A column generation heuristic for congested facility location problem with clearing functions

Nonlinear clearing functions, an idea initially suggested to reflect congestion effects in production planning, are used to express throughput of facilities prone to congestion in a facility location problem where each demand site is served by exactly one facility. The traditional constant capacity constraint for a facility is replaced with the nonlinear clearing function. The resulting nonlinear integer problem is solved by a column generation heuristic in which initial columns for the restricted master problem are generated by known existing algorithms and additional columns by a previously developed dynamic programming algorithm. Computational experimentation in terms of dual gap and CPU time based on both randomly generated and published data sets show not only clear dominance of the column generation over a Lagrangian heuristic previously developed, but also the high quality of results from the suggested heuristic for large problems.     

Model-hierarchical column generation and heuristic for the routing and wavelength assignment problem

The routing and wavelength assignment (RWA) problem typically occurs in wavelength division multiplexing optical networks. Given a number of available wavelengths, we consider here the problem of maximising the number of accepted connections with respect to the clash and continuity constraints. We first propose a new strategy which combines two existing models. This leads to an improved column generation scheme. We also present two heuristics to compute feasible solutions: a hybrid heuristic and the integer solution at the root node of the column generation. Our approaches are compared with the best existing results on a set of classic RWA instances.     

A column generation heuristic for the two-dimensional two-staged guillotine cutting stock problem with multiple stock size

We consider a two-dimensional cutting stock problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as its subproblem the solution of a two-dimensional knapsack problem with two-staged guillotines cuts. A further contribution of the paper consists in the definition of a mixed integer linear programming model for the solution of this knapsack problem, as well as a heuristic procedure based on dynamic programming. Computational experiments show the effectiveness of the proposed approach, which obtains very small optimality gaps and outperforms the heuristic algorithm proposed by Cintra et al. [3].     

A copula-based heuristic for scenario generation

This paper presents a new heuristic for generating scenarios for two-stage stochastic programs. The method uses copulas to describe the dependence between the marginal distributions, instead of the more common correlations. The heuristic is then tested on a simple portfolio-selection model, and compared to two other scenario-generation methods.     

A column generation-based heuristic for rostering with work patterns

This paper addresses the Ground Crew Rostering Problem with Work Patterns, an important manpower planning problem arising in the ground operations of airline companies. We present a cutting stock-based integer programming formulation of the problem and describe a powerful heuristic decomposition approach, which utilizes column generation and variable fixing, to construct efficient rosters for a six-month time horizon. The time horizon is divided into smaller blocks, where overlaps between the blocks ensure continuity. The proposed methodology is able to circumvent one step of the conventional roster construction process by generating rosters directly based on the estimated workload. We demonstrate that this approach has the additional advantage of being able to easily incorporate robustness in the roster. Computational results on real-life instances confirm the efficiency of the approach.     

A column generation based heuristic for sensor placement,activity scheduling and data routing in wireless sensor networks

A wireless sensor network is a network consisting of distributed autonomous electronic devices called sensors. In this work, we develop a mixed-integer linear programming model to maximize the network lifetime by optimally determining locations of sensors and sinks, sensor-to-sink data flows, and activity schedules of the deployed sensors subject to coverage, flow conservation, energy consumption and budget constraints. Since solving this model is difficult except for very small instances, we propose a heuristic method which works on a reformulation of the problem. In the first phase of this heuristic, the linear programming relaxation of the reformulation is solved by column generation. The second phase consists of constructing a feasible solution for the original problem using the columns obtained in the first phase. Computational experiments conducted on a set of test instances indicate that both the accuracy and the efficiency of the proposed heuristic is quite promising.     

A pruning heuristic for use with multisource product design

Products can be improved by integrating multiple viewpoints during the design process. A model has been developed that uses conjoint data from consumers and designers and optimizes a product design based on the total share-of-choices. Because the problem becomes very difficult to solve as size increases, a heuristic is developed, based on pruning techniques, to solve the problem to near-optimality in a shorter period of time as compared to complete enumeration. The performance of the heuristic is demonstrated through the use of test data and by comparison to a Genetic Algorithm (GA) based heuristic and Tabu search. Structural results for the heuristic are also provided.     

A districting procedure for social organizations

The problem dealt with in the paper refers to the decomposition of a geographical region into an unspecified number of non-overlapping regional partitions. Each partition is given by a connected aggregation of indivisible elementary areas and must contain at least one source of a certain social service characterized by assigned capacity and location. Each area is characterized by a service demand and by a measure quantifying its dimension.Two heuristic methods are proposed to obtain a preliminary aggregation of the elementary areas, in order to reduce the computational effort involved in generating the feasible partitions. A fuzzy sets approach is presented for rating and ranking the regional partitions. This approach seems to be particularly suited to planning problems, when some kind of compromise between qualitative and quantitative issues must be sought. A health-care districting problem is then discussed as a case study.     

A column generation algorithm for nonlinear programming

An algorithm using column generation and penalty function techniques is presented. A linear program with a uniformly bounded number of columns, similar to the restricted master in generalized programming, is used to reduce the number of constraints included in forming a penalty function. The penalty function is used as a Lagrangian in an unconstrained subproblem.This work was supported in part by National Science Foundation Grant GS-3032.     

