A comparison of formulations and solution methods for the minimum-envy location problem

We consider a discrete facility location problem with a new form of equity criterion. The model discussed in the paper analyzes the case where demand points only have strict preference order on the sites where the plants can be located. The goal is to find the location of the facilities minimizing the total envy felt by the entire set of demand points. We define this new total envy criterion and provide several integer linear programming formulations that reflect and model this approach. The formulations are illustrated by examples. Extensive computational tests are reported, showing the potentials and limits of each formulation on several types of instances. Finally, some improvements for all the formulations previously presented are developed, obtaining in some cases much better resolution times.     

A comparative study of formulations and solution methods for the discrete ordered p-median problem

This paper presents several new formulations for the Discrete Ordered Median Problem (DOMP) based on its similarity with some scheduling problems. Some of the new formulations present a considerably smaller number of constraints to define the problem with respect to some previously known formulations. Furthermore, the lower bounds provided by their linear relaxations improve the ones obtained with previous formulations in the literature even when strengthening is not applied. We also present a polyhedral study of the assignment polytope of our tightest formulation showing its proximity to the convex hull of the integer solutions of the problem. Several resolution approaches, among which we mention a branch and cut algorithm, are compared. Extensive computational results on two families of instances, namely randomly generated and from Beasley's OR-library, show the power of our methods for solving DOMP.     

When centers can fail: A close second opportunity

This paper presents the p-next center problem, which aims to locate p out of n centers so as to minimize the maximum cost of allocating customers to backup centers. In this problem it is assumed that centers can fail and customers only realize that their closest (reference) center has failed upon arrival. When this happens, they move to their backup center, i.e., to the center that is closest to the reference center. Hence, minimizing the maximum travel distance from a customer to its backup center can be seen as an alternative approach to handle humanitarian logistics, that hedges customers against severe scenario deteriorations when a center fails.For this extension of the p-center problem we have developed several different integer programming formulations with their corresponding strengthenings based on valid inequalities and variable fixing. The suitability of these formulations for solving the p-next center problem using standard software is analyzed in a series of computational experiments. These experiments were carried out using instances taken from the previous discrete location literature.     

Local search heuristics for the mobile facility location problem

In the mobile facility location problem (MFLP), one seeks to relocate (or move) a set of existing facilities and assign clients to these facilities so that the sum of facility movement costs and the client travel costs (each to its assigned facility) is minimized. This paper studies formulations and develops local search heuristics for the MFLP. First, we develop an integer programming (IP) formulation for the MFLP by observing that for a given set of facility destinations the problem may be decomposed into two polynomially solvable subproblems. This IP formulation is quite compact in terms of the number of nonzero coefficients in the constraint matrix and the number of integer variables; and allows for the solution of large-scale MFLP instances. Using the decomposition observation, we propose two local search neighborhoods for the MFLP. We report on extensive computational tests of the new IP formulation and local search heuristics on a large range of instances. These tests demonstrate that the proposed formulation and local search heuristics significantly outperform the existing formulation and a previously developed local search heuristic for the problem.     

Methods based on discrete optimization for finding road network rehabilitation strategies

We study a dynamic optimization problem arising in the (long-term) planning of road rehabilitation activities. In this area one seeks a pavement resurfacing plan for a road network under budget constraints. Our main approach is to model this as an integer programming problem with underlying dynamic programming structure. We investigate properties of this model and propose a solution method based on Lagrangian relaxation where one gets subproblems that are shortest path problems. Some computational experiences based on realistic data are reported.     

Exact approaches for static data segment allocation problem in an information network

In a large distributed database, data are geographically distributed across several separate servers (or data centers). This helps in distributing load in the access network. It also helps to serve data locally where it is required. There are various approaches based on the granularity of data for efficient data distribution in a communication network. The file allocation problem (FAP) locates files to servers, the segment allocation problem (SAP) locates database segments, and the mirror location problem (MLP) locates replicas of the entire database. The placement of such data to multiple servers can be modeled as an optimization problem. The major decisions influencing optimization involves the location of servers, allocation of content and assignment of users. In this paper, we study the segment allocation problem (SAP), which is also known as the partial mirroring problem. This approach is more tractable than the file allocation problem in realistic cases and also eliminates the overhead of (constant) update costs that is incurred in the mirror location problem. Our contribution is two-fold: Firstly, earlier works on SAP assume pre-defined segments. We build a data partitioning method using well-known facility location models. We quantify the performance of the partitioning method. We show that the method partitions the database within a reasonable limit of error. Secondly, we introduce a new model for the segment allocation problem in which the segments are completely connected to each other by high-bandwidth links and contains a cost benefit for inter-segment traffic flows. We formulate this problem as an MILP and build exact solution approaches to solve large scale problems. We demonstrate some structural properties of the problem that make it solvable, using a Benders decomposition algorithm. Computational results validate the superiority of the decomposition approach.     

