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Many seaports worldwide are equipped with one-way navigation channel, in which only one direction is allowed to sail through at a time and vessels thus have to queue up to enter and leave the port alternately. This paper proposes a mixed-integer linear programming (MILP) model for integrated planning of berth allocation and vessel sequencing in such a one-way navigation channel seaport, aiming to minimize weighted dwelling time of all vessels. A tailored adaptive large neighborhood search algorithm is developed for solving the model within a reasonable time. To evaluate the solution quality, a lower bound of the solution of the problem is given by a column generation algorithm that solves a set-partitioning model adapted from the MILP model. Numerical experiments on Jingtang port of China show that (i) the integrated planning model can reduce 20.90%-29.21% of the weighted dwelling time of vessels compared to the current port scheduling schemes; and (ii) the proposed adaptive large neighborhood search algorithm outperforms the GUROBI solver and some existing methods, solving all problem instances within 3 minutes with a 4.83% average optimality gap. Some managerial insights are offered to guide the port operations in a one-way navigation channel seaport.

This paper studies limited-stop operations for rail transit systems and presents an optimization model, which aims to minimize passengers’ travel times and on-board crowdedness. The model combines the design of service itinerary for each vehicle and the allocation of vehicles of various types among multiple lines. Three methods are proposed including a mixed-integer program and two column generation algorithms. Numerical results on generic scenarios show that the column generation algorithm can provide sub-optimal solutions and is computationally efficient. In a case study on Melbourne’s railway network, its solution significantly improves in the passenger travel time compared to the current practice.

This paper presents the congested location-pricing problem under customers’ choice behavior. In the choice-based congested location-pricing problem (CCLPP), the appropriate facilities are selected for offering service by deciding about their fare classes during consecutive time periods. The customer choosing behavior is captured by the discrete choice models. The dominant factors in the customers' decision are proximity and service fare classes offered by the facilities. In the congested systems with immobile facilities, customer waiting time for getting service is important and the M / M / 1 / k queuing system is used for capturing facilities queue in this paper. Customers can choose the competitors for getting service according to the no-service utility. The obtained mathematical model for solving this problem is a nonlinear mixed integer model which is extremely hard to solve and therefore, the alternative modeling approach is developed for solving the problem by the column generation algorithm. The subproblem in this approach determines configurations including open facilities and their fare classes and the master problem specifies the number of time periods for offering each configuration. We also develop a hybrid heuristic including greedy and metaheuristic algorithms for solving the subproblem. The numerical experiments and sensitivity analysis are carried out for demonstrating the efficiency of the proposed algorithm. This analysis indicates that the total profit is the most sensitive to the offering fare classes and available resources.

In the context of large-scale linear programs solved by a column generation algorithm, we present a primal algorithm for handling the master problem. Successive approximations of the latter are created to converge to optimality. The main properties are that, for every approximation except the last one, the cost of the solution decreases whereas the sum of the variable values increases. Moreover, the minimum reduced cost of the variables also increases and converges to zero with a super-geometric growth rate.

Summary Bus driver scheduling aims to find the minimum number of bus drivers to cover a published timetable of a bus company. When scheduling bus drivers, contractual working rules must be enforced, thus complicating the problem. In this research, we develop a column generation algorithm that decomposes this complicated problem into a master problem and a series of pricing subproblems. The master problem selects optimal duties from a set of known feasible duties, and the pricing subproblem augments the feasible duty set to improve the solution obtained in the master problem. The proposed algorithm is empirically applied to the realistic problems of several bus companies. The numerical results show that the proposed column generation algorithm can solve real-world problems and obtain bus driver schedules that are better than those developed and used by the bus companies. Copyright © 2016 John Wiley & Sons, Ltd.

