In standard microeconomic theory, short-run and long-run marginal costs areequal for production equipment with adjusted capacity. When the productionof joint products from interdependent equipment is modeled with a linearprogram, this equality is no longer verified. The short-run marginal costthen takes on a left-hand value and a right-hand value which generallydiffer from the long-run marginal cost. In this article, we demonstrate andinterpret the relationship existing between long-run marginal cost andshortrun marginal costs for a given finished product. That relationship issimply expressed as a function of marginal capacity adjustments (determinedin the long run) and marginal values of capacities (determined in the shortrun).

We present, in this article, a hybrid approach forsolvingthe 0–1 multidimensional knapsack problem (MKP). This approach combineslinearprogramming and Tabu search.The resulting algorithm improves on the best result on many well-knownhard benchmarks.

We propose here a pricing Model which is an extension of the Cooperative Game concept and which includes a notion of Elastic Demand. We present some existence results as well as some algorithms. We conclude by discussing this model in the context of some Production and Transportation problems.