Production and Operation Managements Inventory Control Subject to Known Demand Prof.JIANG Zhibin Dr.GENG Na Department of Industrial Engineering Management Shanghai Jiao Tong University
Production and Operation Managements Prof. JIANG Zhibin Dr. GENG Na Department of Industrial Engineering & Management Shanghai Jiao Tong University Inventory Control Subject to Known Demand
Contents .Introduction .Types of Inventories .Motivation for Holding Inventories; .Characteristics of Inventory System; Relevant Costs; .The EOQ Model: EOQ Model with Finite Production Rate Quantity Discount Models .Resource-constrained multiple product system .EOQ models for production planning Power-of-two policies
Contents •Introduction •Types of Inventories •Motivation for Holding Inventories; •Characteristics of Inventory System; •Relevant Costs; •The EOQ Model; •EOQ Model with Finite Production Rate •Quantity Discount Models •Resource-constrained multiple product system •EOQ models for production planning •Power-of-two policies
The EOO Model-Basic Model 国 Express the average annual cost as a function of the lot size Order cost in each order cycle:C(Q)=K+cQ; The average holding cost during one order cycle is hQ/2; The average annual cost(suppose there are n cycles in a year) G(Q)=(Ktcon ho K+cO hO K元 nT 2 O/1 2 Q +2c+一 2 KA h 2KA >0for9>0 G@)=0→0= 2KA h
The EOQ Model-Basic Model Express the average annual cost as a function of the lot size • Order cost in each order cycle: C(Q)=K+cQ; • The average holding cost during one order cycle is hQ/2; • The average annual cost (suppose there are n cycles in a year) : ( ) ( ) 2 /2 2 K cQ n hQ K cQ hQ K hQ GQ c nT Q Q 2 3 2 '( ) ; ''( ) 0 0; 2 Kh K G Q G Q for Q Q Q * 2 '( ) 0 K GQ Q h
The EOO Model-Basic Model Example 4.1 Pencils are sold at a fairly steady rate of 60 per week; Pencils cost 2 cents each and sell for 15 cents each; Cost $12 to initiate an order,and holding costs are based on annual interest rate of 25%. Determine the optimal number of pencils for the book store to purchase each time and the time between placement of orders Solutions √Annual demand rate=60×52=3,120; The holding cost is the product of the variable cost of the pencil and the annual interest-h=0.02 x0.25=0.05 ○* 2KA 2×12×3,120 =3,870 T= Q 3,870 1.24yr = h 0.05 3,120
• Example 4.1 Pencils are sold at a fairly steady rate of 60 per week; Pencils cost 2 cents each and sell for 15 cents each; Cost $12 to initiate an order, and holding costs are based on annual interest rate of 25%. Determine the optimal number of pencils for the book store to purchase each time and the time between placement of orders The EOQ Model-Basic Model • Solutions Annual demand rate =6052=3,120; The holding cost is the product of the variable cost of the pencil and the annual interest-h=0.02 0.25=0.05 * 2 2 12 3,120 3,870 0.05 K Q h 3,870 1.24 3,120 Q T yr
The EOQ Model-Considering Lead Time Since there exits lead time t(4 moths for Example 4.1),order should be placed some time ahead of the end of a cycle; Reorder point R-determines when to place order in terms of inventory on hand,rather than time. R=A=20m)x3,120mis/W）=l,040 4 E Q=3,870 .1.24 years- 4 months R=1,040 Order placed↑ Order arrives Fig.4-6 Reorder Point Calculation for Example 4.1
Since there exits lead time (4 moths for Example 4.1), order should be placed some time ahead of the end of a cycle; Reorder point R -determines when to place order in terms of inventory on hand, rather than time. The EOQ Model-Considering Lead Time Fig. 4-6 Reorder Point Calculation for Example 4.1 4 ( ) 3,120( / ) 1,040 12 R yr units yr