Multi-period hub location problems in transportation

Many transport service providers operate on hub-and-spoke network structures. Major operators may have several dedicated hub facilities that are leased for a time horizon rather than being owned or constructed. For a given discrete planning horizon, service providers must decide on the location of the hub ports (i.e. terminals), the period when the lease contract starts, the period when the existing contracts must be terminated and the flow routing over the entire planning horizon so as to minimize the total operational cost. Thus, we propose a mathematical model for a Multi-period Uncapacitated Multiple Allocation Hub Location Problem with Budget Constraint. The proposed model incorporates several features of practice, particularly from maritime and land transport practices. We also propose a meta-heuristic solution algorithm that produces high-quality solutions in a reasonable amount of time. By exploiting the decomposable structure of the model, we extended a Benders decomposition approach by proposing several improvements. Extensive computational experiments confirm the efficiency of the proposed methods and also show its limitations.     

Optimal solution for a cargo revenue management problem with allotment and spot arrivals

We consider a single-leg cargo revenue management problem, in which a two-dimensional cargo capacity is sold through allotment contracts and in the spot market. Capacity sold on an allotment basis is guaranteed. We optimally solve the problem of determining how much of the total weight and volume capacity to sell on an allotment basis, by deriving a closed-form expression of the objective function. We provide numerical examples of industry-size problems and perform sensitivity analysis by changing some problem parameters. The sensitivity analysis illustrates the dependency of the optimal decisions on the spot and allotment booking types. The remaining capacity is then sold over a booking horizon in the spot market. Allotment bookings and spot requests can arrive any time over the booking horizon. Since some of the allotment bookings might not show up at departure, cargo carriers tend to overbook the remaining capacity allocated to spot requests. For these requests, we formulate a discrete-time dynamic capacity control model, to decide which of the spot requests to accept, based on the total weight and volume of the allotment show-ups and spot bookings accepted at the time of an arrival. We solve the exact dynamic programming model for medium-size industry problems. Since the booking policy based on critical booking levels or time periods is not optimal, we propose several heuristics to solve large industry problems and derive an upper bound on the value function. We test their performance via simulation against the optimal solution, the upper bound, and the first-come first-served policy, and recommend a heuristic that performs well in a wide variety of numerical cases. Finally, we show via simulation, that our model outperforms the one existing in the literature, for small and medium-size industry problems.     

Dynamic supply chain network design with capacity planning and multi-period pricing

This paper addresses a new problem in designing and planning a multi-echelon and multi-product supply chain network over a multi-period horizon in which customer zones have price-sensitive demands. Based on price-demand relationships, a generic method is presented to obtain price levels for products and then, a mixed-integer linear programming model is developed. Due to the problem intractability, a simulated annealing algorithm that uses some developed linear relaxation-based heuristics for capacity planning and pricing is presented. Numerical results demonstrate the significance of the model as well as the efficiency of the solution algorithm and linear relaxation-based heuristics.     

Scheduling aircraft take-offs and landings on interdependent and heterogeneous runways

This paper presents an optimization method for the aircraft scheduling problem with general runway configurations. Take-offs and landings have to be assigned to a runway and a time while meeting the sequence-dependent separation requirements and minimizing the costs incurred by delays. Some runways can be used only for take-offs, landings, or certain types of aircraft while schedules for interdependent runways have to consider additional diagonal separation constraints.Our dynamic programming approach solves realistic problem instances to optimality within short computation times. In addition, we propose a rolling planning horizon heuristic for large instances that returns close-to-optimal results.     

The multi-period service territory design problem – An introduction,a model and a heuristic approach

In service territory design applications, a field service workforce is responsible for providing recurring services at their customers’ sites. We introduce the associated planning problem, which consists of two subproblems: In the partitioning subproblem, customers must be grouped into service territories. In the scheduling subproblem, customer visits must be scheduled throughout the multi-period planning horizon. The emphasis of this paper is put on the scheduling subproblem. We propose a mixed integer programming model for this subproblem and present a location-allocation heuristic. The results of extensive experiments on real-world instances show that the proposed heuristic produces high-quality solutions.     

