Chapter $12-$ Inventory Management

A wine maker buys glass bottles to bottle his product. He uses $5000$ bottles per year and operates $250$ days per year. Holding costs are $15\%$ of unit cost and ordering costs are $$100$ per order.

His supplier charges $$1\mathrm{.}00$ per bottle for any order less than $1000$ bottles; for orders between $1000$ and $2999$ bottles, he gives a $5\%$ discount; for orders of $3000$ or more bottles, he gives a $10\%$ discount.

a$)$ Determine the optimal order quantity that will minimize total annual costs.

b$)$ Another supplier has offered a fixed price of $$0\mathrm{.}96$ per bottle, regardless of order size. Based on total annual costs, should the wine maker go with this supplier?

c$)$ Based on his experience, the wine maker has a lead time of $60$ days. If he would like to have $100$ bottles as safety stock, at what inventory level should he place an order for bottles?