We investigate the polyhedral structure of the lot-sizing problem with inventory bounds. We consider two models, one with linear costs on inventory, the other with linear and fixed costs on inventory. For both models, we identify facet-defining inequalities that make use of the inventory capacities explicitly and give exact separation algorithms. We also give a … Read more
Recently, Aguilera et al.\ exposed a beautiful relationship between antiblocker duality and the lift-and-project operator proposed by Balas et al. We present a very short proof of their result that the \BCC-rank of the clique polytope is invariant under complementation. The proof of Aguilera et al. relies on their main technical result, which describes a … Read more
We review strong inequalities for fundamental knapsack relaxations of (mixed) integer programs. These relaxations are the 0-1 knapsack set, the mixed 0-1 knapsack set, the integer knapsack set, and the mixed integer knapsack set. Our aim is to give a unified presentation of the inequalities based on covers and packs and highlight the connections among … Read more
In this paper we describe a successful case-study where a Branch-and-Cut algorithm yields the \lq\lq optimal” solution of a real-world timetabling problem of University courses \emph{(University Course Timetabling problem)}. The problem is formulated as a \emph{Set Packing problem} with side constraints. To tighten the initial formulation, we utilize well-known valid inequalities of the Set Packing … Read more
This paper studies the asymptotic behavior of the central path $(X(\nu),S(\nu),y(\nu))$ as $\nu \downarrow 0$ for a class of degenerate semidefinite programming (SDP) problems, namely those that do not have strictly complementary primal-dual optimal solutions and whose “degenerate diagonal blocks” $X_{\cT}(\nu)$ and $S_{\cT}(\nu)$ of the central path are assumed to satisfy $\max\{ \|X_{\cT}(\nu)\|, \|S_{\cT}(\nu)\| \} … Read more
We present formulations for the strategic design of robust and reliable supply chains with long term contracting. The inability to deliver a supply part due to unexpected events in a complex supply chain can have a significant impact on the performance of a supply chain. Reliable and robust supply chains leverage cost and risk of … Read more
We propose a {\em quasi-greedy} algorithm for approximating the classical uncapacitated $2$-level facility location problem ($2$-LFLP). Our algorithm, unlike the standard greedy algorithm, selects a sub-optimal candidate at each step. It also relates the minimization $2$-LFLP problem, in an interesting way, to the maximization version of the single level facility location problem. Another feature of … Read more
We consider the rail car management at industrial in-plant railroads. Demands for materials or empty cars are characterized by a track, a car type, and the desired quantity. If available, we assign cars from the stock, possibly substituting types, otherwise we rent additional cars. Transportation requests are fulfilled as a short sequence of pieces of … Read more
Given N customers and a set F of M potential facilities, the P-median problem consists in finding a subset of F with P facilities such that the cost of serving all customers is minimized. This is a well-known NP-complete problem with important applications in location science and classification (clustering). We present a multistart hybrid heuristic … Read more
We present fully polynomial approximation schemes for concurrent multicommodity flow problems that run in time of minimal dependency on the number of commodities k. We show that by modifying the algorithms by Garg & Konemann and Fleischer we can reduce their running time to a logarithmic dependence on k, and essentially match the running time … Read more