Question

Mr. Smith runs a world-food wholesale store in Nottingham. One of the items he orders from the Far East is Sriracha hot sauce. Every pack costs £10 and requires a six-month lead time for replenishment. Mr. Smith uses a 20% annual interest rate to compute holding costs. Estimated ordering cost is £50. During the six-month replenishment lead time, Mr. Smith estimates that he sells an average of 100 packs of sauce, but there is substantial variation from one six-month period to the next. The standard deviation of demand during each six-month is estimated to be 25. Assume that demand is described by a normal distribution and that excess demand is backordered.

- Mr. Smith estimates that if a customer requests the hot sauce and he is out of stock, the loss-of-goodwill costs is £25 per pack. Calculate the optimal values of;
(i) the reorder quantity Q, (ii) the reorder point R, and (iii) the safety stock.

- Suppose that Mr. Smith is willing to use a 98 service level objective. What would be the reorder point R, the order quantity Q and the safety stock under type 2 service (use a managerial approach)? Calculate also the annual holding cost and ordering cost.

Answer 1

Continuous or Fixed order quantity Model (Q,R Average demand during lead time Standard dev of lead time demand Annual Demand Lead Time (Months Item Cost Annual Holding Cost Rate Annual Holding Cost per Unit Ordering Cost per Order Backorder Cost Type 3 Polic 100 25 200 6 10 20% HD 50 25 VI2SD/H)100 96% 1.75 Iteration 0: Lot Size/ Optimal Order OtyEOQ F(R,) = 1-00H/(PD) Service level Z-value corresponding to F(R) Safety stock Reorder Point NORMISINV(.96 144 0.0161 0.404 110 Iteration 1: Standard Loss function corresponding to Z L(z for z-1.75 Expected backorder Lot Size / Optimal Order Qty EOQ Q1 Q0 and Q1 are not close, so iteration continued F(R2)1- Q,H/(PD) Iteration 2: Service level 95.61% 1.71 43 143 0.0179 0.449 Z-value corresponding to F(R2) Safety stock Reorder Point Standard Loss function corresponding to Z L(z Expected backorder Lot Size / Optimal Order Qty EOQ Q2 NORMSINV(.9561 for z-1.7:1 Q1 and Q2 are close, so iteration stopped Optimal (Q,R) (111, 143)

(i) Reorder quantity, Q = 111

(ii) Reorder point, R = 143

(iii) Safety stock = 43

(iv)

Type 2 Policy Average lead time demand Standard dev of lead time deman Annual Demand Lead Time (Months Item Cost Annual Holding Cost Rate Annual Holding Cost per Unit Ordering Cost per Order Type 2 Fill rate Optimal Order Qty EOQ Standard Loss function Z-value corresponding to L(z) Safety stock Reorder Point 100 25 200 6 10 20% 2 50 98% 100 0.0800 1.0210 Standard loss table 126 Optimal (Q,R) (100, 126)

R = 126

Q = 100

Safety stock = 26

Annual holding cost = 2*100/2+50*200/100+2*26 = 252