Multi-product valid inequalities for the discrete lot-sizing and scheduling problem

We consider a problem arising in the context of industrial production planning, namely the multi-product discrete lot-sizing and scheduling problem with sequence-dependent changeover costs. We aim at developing an exact solution approach based on a Cut & Branch procedure for this combinatorial optimization problem. To achieve this, we propose a new family of multi-product valid inequalities which corresponds to taking into account the conflicts between different products simultaneously requiring production on the resource. We then present both an exact and a heuristic separation algorithm which form the basis of a cutting-plane generation algorithm. We finally discuss computational results which confirm the practical usefulness of the proposed inequalities at strengthening the MILP formulation and at reducing the overall computation time.     

Real time identification of discrete event systems using Petri nets

The paper defines the identification problem for Discrete Event Systems (DES) as the problem of inferring a Petri Net () model using the observation of the events and the available output vectors, that correspond to the markings of the measurable places. Two cases are studied considering different levels of the system knowledge. In the first case the place and transition sets are assumed known. Hence, an integer linear programming problem is defined in order to determine a modelling the DES. In the second case the transition and place sets are assumed unknown and only an upper bound of the number of places is given. Hence, the identification problem is solved by an identification algorithm that observes in real time the occurred events and the corresponding output vectors. The integer linear programming problem is defined at each observation so that the can be recursively identified. Some results and examples characterize the identified systems and show the flexibility and simplicity of the proposed technique. Moreover, an application to the synthesis of supervisory control of systems via monitor places is proposed.     

Hybrid techniques based on solving reduced problem instances for a longest common subsequence problem

Finding the longest common subsequence of a given set of input strings is a relevant problem arising in various practical settings. One of these problems is the so-called longest arc-preserving common subsequence problem. This NP-hard combinatorial optimization problem was introduced for the comparison of arc-annotated ribonucleic acid (RNA) sequences. In this work we present an integer linear programming (ILP) formulation of the problem. As even in the context of rather small problem instances the application of a general purpose ILP solver is not viable due to the size of the model, we study alternative ways based on model reduction in order to take profit from this ILP model. First, we present a heuristic way for reducing the model, with the subsequent application of an ILP solver. Second, we propose the application of an iterative hybrid algorithm that makes use of an ILP solver for generating high quality solutions at each iteration. Experimental results concerning artificial and real problem instances show that the proposed techniques outperform an available technique from the literature.     

The uncapacitated hub location problem in networks under decentralized management

We propose a new hub location model defined by the minimization of costs. The main contribution of this work is to permit the analysis of a hub-and-spoke network operated under “decentralized management”. In this type of network, various transport companies act independently, and each makes its route choices according to its own criteria, which can include cost, time, frequency, security and other factors, including subjective ones. Therefore, due to the diversity of the various companies’ criteria, one can expect that between each origin–destination pair, a fraction of the flow will be carried through hubs and a fraction will be carried by the direct route. to resolve this problem, it becomes necessary to determine the probability that any network user will choose the hub route for each trip to be made (or for each load to be carried). We present an integer programming formulation, subject the new model to experiments with an intermodal general cargo network in Brazil and address questions regarding the solution of the problem in practice.     

An efficient ID-based cryptographic encryption based on discrete logarithm problem and integer factorization problem

ID-based encryption (identity-based) is a very useful tool in cryptography. It has many potential applications. The security of traditional ID-based encryption scheme wholly depends on the security of secret keys. Exposure of secret keys requires reissuing all previously assigned encryptions. This limitation becomes more obvious today as key exposure is more common with increasing use of mobile and unprotected devices. Under this background, mitigating the damage of key exposure in ID-based encryption is an important problem. To deal with this problem, we propose to integrate forward security into ID-based encryption. In this paper, we propose a new construction of ID-based encryption scheme based on integer factorization problem and discrete logarithm problem is semantically secure against chosen plaintext attack (CPA) in random oracle model. We demonstrate that our scheme outperforms the other existing schemes in terms of security, computational cost and the length of public key.     

On-line fault detection in discrete event systems by Petri nets and integer linear programming

The paper addresses the fault detection problem for discrete event systems in a Petri Net (PN) framework. Assuming that the structure of the PN model and the initial marking are known, faults are modelled by unobservable transitions. Moreover, we assume that there may be additional unobservable transitions associated with the system legal behaviour and that the marking reached after the firing of any transition is unknown. The proposed diagnoser works on-line: it waits for the firing of an observable transition and employs an algorithm based on the definition and solution of some integer linear programming problems to decide whether the system behaviour is normal or exhibits some possible faults. The results characterize the properties that the PN modelling the system fault behaviour has to fulfill in order to reduce the on-line computational effort.     

L-class enumeration algorithms for a discrete production planning problem with interval resource quantities

A discrete production planning problem which may be formulated as the multidimensional knapsack problem is considered, while resource quantities of the problem are supposed to be given as intervals. An approach for solving this problem based on using its relaxation set is suggested. Some L-class enumeration algorithms for the problem are described. Results of computational experiments are presented.     