Robust planning and disruption management in roll-on roll-off liner shipping

This paper presents different strategies for handling disruptions in fleet deployment in roll-on roll-off liner shipping, which basically consists of assigning a fleet of vessels to predefined voyages at minimum cost. A new mathematical model of the problem is presented, including a set of robust planning strategies, such as adding slack and rewarding early arrivals. To solve real-life instances a rolling horizon heuristic is proposed. A computational study, where we also propose some recovery planning strategies, is conducted, and simulation results show that adding robustness significantly reduces the actual cost of the plan and the total delays of the voyages.     

A MILP model for planning the trips of dynamic positioned tankers with variable travel time

The transportation of the crude oil produced in offshore oilfields to onshore terminals is performed by vessels, known as shuttle tankers. Scheduling shuttle-tanker operations entails solving complex problems to ensure a timely offloading of the platforms, taking into account several logistics and inventory constraints. This work proposes a new MILP formulation that advances previous works by considering variable travel time between platforms and terminals. The combination of the MILP formulation with an optimization solver constitutes a decision-support tool to aid engineers reach optimal decisions for a planning horizon. To handle large-scale instances, rolling-horizon and relax-and-fix strategies are proposed.     

Empty container management for intermodal transportation networks

We present a computational analysis of the effect of planning horizon length on empty container management for intermodal transportation networks. The analysis is based on an integer program that seeks to minimize total costs related to moving empty containers, subject to meeting requirements for moving loaded containers. A case study of potential container-on-barge operations within the Mississippi River basin illustrates the effects of planning horizon length on mode selection. A longer planning horizon can encourage the use of inexpensive, slow transportation modes, such as barge. The impact depends on the number and location of container storage pools.     

The effect of multi-scenario policies on empty container repositioning

This paper addresses a container maritime-repositioning problem where several parameters are uncertain and historical data are useless for decision-making processes. To address this problem, we propose a time-extended multi-scenario optimization model in which scenarios can be generated taking into account shipping company opinions. We then show that multi-scenario policies put shipping companies in the position of satisfying empty-container demands for different values that may be taken by uncertain parameters.     

The strategic berth template problem

A marine container terminal operator may have a situation with excessive calling requests to be served especially when some new service contracts are under consideration. For this situation, we propose a strategic berth template problem (BTPS) that selects the ships among the requesting ones to be served and arrange their berth-windows within a limited planning horizon. The BTPS employs the subgradient optimization procedure, which is an improved version of the procedure that the authors developed for the operational berth allocation problem. A wide variety of numerical experiments indicate the improved subgradient procedure works well for the BTPS.     

Combined fleet deployment and inventory management in roll-on/roll-off shipping

In maritime transportation of automobiles, roll-on/roll-off (ro–ro) shipping companies operate liner shipping services across major trade routes. Large ro–ro shipping companies are well placed to offer end-to-end integrated logistics services to auto manufacturers engaged in international trade of vehicles. Therefore, we present a new mixed integer programming model for fleet deployment including inventory management at the ports along each trade route. Due to the complexity of the problem, a rolling horizon heuristic (RHH) is proposed. The RHH solves the problem by iteratively solving sub-problems with shorter planning horizon. Computational results based on real instances are presented.     

Multi-period heterogeneous vehicle routing considering carbon emission trading

This study considers the problem of determining heterogeneous vehicle routes in each period of a given planning horizon while satisfying service combinations, customer demands and vehicle capacities. The objective is to minimize the sum of vehicle operation costs and carbon emission trading cost/benefit, where the trading cost is incurred to purchase the carbon emission right if the total emission exceeds an upper limit in each period, while the trading benefit can be obtained by selling the right in each period, otherwise. A mixed integer programming model is developed to formulate the problem mathematically. Then, a tabu search algorithm is proposed that incorporates the characteristics of the heterogeneous and the period vehicle routing problems while considering the amount of carbon emission in each period. Computational experiments were done on modified benchmark instances and additional random instances, and the results show that the multi-period approach outperforms the existing single-period one in overall average. In particular, the test results show that the multi-period approach can reduce carbon emission more significantly than the single-period one without sacrificing the total cost.     

A rolling horizon approach to the high speed train rescheduling problem in case of a partial segment blockage

This paper reschedules train services on a double-track high speed railway in a disrupted situation, where one track of a segment is temporarily unavailable. We have to decide the sequence of train services passing through the blocked segment, the arrival and departure time of each train service at each station, and the canceled train services. Three practical train rescheduling strategies are explicitly compared and formulated by three MILP models. The uncertain duration of the disruption is handled. A rolling horizon approach is applied to solve our models. The models are tested on a real-world instance of the Beijing-Shanghai high speed railway.     

