Question

Annual demand for number 2 pencil at the campus store is normally distributed with mean 1000 and standard deviation 250. The store purchase the pencils for 6 cents each and sells them for 20 cents each. There is a two month lead time from the initiation to the receipt of an order. The store account estimates that the cost in employee time for performing the necessary paperwork to initiate and receive an order is $20, and recommends a 22 percent annual interest rate for determining holding cost. The cost of a stock out is the cost of lost profit plus an additional 20 cents per pencil which represents the cost of loss of goodwill.

Consider the problem of satisfying the demand for number 2 pencils faced by the campus store mentioned in problem 29.

a) Re-solve the problem, substituting a Type 1 service level criterion of 95 percent for the stock out cost.

Answer 1

In solving the problem using a 95% Type 1 service level criterion for the number 2 pencils demand, the reorder point is calculated using the z-score for 95% probability with the given mean and standard deviation, resulting in a reorder point of 1,411 pencils. The EOQ is recalculated to optimize ordering and holding costs, integrating the reorder point in the lead time decision-making process.

Step-by-step explanation:

When addressing the problem of satisfying the demand for number 2 pencils at the campus store, using a Type 1 service level criterion of 95 percent, we first need to acknowledge that this alters the way we handle stock and ordering. A 95% service level implies that the store wants to have enough inventory to meet 95% of the demand without running into a stock out. In a normally distributed demand scenario with a mean (μ) of 1,000 and a standard deviation (σ) of 250, we can determine the appropriate order level (reorder point) by finding the z-score that corresponds to a 95% probability, which for a standard normal distribution is 1.645. The reorder point then would be μ + (z × σ), equating to 1,000 + (1.645 × 250) = 1,411.25, which we would round up to ensure stock availability.The economic order quantity (EOQ) also needs to be recalculated to incorporate the costs of ordering and holding inventory. Given the 22 percent interest rate for holding costs, $20 ordering cost, and the cost per unit of pencil, the EOQ formula can be used to optimize the order quantity. To include the change for a 95% service level criterion, the reorder point of 1,411 (as calculated above) will come into play when determining when to place an order during the two-month lead time.The stock out cost is no longer a primary factor as we are using a service level approach which quantifies the desired in-stock probability, rather than a direct cost for each unit stock out. This approach directly affects the customer satisfaction and retention for the campus store.