Resource-constrained multiple product system We multiply each EOQ value by the ratio 30,000/35,835 0.8372.In order to guarantee that we do not exceed the $30,000 budget,we round each value down,we get the optimal values as follows: Q1=172*0.8372≈144 Q2=63*0.8372≈52 Q3=61*0.8372≈51， Lastly,we can increase the lot sizes of some items if there is remaining budget
We multiply each EOQ value by the ratio 30,000/35,835 = 0.8372. In order to guarantee that we do not exceed the $30,000 budget, we round each value down, we get the optimal values as follows: Q1=172*0.8372 ≈144 Q 2=63*0.8372 ≈52 Q 3=61*0.8372 ≈51, Lastly, we can increase the lot sizes of some items if there is remaining budget. Resource-constrained multiple product system
Resource-constrained multiple product system Suppose that n items have unit costs of cc2....c respectively,and the total budget available for them is C. Then the budget constraint can be written C101+c202+...,cnOn<=C Let EOC,= 2K, h In general,budget-constrained problems can be solved as follow:
Suppose that n items have unit costs of c1, c 2,…, c n, respectively, and the total budget available for them is C. Then the budget constraint can be written c1Q1 + c 2 Q2 +…, c n Q n <=C In general, budget-constrained problems can be solved as follow: 2 Let i i i i K EOQ h Resource-constrained multiple product system
Resource-constrained multiple product system Case 1:IfC.then the optimal solution isE Case 2:If cEoQ>C,then if c/h=c2/==c/h i=l we can prove that the optimal solution is O=m*EO: C where m= 2cio0 Note that c/h=c(Ic)=11,,the condition is equivalent to the requirement that the same interest rate be used,which is reasonable in most circumstances
1 Case 1: If , then the optimal solution is ; n ii i i i c EOQ C Q EOQ Note that ( ) 1 , the condition is equivalent to the requirement that the same interest rate be used, which is reasonable in most circumstances. i i i ii i c h c Ic I Resource-constrained multiple product system 1 12 2 1 * 1 Case 2: If , then if , we can prove that the optimal solution is * ; where . n i i nn i i i n i i i c EOQ C c h c h c h Q m EOQ C m c EOQ