Quantity Discount Model-Optimal Policy for All- Units Discount Schedule Example 4.4:If Weighty uses trash bags at a fairly constant rate of 600 per yr,how to place order? Suppose that fixed cost of placing an order is $8,and holding costs are based on 20%annual interest rate. First compute EOQ values corresponding to each of the unit cost. 2KA 2×8×600 2= =400,C,0≤9<500 ICo 0.2×0.3 2K1 2×8×600 9= = 406,C1for500≤9<1000 IC 0.2×0.29 2KA 2×8×600 2= = IC2 414,C2forQ≥1000 V0.2×0.28
Example 4.4: If Weighty uses trash bags at a fairly constant rate of 600 per yr, how to place order? Suppose that fixed cost of placing an order is $8, and holding costs are based on 20% annual interest rate. First compute EOQ values corresponding to each of the unit cost. Quantity Discount Model- Optimal Policy for AllUnits Discount Schedule 0 0 0 2 2 8 600 400, 0 500 0.2 0.3 K Q CQ IC 1 1 1 2 2 8 600 406, 500 1000 0.2 0.29 K Q C for Q IC 2 2 2 2 2 8 600 414, 1000 0.2 0.28 K Q C for Q IC
Quantity Discount Model-Optimal Policy for All- Units Discount Schedule .Each curve is valid only for certain values of Q,thus the average annual cost function is given by discontinuous curves. 240 2 G,(Q)=c,+元K/Q+1cQ/2 220 GolQ) GlQ) for j=0,1,and 2 210 G2lQ) 200 G(Q)for0≤Q<500, 190 G(Q)=G(2)for500≤Q<1,000, 18 G2(Q)for1,000≤Q 1002003004005006007008009001,0001,1001,200 Q- Fig.4-12 All-Units Discount Average Annual Cost Function
Quantity Discount Model- Optimal Policy for AllUnits Discount Schedule •Each curve is valid only for certain values of Q, thus the average annual cost function is given by discontinuous curves. 0 1 2 ( ) / /2 0,1, 2 ( ) 0 500, ( ) ( ) 500 1,000, ( ) 1,000 j GQ c KQ IQ jj C for j and G Q for Q G Q G Q for Q G Q for Q Fig. 4-12 All-Units Discount Average Annual Cost Function