# supply chain

For all the problems, to receive full scores, you have to show your complete and accurate work. If you only provide the final answers without showing your computations, you will not be assigned a full score (or you will miss the opportunity of receiving partial credit).

Problem 1: Periodic Review System (8 points)

You work for a retailer that uses a monthly periodic system to maintain the inventory of water heaters it sells. Below is the sales data for the last 5 months.

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 Month Jan Feb Mar Apr May Units Sold 265 227 239 238 213

What is the companyâ€™s average monthly demand for water heaters? (2 points)

Assume the standard deviation of demand is 19.1 water heaters and the company wants to be in stock at least 95% of the time. What is the appropriate restocking level? (3 points)

If there are currently 42 water heaters on hand when the order is placed for June, how many water heaters should be ordered? (3 points)

Problem 2: Economic Order Quantity (10 points)

A chemical plant orders barrels of chlorine that is used at the rate of 2,440 barrels per year. Each order that is placed with the supplier costs \$24 to process and the annual cost to hold inventory is \$150 per barrel. Delivery lead time of the barrelshas averaged 5 days and the plant manager has set a safety stock level of 40 barrels.

What is the economic order quantity? (2 points)

What is the total holding cost for the year? (2 points)

What is the total ordering cost for the year? (2 points)

How many orders will be placed each year? You can leave this answer as a decimal. (2 points)

The next order should be placed when chlorine inventory drops to what amount? (assume 365 days in one year for converting annual demand to daily demand) (2 points)

Problem 3: Quantity Discounts (7 points)

The UWM Bookstore orders keychains out of a catalog from a supplier. The demand for these keychains is 5,982 per year. There is a \$15 charge for placing an order and a \$9 cost per keychain to hold it in inventory for the year.

What is the economic order quantity? (2 points)

For part b) assume prices for the keychains are based on the quantity purchased with each order, so if less than 400 are ordered, the unit price is \$1.35, if 400 to 599 are ordered the unit price is \$1.25, and if 600 or more are ordered the unit price is \$1.10.

What is the total annual cost (holding + ordering + purchase price) at the economic order quantity? (2 points)

What order quantity will result in the lowest total annual cost (holding + ordering + purchase price) to the UWM Bookstore? Be sure to show your work for full credit. (3 points)

Extra Credit: Single-Period Inventory System (5 points)

The restaurant you are working at makes one massive batch of soup each day. If you run out before the end of the day, the last few customers are less than satisfied, but if you make too much, it can be sold to the local farmer for animal food.Every serving costs \$0.22 to make and can be sold for \$2.50 to customers. You have to pay \$0.02 per serving to transport the extra servings to the farmer, but the farmer will pay you \$0.16 per serving. The average daily demand is 191 servings with a standard deviation of 19 servings.

What is the Shortage Cost? (1 point)

What is the Overage Cost? (1 point)

What is the target service level? (1 point)

How many servings of soup should your restaurant make each day to meet this service level? (2 points)