A restaurant supply store is trying to determine how many boxes of a certain commonly used item to order. They estimate that that the demand for the item averages 30 boxes per week. The ordering cost is $10 per order and it costs $20 to hold one box in inventory for one year. The lead time for orders is always 1.5 weeks and inventory is managed with a continuous review policy. Show all your work for all parts.

(8 pts.) a) Determine the economic order quantity (that is, how many boxes they should order to minimize their cost) and the corresponding total annual cost.

(4 pts.) b) Calculate the reorder point and state when they should place an order.

(6 pts.) c) Suppose the store orders every two weeks (rather than your answer to part a). How large is an order on average and what is the total annual cost? How much more does this cost than using the best order size?

Part a:

EOQ = 40 units

Part b:

Re-order point = 45

Place an order when inventory falls to 45 units.

Part c:

Annual cost= Q*H/2+ D*S/Q = $861

The difference in cost= 861- 791 = $70 more than best order size.

Calculate the reorder point and state when they should place an order.

Explanation:

Demand per week = 30 boxes

Weeks per year = 52

Annual demand = Demand per week × Weeks per year

Annual demand = 30 boxes × 52 weeks

Annual demand = 1,560 boxes per year

Task a:

Determine the economic order quantity (that is, how many boxes they should order to minimize their cost) and the corresponding total annual cost.

Part 1: Economic Order quantity

EOQ =

Where Co = Ordering cost = $10

D = Annual demand = 1,560

Ch = Holding cost = $20

EOQ =

EOQ = 39.49 units = 40 units

Part 2: Total annual cost at EOQ level:

At Economic Order Quantity (EOQ), the total annual ordering cost and holding cost are all equal:

Annual ordering cost = (Annual demand × Ordering cost per order ) ÷ EOQ

Annual ordering cost = (1,560 × $10) ÷ 40

Annual ordering cost = $390

Annual holding cost = ((1,560 × 20)/40) ÷ 2

Annual holding cost = $390

Part b:

Calculate the reorder point and state when they should place an order.

Part 1: Re-order point

Re-order point = (Annual demand÷week)×lead time

Re-order point = (1,560 ÷ 52) × 1.5

Re-order point = 45

Part 2: When they should place an order.

Place an order when inventory falls to 45 units.

Part c

Suppose the store orders every two weeks (rather than your answer to part a). How large is an order on average and what is the total annual cost? How much more does this cost than using the best order size?

Order size= 30 per week* 2weeks= 60 units

Annual cost= Q*H/2+ D*S/Q = $861

The difference in cost= 861- 791 = $70 more than best order size.

c is the correct answer.