Reorder Point Systems

Transcription

1 Reorder Point Systems EOQ with a reorder point The reorder point problem The service level method Fixed-order-interval model Reading: Page Oct 23 ISMT162/Stuart Zhu 1

2 EOQ with a Reorder Point The replenishment leadtime or simply leadtime is denoted by L (we assume L < T ) With deterministic demand, the leadtime demand = DL and R=DL is called the reorder point The deterministic reorder point policy: whenever the remaining inventory is reduced to R, we order exactly the EOQ so that there will be no stock out and inventory cost is minimized What is R if L T? Oct 23 ISMT162/Stuart Zhu 2

3 Leadtime and Reorder Point Q I Order in advance so that the remaining inventory can satisfy the leadtime demand Reorder point R Place order Leadtime Receive order Place order Receive order Time Oct 23 ISMT162/Stuart Zhu 3

4 What should you do if leadtime demand is not known exactly? We now consider the problem of when to order Oct 23 ISMT162/Stuart Zhu 4

5 The Reorder Point Problem Inventory depletion (by demand) monitored continuously Good estimate for the total demand in a year Usually impossible to forecast future demand very accurately for a short time period How to compute the reorder point when leadtime demand is known probabilistically? Oct 23 ISMT162/Stuart Zhu 5

6 The Reorder Point When placing an replenishment order, the remaining stock should cover the leadtime demand Any new order can only be used for demands after L Demand in L is uncertain How to determine the remaining inventory R when an order is placed? R 1 R 2 Inventory on hand order L L Oct 23 ISMT162/Stuart Zhu 6

7 The Service Level Method Service level: Service level is a measure of the degree of stockout protection provided by a given amount of safety inventory β = Probability that all leadtime demands are satisfied immediately, i.e., β = Prob.( Leadtime Demand R) (1) Oct 23 ISMT162/Stuart Zhu 7

8 Normal Leadtime Demand R = μ + z β σ (2) s = z β σ R = mean leadtime demand + safety stock Oct 23 ISMT162/Stuart Zhu 8

9 Safety Stock Assuming normally distributed leadtime demand, the problem is transformed to that of determining the safety stock Q Inventory on hand R order order order mean demand during supply leadtime safety stock Time t L L Oct 23 ISMT162/Stuart Zhu 9

10 Example: Southern Metal Doors (SMD) The weekly sales of metal doors at SMD Ltd. in Dong Guan vary, with an average of 1000/week and a standard deviation of 250/week. SMD s production follows the sales closely, so that the consumption of a main metal material follows the same distribution The replenishment leadtime of this main metal material from the supplier is 1 week SMD is currently placing an order whenever the remaining material is only enough to make 1200 doors What is the probability of no stockout in the leadtime? If SMD wants the service level to be 95%, what should the safety stock be? Oct 23 ISMT162/Stuart Zhu 10

11 SMD s Service Level Service Level: SL =? (The area of the shaded part under the curve) Mean: µ = 1000 R = 1200 Oct 23 ISMT162/Stuart Zhu 11

12 Computing Service Level Average weekly demand µ = 1000 Standard deviation of demand σ = 250 R = 1200, We assume the sales (demand) is normally distributed: z β = (R µ) / σ = 0.8 Service Level SL = Probability (Leadtime Demand 1200) = 78.8% Oct 23 ISMT162/Stuart Zhu 12

13 Computing Safety Stock and Reorder Point What should the reorder point and safety stock for a β = 95% service level be? From the normal table z 0.95 = Safety stock: s = z 0.95 σ= 412 Reorder point: R =μ+s = 1412 Oct 23 ISMT162/Stuart Zhu 13

14 The Impact of Service Level β 79% 90% 95% 98% 99% s increase 61% 28% 25% 13% Observations: The higher the service level is, the higher the safety stock is required; When service level is high, it takes relatively more stock to increase it. Oct 23 ISMT162/Stuart Zhu 14

15 Fixed-Order-Interval Model Key Periodic review model Fixed time interval for each order Decision How much to order (Q) Oct 23 ISMT162/Stuart Zhu 15

16 Oct 23 ISMT162/Stuart Zhu 16

17 Computing Q Q OI = Order interval (length of time between orders) Oct 23 ISMT162/Stuart Zhu 17

18 Inventory on hand A order Q order Safety stock LT OL Time t LT+OL Oct 23 ISMT162/Stuart Zhu 18

19 Risk of a Stockout for SMD Suppose OI = 3 weeks, A =1300 units, Q= 3500 units mean demand per week = 1000 units, standard deviation = 250 units Risk at the end of the initial lead time z β = ( )/250 =1.2 By Normal table, SL = =88.5% Risk = % = 11.5% Risk at the end of the second leadtime z β = ( )/( /2 ) =1.6 By Normal table, SL = =94.5% Risk = % = 5.5% Oct 23 ISMT162/Stuart Zhu 19

20 Review Problems Problem 21 at Page 588 Problem 27 at Page 589 Problem 29 at Page 589 Oct 23 ISMT162/Stuart Zhu 20