's sensitivity to changes in our situation.

We've analyzed our potential suppliers for each gauge, taking into account their capacity, cost of production for each plant, and transportation costs (The model and our objective function can be found in the appendix.) Our goal was to allocate spinning production (at Filatoi Riuniti and six local mills) in a manner that would minimize overall costs, while meeting the demand and operating within the capacity constraint of each plant. Given the output of our optimization model, we should be outsourcing the spinning of our yarn in this way:

Sensitivity Analysis for Linear Optimization model:

Keep in mind that this model is sensitive to changes in each constraint, and there are ways that we can reduce our costs in the long run. We took into account several specific changes that management identified as probable and sought to see how they would change our optimal production strategy.

First, we wanted to consider the proposal that we rent upgrades to our in-house spinning capacity. Based on the options available, it would not be cost-effective to invest more than $1270 per month in upgrades. The equipment we are looking at costs $1500 per month and...

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