We present a fully polynomial time approximation scheme (FPTAS) for a capacitated economic lot-sizing problem with a monotone cost structure. An FPTAS delivers a solution with a given relative error ε in time polynomial in the problem size and in 1/ε. Such a scheme was developed by van Hoesel and Wagelmans [8] for a capacitated economic lot-sizing problem with monotone concave (convex) producti...

In the present work, we are interested in the practical behavior of a new fptas to solve the approximation version of the 0-1 multiobjective knapsack problem. Nevertheless, our methodology focuses on very general techniques (such as dominance relations in dynamic programming) and thus may be applicable in the implementation of fptas for other problems as well. Extensive numerical experiments on...

In this paper, we study the Optimal Inspection Points (OIP) problem, which asks us to find a subset of vertices in a given network to perform the Deep Packet Inspection so as to maximize the number of scanned packets while satisfying the delay constraints. This problem finds many applications for malicious attack detection, especially those where packet scanning is a must. Accordingly, we prove...

We consider multiobjective shortest paths, a fundamental (NP-hard) problem in multiobjective optimization, where we are interested not in optimizing a single objective, but in finding a set of paths that captures the trade-off (the so-called Pareto curve) among several objectives in a digraph whose edges are associated with multidimensional cost vectors. We provide a new FPTAS for computing an ...

Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing. This, roughly, means that one uses worst...

Approximate counting via correlation decay is the core algorithmic technique used in the sharp delineation of the computational phase transition that arises in the approximation of the partition function of anti-ferromagnetic two-spin models. Previous analyses of correlation-decay algorithms implicitly depended on the occurrence of strong spatial mixing. This, roughly, means that one uses worst...

We study a single machine scheduling problem with batch setup time and batch delivery cost. In this problem, n jobs have to be scheduled on a single machine and delivered to a customer. Each job has a due date, a processing time and a weight. To save delivery cost, several jobs can be delivered together as a batch including the late jobs. The completion (delivery) time of each job in the same b...

Assortment optimization is an important problem that arises in many practical applications such as retailing and online advertising. In an assortment optimization problem, the goal is to select a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a choice model. In this paper, we consider the capacity constrained version of...