# Question: When using the stochastic continuous review model presented in Sec 18 6

When using the stochastic continuous-review model presented in Sec. 18.6, a difficult managerial judgment decision needs to be made on the level of service to provide to customers. The purpose of this problem is to enable you to explore the trade-off involved in making this decision.

Assume that the measure of service level being used is L probability that a stockout will not occur during the lead time. Since management generally places a high priority on providing excellent service to customers, the temptation is to assign a very high value to L. However, this would result in providing a very large amount of safety stock, which runs counter to management’s desire to eliminate unnecessary inventory. (Remember the just-in time philosophy discussed in Sec. 18.3 that is heavily influencing managerial thinking today.) Management needs to address the question of what the best trade-off is between providing good service and eliminating unnecessary inventory.

Assume that the probability distribution of demand during the lead time is a normal distribution with mean μ and standard deviation σ. Then the reorder point R is R = μ + K1Lσ, where K1L is obtained from Appendix 5. The amount of safety stock provided by this reorder point is K1L σ. Thus, if h denotes the holding cost for each unit held in inventory per year, the average annual holding cost for safety stock (denoted by C) is C = hK1L σ.

(a) Construct a table with five columns. The first column is the service level L, with values 0.5, 0.75, 0.9, 0.95, 0.99, and 0.999. The next four columns give C for four cases. Case 1 is h = $1 and σ = 1. Case 2 is h = $100 and σ = 1. Case 3 is h = $1 and σ = 100. Case 4 is h = $100 and σ = 100.

(b) Construct a second table that is based on the table obtained in part (a). The new table has five rows and the same five columns as the first table. Each entry in the new table is obtained by subtracting the corresponding entry in the first table from the entry in the next row of the first table. For example, the entries in the first column of the new table are 0.75 0.5 = 0.25, 0.9 – 0.75 = 0.15, 0.95 0.9 = 0.05, 0.99 0.95 = 0.04, and 0.999 0.99 = 0.009. Since these entries represent increases in the service level L, each entry in the next four columns represents the increase in C that would result from increasing L by the amount shown in the first column.

(c) Based on these two tables, what advice would you give a manager who needs to make a decision on the value of L to use?

Assume that the measure of service level being used is L probability that a stockout will not occur during the lead time. Since management generally places a high priority on providing excellent service to customers, the temptation is to assign a very high value to L. However, this would result in providing a very large amount of safety stock, which runs counter to management’s desire to eliminate unnecessary inventory. (Remember the just-in time philosophy discussed in Sec. 18.3 that is heavily influencing managerial thinking today.) Management needs to address the question of what the best trade-off is between providing good service and eliminating unnecessary inventory.

Assume that the probability distribution of demand during the lead time is a normal distribution with mean μ and standard deviation σ. Then the reorder point R is R = μ + K1Lσ, where K1L is obtained from Appendix 5. The amount of safety stock provided by this reorder point is K1L σ. Thus, if h denotes the holding cost for each unit held in inventory per year, the average annual holding cost for safety stock (denoted by C) is C = hK1L σ.

(a) Construct a table with five columns. The first column is the service level L, with values 0.5, 0.75, 0.9, 0.95, 0.99, and 0.999. The next four columns give C for four cases. Case 1 is h = $1 and σ = 1. Case 2 is h = $100 and σ = 1. Case 3 is h = $1 and σ = 100. Case 4 is h = $100 and σ = 100.

(b) Construct a second table that is based on the table obtained in part (a). The new table has five rows and the same five columns as the first table. Each entry in the new table is obtained by subtracting the corresponding entry in the first table from the entry in the next row of the first table. For example, the entries in the first column of the new table are 0.75 0.5 = 0.25, 0.9 – 0.75 = 0.15, 0.95 0.9 = 0.05, 0.99 0.95 = 0.04, and 0.999 0.99 = 0.009. Since these entries represent increases in the service level L, each entry in the next four columns represents the increase in C that would result from increasing L by the amount shown in the first column.

(c) Based on these two tables, what advice would you give a manager who needs to make a decision on the value of L to use?

**View Solution:**## Answer to relevant Questions

The preceding problem describes the factors involved in making a managerial decision on the service level L to use. It also points out that for any given values of L, h (the unit holding cost per year), and σ (the standard ...To help fill its seats for a particular flight, an airline offers a special nonrefundable fare of $100 for customers who make a reservation at least 21 days in advance and satisfy other restrictions. Thereafter, the fare ...A young entrepreneur will be operating a firecracker stand for the Fourth of July. He has time to place only one order for the firecrackers he will sell from his stand. After obtaining the relevant financial data and some ...Reconsider Prob. 18.7-5. The bakery owner, Ken Swanson, now has developed a new plan to decrease the size of shortages. The bread will be baked twice a day, once before the bakery opens (as before) and the other during the ...Every Saturday night a man plays poker at his home with the same group of friends. If he provides refreshments for the group (at an expected cost of $14) on any given Saturday night, the group will begin the following ...Post your question