Problem Set

Inventory Management: EOQ

Emma's Home Store sells beds and other home goods. Her winning product has an annual demand of $400$ units. Ordering cost is $\backslash (\backslash$$ $40\backslash )$ and holding cost is $\backslash (\backslash$$ $5\backslash )$ per unit per year. To minimize the total cost, how many units should be ordered each time an order is placed?

Inventory Management: POQ

Alfa Car Manufacturer produces parts at a rate of $300$ daily and uses these parts at a rate of $12500$ per year $(250$ working days$).$ Holding costs are $\backslash (\backslash$$ $2\backslash )$ per unit per year and ordering costs are $\backslash (\backslash$$ $30\backslash )$ per order.

a$)$ What is the economic production quantity?

b$)$ How many production runs per year will be made?

c$)$ What will be the maximum inventory level?

d$)$ What percentage of time will the facility be producing parts?

e$)$ What is the total annual cost?

Inventory Management: Order Quantity Discount Model

A laptop company purchases integrated chips at $\backslash (\backslash$$ $350\backslash )$ per chip. The interest rate is $\backslash (10\backslash \%\backslash )$ per unit per year, the ordering cost is $\backslash (\backslash$$ $120\backslash )$ per order, and sales are steady, at $400$ per month. The company's supplier decides to offer price discounts to attract large orders and the price structure is shown below.

What is the optimal order quantity and cost?

Inventory Management: Newsvendor

Good Times Restaurant buys fresh blue crab for $\backslash (\backslash$$ $5\backslash )$ per pound and sells them for $\backslash (\backslash$$ $9\backslash )$ per pound. Any unsold blue crabs are sold to a small grocery store for $\backslash (\backslash$$ $2\backslash )$ per pound. Good Times Restaurant believes that the demand follows the normal distribution, with a mean of $100$ pounds and a standard deviation of $15$ pounds. How many pounds should be ordered every day?