DLP and Extensions: An Optimization Model and Decision by Professor John Lawrence Nazareth (auth.)

By Professor John Lawrence Nazareth (auth.)

DLP denotes a dynamic-linear modeling and optimization method of computational selection help for source making plans difficulties that come up, quite often, in the normal source sciences and the disciplines of operations examine and operational engineering. It integrates recommendations of dynamic programming (DP) and linear programming (LP) and will be discovered in a right away, functional and usable manner. concurrently DLP connotes a extensive and extremely common modeling/ algorithmic idea that has a variety of parts of software and chances for extension. motivating examples offer a linking thread throughout the major chapters, and an appendix presents an illustration application, executable on a computer, for hands-on event with the DLP approach.

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L. Nazareth, DLP and Extensions © Springer-Verlag Berlin Heidelberg 2001 24 CHAPTER 2. DLP NUCLEUS MODEL decisions. At the level at which planning is being conducted, it is assumed to be reasonable to consider such an aggregate of resource parcels as a homogenous entity for which a common set of decision alternatives can be explored. We will measure each resource class in appropriate units, henceforth denoted by the symbol DU (decision units). For example, a decision unit is an acre for the range resource example of Chapter 1.

3. 4 29 Network of Decision Alternatives Finally, suppose the set of states Sk for class C k are displayed simultaneously for each interval , and directed arcs connecting them are defined by the foregoing transformations (viable actions) for each state, along with their associated costs and benefits. We then obtain a directed network of alternatives for the class c- . We call it the (formal) D LP network of alternatives for c«. Its formulation mayor may not have been preceded by setting up an informal , 'decision-maker' network as discussed earlier.

In general, nt could be an astronomically large number. Consider a resource class Ok with ten states in Sk and, for convenience, assume that there are viable actions capable of converting each state to any other. For example, the resource class could be a storage facility for a grain wholesaler, where the states correspond to a discrete number of amounts of grain in storage; control actions correspond to either the removal of grain to market or the purchase of additional grain from producers. For a planning period of ten intervals, this resource class would have close to a billion decision alternatives.

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