### Projects (1999 - Spring 2008)

Engineering >> Industrial & Management Systems

## by Haley Beutler

Submitted : Spring 2012

The problem of Inventory Management involves information about a company’s product. You are given the company’s projected number of units they are going to sell in one year, the fixed ordering charge for the product, and the annual cost of the inventory storage facility per unit. You are then asked to determine the optimal number of ordering cycles per year, the number of units ordered per cycle, and the total annual cost.

In order to determine the ideal number of ordering cycles, optimization should be used. Since you are looking for the amount of ordering cycles that would benefit the company, and therefore have the lowest cost, the minimization technique should be used. You should begin the problem by creating two functions: one showing the units per order, and one showing the orders per year. Then, you should substitute the value of units per order into a function of units per year so that you can create a single-variable equation that demonstrates the value of cost per year. Next, you should take the derivative of the equation and solve for zeroes to find the minimum value on the original function. You can check your answer by graphing the original function and visibly looking for the minimum curve on the graph. After performing minimization, you should determine the number of ordering cycles per year that would be the best choice for the company. By plugging the value back into original equations, you are also able to solve for the number of units ordered per cycle, and the total annual cost.

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 Advisors : Scott Rimbey, Mathematics and Statistics Scott Campbell, Chemical & Biomedical Engineering Suggested By : Scott Campbell