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
Quantity Discount Model The suppliers may charge less per unit for larger orders to encourage the customer to buy their products in larger batches. Two popular ways of discounts: All-units:discount is applied to all of the units in an order; Incremental:only applied to additional units beyond the breakpoints;
•The suppliers may charge less per unit for larger orders to encourage the customer to buy their products in larger batches. •Two popular ways of discounts: All-units: discount is applied to all of the units in an order; Incremental: only applied to additional units beyond the breakpoints; Quantity Discount Model
Quantity Discount Model Example 4.4 Weighty Trash Bag Company's pricing schedule for its large trash can liners: .For orders of less than 500 bags,charges 30 cents per bag; .for orders of 500 or more but fewer than 1,000 bags,charges 29 cents per bag;and .for orders of 1,000 or more,charges 28 cents per bag
Quantity Discount Model Example 4.4 Weighty Trash Bag Company’s pricing schedule for its large trash can liners: •For orders of less than 500 bags, charges 30 cents per bag; •for orders of 500 or more but fewer than 1,000 bags, charges 29 cents per bag; and •for orders of 1,000 or more, charges 28 cents per bag
Quantity Discount Model-Optimal Policy for All- Units Discount Schedule The breakpoints are 500 and 1,000.The discount schedule is all-units; The order cost function C(Q)is defined as 0.309for0≤9<500， g c2-28 0=.301.29 C(Q)=0.299for500≤9<1,000， 0.28Qfor1,000≤Q 5001.000 Q- Fig 4-9 All-Units Discount Order Cost Function
The breakpoints are 500 and 1,000. The discount schedule is all-units; The order cost function C(Q) is defined as Fig 4-9 All-Units Discount Order Cost Function Quantity Discount Model- Optimal Policy for AllUnits Discount Schedule 0.30 0 500, ( ) 0.29 500 1,000, 0.28 1,000 Q for Q C Q Q for Q Q for Q