Linear Programming and Capacity Essay Example
Linear Programming and Capacity Essay Example

Linear Programming and Capacity Essay Example

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  • Pages: 3 (747 words)
  • Published: March 15, 2017
  • Type: Essay
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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 is not recommended.

We could also rent an upgrade specifically to increase our capacity to spin medium-sized yarn.

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The machine we're looking at costs $3000 per month, and we estimate the cost of outsourcing medium-sized yarn to be $4023 per month—the machine would save us $1023 per month and is recommended.

If our demand for medium yarn increased in the short-run (before we have the chance to increase our in-house capacity) we would need to add an additional supplier to meet any additional demand over 5388 kg/month. The first 5388 cost us $12.30 per kg the rest cost us $13.76 per kg. To meet an order of 6000 kg/mo, we would need to charge at least $12.44 per kg. It would be interesting to know if they could substitute the last 612 for another kind of yarn, which would allow us to keep our current allocation and charge a lower price.

We also wanted to know the sensitivity of our model to changes in prices charged by suppliers. Your accounting manager expressed concern that price may vary by 5%. We looked at each supplier and concluded that 5% increases in prices for Ambrosi, Bresciani, De Blasi, and Estensi would change our recommendations, because other alternatives would start to look cheaper. Castri could raise their prices up to 6.6% without losing our business.

It's also possible that a supplier would change their capacity. Currently, we are working up to capacity in most of our mills, and a capacity change would effect our outsourcing plan. A notable exception to this is De Blasi, where we are using less than 30% of the available capacity—they could decrease capacity up to 72% without effecting our decision.

Spinning fine yarn at the Ambrosi mill is saving us $45,000 over our one-year contract

with them. We would be willing to share up to $45,000 of the set-up costs to help Ambrosi produce fine yarn.

We discovered that Giuliani may be able to run an over-time shift, paying their workers a little more to increase their capacity. We ran the model again, including increased costs and increased capacity and found that it would not give us an advantage—we would not use the overtime shift.

Our model is based on current needs and gives us a good picture of our short-term options. If management would like to increase in-house spinning capacity to meet the capacity available for the other steps in the process, they should use the model to compare monthly machine rental costs with outsourcing costs. They may also consider the added value of decreased reliance on other mills whose decisions are out of our control. Purchasing rather than renting machines that increase in-house capacity may decrease our monthly costs and make spinning in-house cheaper than outsourcing in the long run. Using a linear optimization model to analyze new opportunities will help Filatoi Riuniti make efficient decisions as demand, capacity and costs change in the future or unforeseeable events change our options.

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