6 Nonserial DP

# 6 Nonserial DP - 1 Nonserial Problem Consider the nonlinear...

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1 Nonserial Problem Consider the nonlinear integer programming problem max ( )( ) ,. zx x x x x x xx xx xx xi i =++ + + ++++ +≤ 36 42 3 2442 5 2 0 0 1 2 23 2 4 5 2 6 1234 5 6 st and integer for all This problem does not have the characteristics need to apply most standard nonlinear programming techniques because of the integer nature of the variables, the non-concavity of the objective function, and the product form of sums of return functions. The problem does, however, very nearly fit the nature of most of the dynamic programming problems that we have been studying. After some thought about this problem, one can see that we will need to utilize both additive and multiplicative recursion functions. We have dealt with multiplicative recursion functions in the reliability problem. We must first build up a recursion function of the sum of the x 3 and x 4 returns, call this f 34 , then a recursion function of the sum of the x 5 and x 6 return function, call this f 56 . Then we can accomplish the multiplication by developing another recursion function that is the product of the f 34 and f 56 recursion functions, which we will call f 3456 . From this function, we can perform standard additive recursions on both the x 1 and x 2 return function to develop the final solution. We can develop the recursion functions f 34 and f 56 in either order. They must both be developed, however, before we can proceed with their combination using multiplication to develop the f 3456 recursion function.

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## This note was uploaded on 10/16/2010 for the course ISEN 689 taught by Professor Klutke during the Spring '07 term at Texas A&M.

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6 Nonserial DP - 1 Nonserial Problem Consider the nonlinear...

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