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
The newsboy model-Optimal Policy for Discrete Demand .In some cases,accurate representation of the observed pattern of demand in term of continuous distribution is difficult or impossible. .In the discrete case,the critical ratio will generally fall between two values of F(Q) The optimal solution procedure is to locate the critical ratio between two values of F(Q)and choose the Q corresponding to the higher value
The newsboy model- Optimal Policy for Discrete Demand •In some cases, accurate representation of the observed pattern of demand in term of continuous distribution is difficult or impossible. •In the discrete case, the critical ratio will generally fall between two values of F(Q). • The optimal solution procedure is to locate the critical ratio between two values of F(Q) and choose the Q corresponding to the higher value
The newsboy model-Optimal Policy for Discrete Demand Example 5.2-Mac's newsstand f(4)=3/52 is obtained by dividing frequencies 4(the numbers of times 3 that a given weekly demand 4 occur during a year,i.e. 52 weeks)by 52; The critical ratio is 0.77,which corresponds to a value of F(Q) between Q=14 and Q=15. Q fQ) F(Q) Q fQ) F(Q) Q fQ) F(Q) 0 1/52 0.02 8 4/52 0.25 16 1/52 0.81 1 0 0.02 9 6/52 0.37 17 3/52 0.87 2 0 0.02 10 2/52 0.40 18 3/52 0.92 3 0 0.02 11 5/52 0.50 19 3/52 0.98 4 3/52 0.08 12 4/52 0.58 20 0 0.98 5 1/52 0.10 13 1/52 0.60 21 0 0.98 6 2/52 0.13 14 5/52 0.69 22 1/52 1.00 7 2/52 0.17 15 5/52 0.79
The newsboy model- Optimal Policy for Discrete Demand Example 5.2- Mac’s newsstand • f(4) =3/52 is obtained by dividing frequencies 4 (the numbers of times 3 that a given weekly demand 4 occur during a year, i.e. 52 weeks) by 52; • The critical ratio is 0.77, which corresponds to a value of F(Q) between Q=14 and Q=15. Q f(Q) F(Q) Q f(Q) F(Q) Q f(Q) F(Q) 0 1/52 0.02 8 4/52 0.25 16 1/52 0.81 1 0 0.02 9 6/52 0.37 17 3/52 0.87 2 0 0.02 10 2/52 0.40 18 3/52 0.92 3 0 0.02 11 5/52 0.50 19 3/52 0.98 4 3/52 0.08 12 4/52 0.58 20 0 0.98 5 1/52 0.10 13 1/52 0.60 21 0 0.98 6 2/52 0.13 14 5/52 0.69 22 1/52 1.00 7 2/52 0.17 15 5/52 0.79
The newsboy model-Extension to Include Starting Inventory Suppose that the starting inventory is some value u and u>0 The optimal policy is simply to modify that for u-=0. The same ideal is that we still want to be at Q*after ordering If u<Q*,order Q*-u;If u>Q*,do not order. Note that Q*should be understood as order-up-to point rather than the order quantity when u>0. Example 5.2 (Cont.)-Suppose that Mac has received 6 copies of the Journal at the beginning of the week from other supplier.The optimal policy still calls for having 15 copies on hand after ordering,thus he would order the difference 15-6=9 copies
The newsboy model- Extension to Include Starting Inventory Suppose that the starting inventory is some value u and u>0. The optimal policy is simply to modify that for u=0. The same ideal is that we still want to be at Q* after ordering. If u<Q*, order Q*-u; If u>Q*, do not order. Note that Q* should be understood as order-up-to point rather than the order quantity when u>0. Example 5.2 (Cont.)-Suppose that Mac has received 6 copies of the Journal at the beginning of the week from other supplier. The optimal policy still calls for having 15 copies on hand after ordering, thus he would order the difference 15-6=9 copies