A two-stage heuristic for disassembly scheduling with assembly product structure

Disassembly scheduling, one of the important operational problems in disassembly systems, is the problem of determining the ordering and disassembly schedules of used or end-of-life products while satisfying the demand of their parts or components over a certain planning horizon. This paper considers products with assembly structure for the objective of minimizing the sum of purchase, set up, inventory holding, and disassembly operation costs, and suggests a two-stage heuristic, in which an initial solution is obtained in the form of the minimal latest ordering and disassembly schedule, and then improved iteratively considering trade-offs among different cost factors. To show the performance of the heuristic, computational experiments were done on the example obtained from the literature and a number of randomly generated test problems, and the results show that the heuristic can give optimal or very near-optimal solutions within very short computation times.     

The Single Period Coverage Facility Location Problem: Lagrangean heuristic and column generation approaches

In this paper we introduce the Single Period Coverage Facility Location Problem. It is a multi-period discrete location problem in which each customer is serviced in exactly one period of the planning horizon. The locational decisions are made independently for each period, so that the facilities that are open need not be the same in different time periods. It is also assumed that at each period there is a minimum number of customers that can be assigned to the facilities that are open. The decisions to be made include not only the facilities to open at each time period and the time period in which each customer will be served, but also the allocation of customers to open facilities in their service period.     

A column generation method for the multiple-choice multi-dimensional knapsack problem

In this paper, we propose to solve large-scale multiple-choice multi-dimensional knapsack problems. We investigate the use of the column generation and effective solution procedures. The method is in the spirit of well-known local search metaheuristics, in which the search process is composed of two complementary stages: (i) a rounding solution stage and (ii) a restricted exact solution procedure. The method is analyzed computationally on a set of problem instances of the literature and compared to the results reached by both Cplex solver and a recent reactive local search. For these instances, most of which cannot be solved to proven optimality in a reasonable runtime, the proposed method improves 21 out of 27.     

A column generation approach for the rail crew re-scheduling problem

When tracks are out of service for maintenance during a certain period, trains cannot be operated on those tracks. This leads to a modified timetable, and results in infeasible rolling stock and crew schedules. Therefore, these schedules need to be repaired. The topic of this paper is the re-scheduling of crew.     

A column generation approach for aircraft sequencing problems: a computational study

This paper investigates the computational tractability of aircraft sequencing problems over multiple runways under mixed mode operations, contrasting an enhanced mixed-integer programme (MIP) and an accelerated column generation approach. First, we examine the benefit of augmenting a base MIP with valid inequalities, preprocessing routines, and symmetry-defeating hierarchical constraints in order to improve the performance of branch-and-bound (B&B)/cut techniques as implemented in commercial solvers. Second, we alternatively reformulate the problem as a set partitioning model that prompts the development of a specialized column generation approach. The latter is accelerated by incorporating an interior point dual stabilization scheme and a complementary column generation routine. Empirical results using a set of new, computationally challenging instances and classical instances in the OR Library reveal the potential and limitations of the two methodologies.     

A column generation-based heuristic algorithm for an inventory routing problem with perishable goods

An inventory routing problem is a variation of the vehicle routing problem in which inventory and routing decisions are determined simultaneously over a given time horizon. The objective is to minimize the sum of transportation and inventory costs. In this paper, we study a specific inventory routing problem in which goods are perishable (PIRP). We develop a mathematical model for PIRP and exploit its structure to develop a column generation-based solution approach. Cutting planes are added to improve the formulation. We present computational experiments to demonstrate that our methodology is effective, and that the integration of routing and inventory can yield significant cost savings.     

A column generation algorithm for tactical timber transportation planning

We present a tactical wood flow model that appears in the context of the Canadian forestry industry, and describe the implementation of a decision support system created for use by an industrial partner. In this problem, mill demands and harvested volumes of a heterogeneous set of log types are given over a multi-period planning horizon. Wood can be stored at the forest roadside before delivery at a financial cost. Rather than solve this as a network linear programme on the basis of out-and-back deliveries, we choose to model this problem as a generalization of a log-truck scheduling problem. By routing and scheduling the trucks in the resolution, this allows us to both anticipate potential backhaul opportunities for cost and fuel savings, and also minimize queuing times at log-loaders, management of which is a major concern in the industry. We model this problem as a mixed integer linear programme and solve it via column generation. The methodology is tested on several case studies.     

A column generation method for inverse shortest path problems

In this paper we formulate an inverse shortest path problem as a special linear programming problem. A column generation scheme is developed that is able to keep most columns of the LP model implicit and to generate necessary columns by shortest path algorithms. This method can get an optimal solution in finitely many steps. Some numerical results are reported to show that the algorithm has a good performance.The authors gratefully acknowledge the partial support of Croucher Foundation.     

A stabilized column generation scheme for the traveling salesman subtour problem

Given an undirected graph with edge costs and both revenues and weights on the vertices, the traveling salesman subtour problem is to find a subtour that includes a depot vertex, satisfies a knapsack constraint on the vertex weights, and that minimizes edge costs minus vertex revenues along the subtour.We propose a decomposition scheme for this problem. It is inspired by the classic side-constrained 1-tree formulation of the traveling salesman problem, and uses stabilized column generation for the solution of the linear programming relaxation. Further, this decomposition procedure is combined with the addition of variable upper bound (VUB) constraints, which improves the linear programming bound. Furthermore, we present a heuristic procedure for finding feasible subtours from solutions to the column generation problems. An extensive experimental analysis of the behavior of the computational scheme is presented.