HW9_solution

HW9_solution - solution of homework 9 Problem 1 a. Let fn...

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solution of homework 9 Problem 1 a. Let f n ( x ) denote the minimal cost from n to the end of the planning hori- zon given that x is the cumulative requisitions after the requisitions of the nth period have arrived. Because you could choose either processing the requisitions or not. The dynamic program should be as the following: f n ( x ) = min { K + X j P j f n +1 ( j ) ,cx + X j P j f n +1 ( x + j ) } The boundary condition is: f N +1 ( x ) K b. From the dynamic program, we can see that in the nth period: if K + j P j f n +1 ( j ) > cx + j P j f n +1 ( x + j ), we will decide not processing the requisitions if K + j P j f n +1 ( j ) < cx + j P j f n +1 ( x + j ), we will decide processing the requisitions. K + j P j f n +1 ( j ) is a constant value we do not know. cx + j P j f n +1 ( x + j ) is nondecreasing in x, this could be explained in two ways: 1) By intuition. More requisitions will cause the cost nondecreasing 2) By induction. Since f N +1 ( x ) K
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HW9_solution - solution of homework 9 Problem 1 a. Let fn...

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