The Texas Gladiators won the Super Bowl last year. As a result, sportswear such

Question

The Texas Gladiators won the Super Bowl last year. As a result, sportswear such as hats, sweatshirts, sweatpants. and jackets with the Gladiator's logo are popular. The Gladiators operate an apparel store outside the football stadium. It is near a busy highway, so the store has heavy customer traffic throughout the year, not just on game days. In addition, the stadium has high school or college football and soccer games almost every week in the fall, and baseball games in the spring and summer. The most popular single item the stadium store sells is a red and silver baseball-style cap with the Gladiators' logo on it. The cap has an elastic headband inside it, which conforms to different head sizes. However, the store has had a difficult time keeping the cap in stock, especially during the time between the placement and receipt of an order. Often customers come to the store just for the hat; when it is not in stock, customers are upset, and the store management believes they tend to go to other competing stores to purchase their Gladiators' clothing. To rectify this problem, the store manager, Jessica James, would like to develop an inventory control policy that would ensure that customers would be able to purchase the cap 99% of the time they asked for it. Jessica has accumulated the following demand data for the cap for a 30-week period. (Demand includes actual sales plus a record of the times a cap has been requested but not available and an estimate of the number of times a customer wanted a cap when it was not available but did not ask for it.) The store purchases the hats from a small manufacturing company in Jamaica. The shipments from Jamaica are erratic, with a lead time of 20 days. In the past, Ms. James has placed an order whenever the stock got down to 150 caps. What level of service does this reorder point correspond to? What would the reorder point and safety stock need to be to achieve the desired service level? Discuss how Jessica James might determine the order size of caps and what additional, if any, information would be needed to determine the order size.

Explanation / Answer

The weekly demand follows the following distribution:

From the above table we can assume that on the average 43 caps are demanded per week and the weekly demand has standard deviation of 10. 4. In other words assuming demand follows normal distribution with mean 43 and s.d. 10.4, the expected weekly demand may be mean (+/- )3s.d. from 11 to 74 approximately.

For 99% of the time we can have the upper limit as 42.5 + 2.58*10.4 = 70approximately

Therefore it is recommended to have 70 caps per week. As the lead time is 20days and erratic, therefore it is better to have reorder point equivalent to three weeks demand of 210 caps.(70*3)

The reorder level of 150 caps may be sufficient for 150/70 weeks, say for 15 days whereas the lead time is minimum 20days.

For determination of lot size ordering, it is required to have ordering cost per order and inventory carrying cost.

Week Demand 1 38 2 51 3 25 4 60 5 35 6 42 7 29 8 46 9 55 10 19 11 28 12 41 13 37 14 44 15 45 16 56 17 62 18 53 19 46 20 41 21 52 22 38 23 49 24 46 25 47 26 41 27 39 28 50 29 28 30 34 Mean 1277 42.56667 Standard deviation 10.40783

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