Production and Operation Managements Inventory Control Subject to Unknown Demand Dr.Na GENG Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Dr. Na GENG Department of Industrial Engineering & Management Shanghai Jiao Tong University Inventory Control Subject to Unknown Demand
Inventory Control Subject to Unknown Demand Contents ·Introduction ·The newsboy model Lot Size-Reorder Point System Service Level in (Q,R)System Additional Discussion of Periodic-review Systems Multiproduct Systems
Inventory Control Subject to Unknown Demand Contents • Introduction • The newsboy model • Lot Size-Reorder Point System • Service Level in (Q, R) System • Additional Discussion of Periodic-review Systems • Multiproduct Systems
Lot Size-Reorder Point System The procedure of computing Q and R:Qo=EOQ 1-F(R)=2h/pa check z,and L(z,value in Table A-4 R=u+2,0 n(R)=oL(3) =K+pn(R,)/h No,i=i+1 Qi,Qit close? ↓Yes Stop
The procedure of computing Q and R: Q 0=EOQ Lot Size-Reorder Point System 1 () / F R Qh p i i check z and L(z ) value in Table A-4 i i R z i i ( ) i i n R Lz 1 2 [ ( )] / Q K pn R h i i Qi, Qi+1 close? Yes Stop No, i=i+1
Lot Size-Reorder Point System Example 5.4 Harvey's Specialty Shop sells a popular mustard that purchased from English company.The mustard costs $10 a jar and requires a six-month lead time for replenishment stock.The holding cost is computed on basis 20%annual interest rate;the lost-of-goodwill cost is $25 a jar;and bookkeeping expenses for placing an order amount to about $50.During the six-month lead time,average 100 jars are sold,but with substantial variation from one six-month period to the next.The demand follows normal distribution and the standard deviation of demand during each six- month period is 25.How should Harvey control the replenishment of the mustard?
Lot Size-Reorder Point System Example 5.4 Harvey’s Specialty Shop sells a popular mustard that purchased from English company. The mustard costs $10 a jar and requires a six-month lead time for replenishment stock. The holding cost is computed on basis 20% annual interest rate; the lost-of-goodwill cost is $25 a jar; and bookkeeping expenses for placing an order amount to about $50. During the six-month lead time, average 100 jars are sold, but with substantial variation from one six-month period to the next. The demand follows normal distribution and the standard deviation of demand during each sixmonth period is 25. How should Harvey control the replenishment of the mustard?
Lot Size-Reorder Point System Solution to Example 5.4 To find the optimal values of R and Q The mean lead time demand in six-month lead time is 100,the mean yearly demand is 200,giving A=200; ·h=10×0.20=2,K=50;P=25; Initialization:Q,=E0Q=V2K/h=√2×50×200/2=100， Step1:1-F(R)=Qh/p2=100*2/(25*200)=0.04; Step 2:check in Table A-4Zo=1.75 and L(zo)=0.0162; Step3:R=4+2oo=100+1.75*25=144; Step4:n(R)=oL(zo)=25*0.0162=0.405, 22K+pnR】=,2×20050+25×0.405] Step =110, h 2 Compare:Qo and Q are not close,so return to step 1 and continue
Lot Size-Reorder Point System Solution to Example 5.4 To find the optimal values of R and Q • The mean lead time demand in six-month lead time is 100, the mean yearly demand is 200, giving =200; • h=10 0.20=2; K=50; P=25; 0 Initialization: =EOQ= 2 / 2 50 200 Q Kh / 2 1 0 0; Step 1: 1 ( ) / 100*2 / 25*200 0.04; F R Qh p 0 0 Step 2: check in Table A-4 z =1.75 and L(z ) =0.0162; 0 0 Step 3: 100 1.75*25 144; R z 0 0 Step 4: ( ) 25*0.0162 0.405; n R Lz 0 0 0 1 2 [ ( )] 2 200[50 25 0.40 11 5] Step 5: 2 0; K pn R Q h Compare: Q and Q are not close, so return to step 1 and continue. 0 1