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A class of production planning problems is considered in which known demands have to be satisfied over a finite horizon at minimum total costs. For each period, production and storage cost functions are specified. The production costs may include set-up costs and the production levels may he subject to capacity limits. The computational complexity of the problems in this class is investigated. Several algorithms proposed for their solution are described and analyzed. It is also shown that some special cases are NP-hard and hence unlikely to be solvable in polynomial time.inventory/production: deterministic models, inventory/production: surveys, dynamic programming: deterministic, discrete time

A multi-period single commodity production planning problem is studied in which known requirements have to be satisfied. The model differs from earlier well-known studies involving concave cost functions in the introduction of production capacity constraints. The structure of an optimal solution is characterized and then used in a simple dynamic programming algorithm for problems in which the capacities are the same in every period. Both the nonbacklog and backlog allowed cases are considered.

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The continuous dynamic network loading problem (CDNLP) consists in determining, on a congested network, time-dependent arc volumes, together with arc and path travel times, given the time-varying path flow departue rates over a finite time horizon. This problem constitutes an intrinsic part of the dynamic traffic assignment problem. In this paper, we present a formulation of the CDNLP where travel delays may be nonlinear functions of arc traffic volumes. We prove, under a boundedness condition, that there exists a unique solution to the problem and propose for its solution a finite-step algorithm. Some computational results are reported for a discretized version of the algorithm.

In this paper we propose a model for the transit equilibrium assignment problem (TEAP) and develop two algorithms for its solution. The behavior of the transit users is modeled by using the concept of hyperpaths (strategies) on an appropriate network (general network) which is obtained from the road network and the transit lines by a transformation which makes explicit the walk, wait, in-vehicle, transfer and alight arcs. The waiting (generalized) cost is a function of both frequency of the transit lines and congestion effects due to queues at stops. The TEAP is stated and formulated as a variational inequality problem, in the space of hyperpath flows, and then solved by the linearized Jacobi method and the projection method. We prove the global convergence of these two algorithms for strongly monotone arc cost mappings. The implementation of the algorithms and computational experiments are presented as well.

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