Formulating and solving splittable capacitated multiple allocation hub location problems

It is only recently that good formulations and properties for the basic versions of the hub location problem have become available. Now, versions closer to reality can be tackled with greater guarantees of success. This article deals with the case in which the capacity of the hubs is limited. The focus is on the following interpretation of this capacity: there is, for each hub, an upper bound on the total flow coming directly from the origins. Our problem has the so-called multiple allocation possibility, i.e., there is no hub associated to each node; on the contrary, flows with, say, the same origin but different destinations, can be sent through different routes. Moreover, it is assumed that the flow between a given origin–destination pair can be split into several routes; if this is not the case, the problem becomes quite different and cannot be approached by means of the techniques used in this paper.Tight integer linear programming formulations for the problem are presented, along with some useful properties of the optimal solutions which can be used to speed up the resolution.The computational experience shows that instances of medium size can be solved very efficiently using the new method, which outperforms other methods given in the literature.     

改进离散粒子群算法求解柔性流水车间调度问题

针对以最小化完工时间为目标的柔性流水车间调度问题(FFSP),提出了一种改进离散粒子群(DPSO)算法.所提算法重新定义粒子速度和位置的相关算子,并引入编码矩阵和解码矩阵来表示工件、机器以及调度之间的关系.为了提高柔性流水车间调度问题求解的改进离散粒子群算法的初始群体质量,通过分析初始机器选择与调度总完工时间的关系,首次提出一种基于NEH算法的最短用时分解策略算法.仿真实验结果表明,该算法在求解柔性流水车间调度问题上有很好的性能,是一种有效的调度算法.     

Single-allocation ordered median hub location problems

The discrete ordered median location model is a powerful tool in modeling classic and alternative location problems that have been applied with success to a large variety of discrete location problems. Nevertheless, although hub location models have been analyzed from the sum, maximum and coverage point of views, as far as we know, they have never been considered under an alternative unifying point of view. In this paper we consider new formulations, based on the ordered median objective function, for hub location problems with new distribution patterns induced by the different users’ roles within the supply chain network. This approach introduces some penalty factors associated with the position of an allocation cost with respect to the sorted sequence of these costs. First we present basic formulations for this problem, and then develop stronger formulations by exploiting properties of the model. The performance of all these formulations is compared by means of a computational analysis.     

Exact algorithms for a generalization of the order acceptance and scheduling problem in a single-machine environment

This paper studies a generalization of the order acceptance and scheduling problem in a single-machine environment where a pool consisting of firm planned orders as well as potential orders is available from which an over-demanded company can select. The capacity available for processing the accepted orders is limited and each order is characterized by a known processing time, delivery date, revenue and a weight representing a penalty per unit-time delay beyond the delivery date. We prove that the existence of a constant-factor approximation algorithm for this problem is unlikely. We propose two linear formulations that are solved using an IP solver and we devise two exact branch-and-bound procedures able to solve instances with up to 50 jobs within reasonable CPU times. We compare the efficiency and quality of the results obtained using the different solution approaches.     

Branch and bound for the cutwidth minimization problem

The cutwidth minimization problem consists of finding a linear arrangement of the vertices of a graph where the maximum number of cuts between the edges of the graph and a line separating consecutive vertices is minimized. We first review previous approaches for special classes of graphs, followed by lower bounds and then a linear integer formulation for the general problem. We then propose a branch-and-bound algorithm based on different lower bounds on the cutwidth of partial solutions. Additionally, we introduce a Greedy Randomized Adaptive Search Procedure (GRASP) heuristic to obtain good initial solutions. The combination of the branch-and-bound and GRASP methods results in optimal solutions or a reduced relative gap (difference between upper and lower bounds) on the instances tested. Empirical results with a collection of previously reported instances indicate that the proposed algorithm is able to solve all the small instances (up to 32 vertices) as well as some of the large instances tested (up to 158 vertices) using less than 30 minutes of CPU time. We compare the results of our method with previous lower bounds, and with the best previous linear integer formulation solved using Cplex. Both comparisons favor the proposed procedure.     

A computational comparison of several models for the exact solution of the capacity and distance constrained plant location problem

The Capacity and Distance Constrained Plant Location Problem is an extension of the discrete capacitated plant location problem, where the customers assigned to each plant have to be assigned to vehicles. In addition to the capacity constraints on the plants, there is a limit on the total distance traveled by each vehicle to serve its assigned customers by means of round trips. This paper presents several formulations for the problem and proposes different families of valid inequalities. The results of extensive computational experiments are presented and analyzed.     

Generalized Weber problem for discrete median spaces

We propose a polynomial-time algorithm for solving the generalized Weber problem in median metric spaces.Translated from Kibernetika, No. 1, pp. 61–69, 93, January–February, 1991.