Lot Size-Reorder Point System 9=110; Step1:1-F(R)=2h/p2=110*2/(25*200)=0.044; Step 2:check in Table A-4z=1.70 and L(z)=0.0183; Step3:R=4+z,o=100+1.70*25=143, Step4:n(R)=oL(z)=25*0.0183=0.4575, 22[K+pn(R】_ 2×200[50+25×0.4575] ≈111 2 Compare:Q and Q,are close,stop. Substitue Q,=111 into 1-F(R)=Oh/pA=0.044, z2=Z,=1.70,R2=R1=143
Lot Size-Reorder Point System 1 1 1 1 1 1 1 1 1 2 =110; Step 1: 1 ( ) / 110*2 / 25*200 0.044; Step 2: check in Table A-4 z =1.70 and L(z ) =0.0183; Step 3: 100 1.70*25 143; Step 4: ( ) 25*0.0183 0.4575; 2 [ Step 5: Q F R Qh p R z n R Lz K Q 1 1 2 ( )] 2 200[50 25 0.4575] ; 2 Compare: Q and Q are close, sto 1 . 1 1 p pn R h 2 22 21 2 1 Substitue Q =111 into 1 ( ) / 0.044, z =z =1.70, R =R =143 F R Qh p
Lot Size-Reorder Point System Results for Example 5.4:The optimal values of(Q,R)=(111, 143),that is,when Harvey's inventory of this type mustard hits 143 jars,he should place an order for 111 jars. Example 5.4 (Cont.):determine the following (1)Safety stock; (2)The average annual holding,setup,and penalty costs associated with the inventory control of the mustard: (3)The average time between placement of orders; (4)The proportion of order cycles in which no stock-outs occur>Among given number of order cycles,how many order cycles do not have stock-outs? (5)The proportion of demands that are not met
Lot Size-Reorder Point System • Results for Example 5.4: The optimal values of (Q, R)=(111, 143), that is, when Harvey’s inventory of this type mustard hits 143 jars, he should place an order for 111 jars. • Example 5.4 (Cont.): determine the following (1) Safety stock; (2) The average annual holding, setup, and penalty costs associated with the inventory control of the mustard; (3) The average time between placement of orders; (4) The proportion of order cycles in which no stock-outs occur>Among given number of order cycles, how many order cycles do not have stock-outs? (5) The proportion of demands that are not met
Lot Size-Reorder Point System Solution to Example 5.4(Cont.) 1)The safety stock is s=R-u=143-100=43 jars; 2)Three costs: The holding cost is h(Q/2+s)=2(111/2+43)=$197/jar; The setup cost is KA/Q=50x200/111=$90.09/jar; The penalty cost is pA n(R)/Q=25 x 200x0.4575/111=$20.61/jar Hence,the total average cost under optimal inventory control policy is $307.70/iar. 3)The average time between placement of orders: T=Q/=111/200=0.556yr=6.7 months; 3)Compute the probability that no stock-out occurs in the lead time,which is the same as that the probability that the lead time demand does not exceeds the reorder point:P(D<R)=F(R)=1-Qh/p=1-0.044=0.956: 4)The proportion of demand that stock out is n(R)/Q=0.4575/111=0.004
Lot Size-Reorder Point System Solution to Example 5.4 (Cont.) 1) The safety stock is s=R- =143-100=43 jars; 2) Three costs: The holding cost is h(Q/2+s)=2(111/2+43)=$197/jar; The setup cost is K /Q=50 200/111=$90.09/jar; The penalty cost is p n(R)/Q=25 200 0.4575/111=$20.61/jar Hence, the total average cost under optimal inventory control policy is $307.70/jar. 3) The average time between placement of orders: T=Q/ =111/200=0.556 yr=6.7months; 3) Compute the probability that no stock-out occurs in the lead time, which is the same as that the probability that the lead time demand does not exceeds the reorder point: P(D R)=F(R)=1-Qh/p =1-0.044=0.956; 4 ) The pro portion of demand that stock out is n ( R ) / Q=0.4575/111=0.004
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