By Art Lew

This publication presents a pragmatic advent to computationally fixing discrete optimization difficulties utilizing dynamic programming. From the examples offered, readers may still extra simply be capable to formulate dynamic programming options to their very own difficulties of curiosity. We additionally supply and describe the layout, implementation, and use of a software program device that has been used to numerically remedy all the difficulties provided previous within the booklet.

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If the graph is acyclic, then the graph can be topologically sorted and the DPFE can be evaluated for p in this order such that evaluation of f (p) will always be in terms of previously calculated values of f (q). On the other hand, if the graph is cyclic, so that for example p and q are successors of each other, then f (p) may be defined in terms of f (q), and f (q) may be defined in terms of f (p). This circular definition presents difficulties that require special handling. , branches from a node p to itself.

The optimal distribution problem ODP (Sect. 31) may be regarded as an allotment problem. The problem may also be regarded as a variation of the knapsack problem KSINT (Sect. 22). Assume there are M total units of the resource, and let C(k, d) be the cost or profit associated with allotting d units to user k, where d = 0, . . , M and k = 1, . . , N . Suppose we make the allotment decisions in stages, initially allotting d1 units to user 1, then d2 units to user 2, etc. This arbitrary sequencing 1, 2, .

8, we describe Phase 1 of our DP tool, which parses DPFE source code and outputs its Bellman net representation. This Bellman net is produced indirectly: the parser generates intermediate “builder code” which when executed outputs the Bellman net. In Chap. 9, we describe Phase 2 of our DP tool, which inputs a Bellman net and produces solver code which when executed outputs a numerical solution of the associated DPFE. This solver code can be Java code, a spreadsheet, or an XML-coded Petri net (using a Petri net simulation language).

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