exercise supply chain

Topics: Normal distribution, Inventory, Economic order quantity Pages: 8 (1318 words) Published: April 15, 2014
Exercise Lecture 1 – Chapter 2 Inventory Management
1. A drugstore sells bandages for $5 per box. The monthly demand for this product has a normal distribution with a mean of 100 and a standard deviation of 30. The store adopts a continuous review policy in which the order quantity equals the average demand for one month and the reorder point equals 43 boxes. The lead time for an order is one week, where each month contains exactly four weeks. a. What is the cycle service level for this product? (see appendix for the look-up tables of a standard normal distribution) b. What is the fill rate for this product?

c. The drugstore wants to guarantee a cycle service level of 95% by adjusting the reorder level. What should be the minimal value of the reorder point? d. The drugstore wants to guarantee a fill rate of 95% by adjusting the reorder level. What should be the minimal value of the reorder point? e. What would be the average relative difference in holding cost when the drugstore switches from the policy provided by the answer in part c to the policy provided by the answer in part d?

2. Suppose you are a trader in the vegetable and fruit business and you want to buy fresh tomatoes. A box of tomatoes costs $0.40 and you sell it for $1.20. When a customer observes a stock out, the customer is likely to change to a competitor, which results in a loss of goodwill that is quantified as $0.50. Any remaining boxes at the end of the week are sold for $0.15. Suppose it was observed that the demand per week ranges from 15 boxes to 21 boxes. Based on the demand observations in the last 50 weeks, the weekly demand forecast is as follows:

The owner needs to place an order for tomatoes for the next week. How many boxes should (s)he order to maximize the expected profit?

3. Wohl's Discount Store sells toy race cars with a wholesale price of $5. The estimated annual demand ranges from 4,225 to 5,625 race cars. The fixed order cost is $50, whereas the annual inventory carrying cost is 20% of the wholesale price. a. What would be the range in which the optimal order quantity is in? b. As it turns out the actual demand was 5,041 race cars. What would have been the optimal order quantity? c. What would be the maximum cost penalty when you compare the range that you found in the answer to part a to the order quantity that you found in the answer to part b?

4. Sarah’s Discount Emporium is selling 52’’ LCD TVs, which she buys for $250 at the manufacturer and sells for $600 in her store. It is difficult to predict demand for the LCD TVS. Based on data from previous years, the following forecast is made:

demand
10
15
20
25
35
45
50
probability
0.08
0.13
0.25
0.29
0.15
0.07
0.03

The TVs can only be ordered once at the manufacturer in January and everything which remains unsold after December can be returned to the manufacturer for a $100 salvage value. However, if Sarah has sold all her TVs before the end of December, the customers face a stock out. This will cost Sarah $200 loss of goodwill. a. What would be the optimal number of TVs to order?

b. How would your answer differ when Sarah assumes that the demand follows a normal distribution with mean 24.9 and standard deviation 9.95?

5. Madeline Thimmes’s Dream Store sells water beds and assorted supplies. Her best-selling bed has a normally distributed demand. The mean demand per day is 1 unit, and the standard deviation is 0.3 units. Madeline can order once a month (equal to 30 days). The lead time for every order is stochastic with an average of 7 days and a standard deviation of 2 days. Since she is able to share fixed ordering costs with other retailers, these costs are negligible per product. a. What type of replenishment policy should be used by Madeline? b. What should be the minimal value of the base-stock level when she wants to guarantee a cycle service level of 90%? (see appendix for the look-up table for a standard normal distribution) c....
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