There is a trade-off between the total penalty paid to customers (TPC) and the total transportation cost (TTC) in depot for vehicle routing problems under uncertainty (VRPU). The trade-off refers to the fact that the TTC in depot inevitably increases when the TPC decreases andvice versa. With respect to this issue, the vehicle routing problem (VRP) with uncertain customer demand and travel time was studied to optimise the TPC and the TTC in depot. In addition, an inverse robust optimisation approach was proposed to solve this kind of VRPU by combining the ideas of inverse optimisation and robust optimisation so as to improve both the TPC and the TTC in depot. The method aimed to improve the corresponding TTC of the robust optimisation solution under the minimum TPC through minimising the adjustment of benchmark road transportation cost. According to the characteristics of the inverse robust optimisation model, a genetic algorithm (GA) and column generation algorithm are combined to solve the problem. Moreover, 39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and TTC obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach.

This paper aims to optimize high-speed railroad timetables for a corridor. We propose an integer programming model using a time-space network-based approach to consider passenger service demands, train scheduling, and station service demands simultaneously. A modified branch-and-price algorithm is used for the computation. This algorithm solves the linear relaxation of all nodes in a branch-and-bound tree using a column generation algorithm to derive a lower-bound value (LB) and derive an upper-bound value (UB) using a rapid branching strategy. The optimal solution is derived by iteratively updating the upper- and lower-bound values. Three acceleration strategies, namely, initial solution iteration, delayed constraints, and column removal, were designed to accelerate the computation. The effectiveness and efficiency of the proposed model and algorithm were tested using Wuhan-Guangzhou high-speed railroad data. The results show that the proposed model and algorithm can quickly reduce the defined cost function by 38.2% and improve the average travel speed by 10.7 km/h, which indicates that our proposed model and algorithm can effectively improve the quality of a constructed train timetable and the travel efficiency for passengers.

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.

The planning of outbound baggage handling at international airports is challenging. Outgoing flights have to be assigned and scheduled to handling facilities at which the outgoing baggage is loaded into containers. To avoid disruptions of the system the objective is to minimize workload peaks over the entire system. The resource demand of the jobs that have to be scheduled depends on the arrival process of the baggage. In this paper we present a time-indexed mathematical programming formulation for planning the outbound baggage. We propose an innovative decomposition procedure in combination with a column generation scheme to solve practical problem instances. The decomposition significantly reduces the symmetry effect in the time-indexed formulation and also speeds up the computational time of the corresponding Dantzig–Wolfe formulation. To further improve our column generation algorithm we propose state-of-the-art acceleration techniques for the primal problem and the pricing problem. Computational results based on real data from a major European airport show that the proposed procedure reduces the maximal workloads by more than 60% compared to the current assignment procedure used. The online appendix is available at https://doi.org/10.1287/trsc.2017.0739 .

Unmanned Aerial Vecicles (UAVs) in civil and military applications are becoming increasingly popular. Various platform types have already shown their great potential in missions that require rapid surveillance capabilities or logistic support. Large scale incidents require the deployment of several platforms with various capabilities. In this case, coordinated use will lead to more efficient use of the given resources. Problems to resolve resemble known optimization problems from the field of vehicle routing or scheduling. The problem considered in this work includes a given team of homogenous UAVs and a set of target locations with certain requests that need to be served. It is modeled as a variant of the Vehicle Routing Problem (VRP) that is known to be NP hard, i.e. until now no algorithm is known that can solve the problem in polynomial run-time. In this paper, the problem is formulated using a path flow formulation and a column generation algorithm has been implemented and tested to solve simulated realtime instances of the problem in suitable time∗.

This article addresses three problems that arise in coverage scheduling for wireless sensor networks subject to bandwidth constraints. The first problem focuses on minimizing the total breach under a lifetime constraint, where a breach occurs when some targets are not covered by active sensors. The second problem aims at maximizing the network lifetime under a breach constraint. Finally, the problem of computing the possible trade-offs between breach and lifetime offered by the sensor network is also addressed. An exact approach based on a column generation algorithm is proposed for solving these problems, and a heuristic is also derived from it and briefly presented. The use of a genetic algorithm within the column generation scheme appears to significantly decrease computation time. © 2011 Wiley Periodicals, Inc. NETWORKS, 2012 © 2012 Wiley Periodicals, Inc.