12 research outputs found
An Algorithm for Single-item Capacitated Economic Lot Sizing with Piecewise Linear Production Costs and General Holding Costs
We consider the Capacitated Economic Lot Size problem with piecewise linear production costs and general holding costs, which is an NP-hard problem but solvable in pseudo-polynomial time. A straightforward dynamic programming approach to this problem results in an [TeX: ] algorithm, where [TeX: ] is the number of periods, and [TeX: and ] are the average demand and the average production capacity over the periods, respectively.
However, we present a dynamic programming procedure with complexity [TeX: ], where [TeX: ] is the average number of pieces of the production cost functions. In particular, this means that problems in which the production functions consist of a fixed set-up cost plus a linear variable cost are solved in [TeX: ] time. Hence, the running time of our algorithm is only linearly dependent on the magnitude of the data. This result also holds if extensions such as backlogging and start-up costs are considered. Moreover, computational experiments indicate that the algorithm is capable of solving quite large problem instances within a reasonable amount of time. For example, the average time needed to solve test instances with 96 periods, 8 pieces in every production function and average demand of 100 units, is approximately 40 seconds on a SUN SPARC 5 workstation
Successive Convex Approximations to Cardinality-Constrained Convex Programs: A Piecewise-Linear DC Approach
In this paper we consider cardinality-constrained convex programs that minimize a convex function subject to a cardinality constraint and other linear constraints. This class of problems has found many applications, including portfolio selection, subset selection and compressed sensing. We propose a successive convex approximation method for this class of problems in which the cardinality function is first approximated by a piecewise linear DC function (difference of two convexfunctions) and a sequence of convex subproblems is then constructed by successively linearizing the concave terms of the DC function. Under some mild assumptions, we establish that any accumulation point of the sequence generated by the method is a KKT point of the DC approximation problem. We show that the basic algorithm can be refined by adding strengthening cuts in the subproblems. Finally, we report some preliminary computational results on cardinality-constrained portfolio selection problems
A two-echelon inventory optimization model with demand time window considerations
10.1007/s10898-004-6092-yJournal of Global Optimization304347-366JGOP