A local retailer of party supplies purchases special paper cups from a local dis

Question

A local retailer of party supplies purchases special paper cups from a local distributor for $10/case and sells them to customers for $16.99 per case.   Traditionally they have purchased in lot sizes of 500 cases, which means about ten orders per year given the average annual demand of 5,000 cases. Orders have a two week lead time. The company is currently doing an analysis of their ordering policies, including lot sizes. A recent project by a co-op student has estimated an annual inventory holding cost of 22% of unit cost, and a fixed cost to place an order, independent of order quantity, of $37. For each of the following question, provide answers to two decimals and without commas or dollar signs.

I. What is the annual ordering cost (of their current lot size)?

II. What is the annual holding cost, related to the cycle stock(again, based on current lot size)?

III. What is the optimal order quantity that minimizes the sum of annual holding and ordering costs?

Explanation / Answer

Annual demand (D) = 5000 cases

Ordering cost (S) = $37

Holding cost (H) = 22% of unit cost = 22% of $10 = $2.20

Current lot size (Q) = 500 cases

I) For current lot size, Annual Ordering cost= (D/Q) S

= (5000/500)37

= $370

II) Annual holding cost = (Q/2)H = (500/2)2.20 = $550

III) optimal order quantity = sqrt of (2DS /H)

= sqrt of [(2 x 5000 x 37) / 2.20]

= 410.10 cases

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