The benefit of advance load information for truckload carriers

This paper models and measures the profit improvement trucking companies can achieve by collaborating with their clients to obtain advance load information (ALI). The main approach is to formulate a comprehensive and flexible mixed integer mathematical model and implement it in a dynamic rolling horizon context. The findings illustrate that access to the second and the third day ALI can improve the profit by averages of 22% and 6%, respectively. We also found that the impact of ALI depends on radius of service and trip length but is statistically independent of load density and fleet size.     

Scenario tree airline fleet planning for demand uncertainty

This paper proposes an innovative multi-period modeling approach to solve the airline fleet planning problem under demand uncertainty. The problem is modeled using a scenario tree approach. The tree is composed of nodes, which represent points of decision in multiple time stages of the planning horizon, and branches, representing demand variation scenarios. The branches link the decision nodes in consequent time stages and compose scenario paths. Fleet decisions are modeled according to these scenario paths, resembling the real-life process in which fleet plans are not defined in a single moment but instead are adjusted according to the demand development. Given that some scenario paths share common decision nodes, decisions among scenarios need to be synchronized. A mixed-integer linear programming model is proposed to determine the ideal fleet composition for each scenario in the tree and to describe this interdependency between scenarios. Considering the probability of a scenario, fleet composition probabilities for each time-period can be determined. Two real-world based case studies are performed to show the validity of the model. Results show that the proposed scenario tree approach can provide flexible multi-period airline fleet plans, which are more robust to future demand scenarios than fleet solutions obtained using the traditional approach of considering a single deterministic demand evolution scenario.     

Optimizing a bi-objective inventory model of a three-echelon supply chain using a tuned hybrid bat algorithm

This paper presents a bi-objective VMI problem in a single manufacturer-single vendor multi-retailer (SM-SV-MR) supply chain, which a redundancy allocation problem is incorporated. In the hybridized problem, a manufacturer produces a single item using several machines that work in series, and stores it in a warehouse to replenish one vendor who delivers it to several retailers using the shortest possible route. A novel meta-heuristic, called hybrid bat algorithm (HBA), with calibrated parameters is utilized to find a near-optimum solution. To show the efficiency of HBA, the results are compared to the ones using the traditional BA and a genetic algorithm.     

A comprehensive evacuation planning model and genetic solution algorithm

We consider the problem of evacuating an urban area. Several planning aspects need to be considered in such a scenario, which are usually considered separately. We propose a macroscopic multi-criteria optimization model that includes several such questions simultaneously, and develop a genetic algorithm to solve the problem heuristically. Its applicability is extended by also considering how to aggregate instance data, and how to generate solutions for the original instance starting from a reduced solution. In computational experiments using real-world data, we demonstrate the effectiveness of our approach and compare different levels of data aggregation.     

Optimal extension of rail transit lines

A bilevel model for optimizing the extension of a rail transit line over a planning horizon is presented. In the upper level planning problem, planners make decisions regarding construction and investment in each period with the objective of net present worth maximization. In the lower level operational program, transit operators maximize the social welfare by setting the fare, headway, and vehicle size subject to the train capacity constraint. After the exploration of the model's structure, a tighter reformulated program is proposed and solved as a dynamic program. Numerical studies demonstrate that even without a budget limit phased development can be preferable to a one-time extension.     

Supply chain network design under profit maximization and oligopolistic competition

In this paper, we model the supply chain network design problem with oligopolistic firms who are involved in the competitive production, storage, and distribution of a homogeneous product to multiple demand markets. The profit-maximizing firms select both the capacities associated with the various supply chain network activities as well as the product quantities. We formulate the governing Nash–Cournot equilibrium conditions as a variational inequality problem and identify several special cases of the model, notably, a generalization of a spatial oligopoly and a classical oligopoly problem to include design capacity variables. The proposed computational approach, which is based on projected dynamical systems, fully exploits the network structure of the problems and yields closed form solutions at each iteration. In order to illustrate the modeling framework and the algorithm, we also provide solutions to a spectrum of numerical supply chain network oligopoly design examples.This paper makes a contribution to game theoretic modeling of competitive supply chain network design problems in an oligopolistic setting.     

Adaptive large neighborhood search heuristics for the vehicle routing problem with stochastic demands and weight-related cost

The vehicle routing problem (VRP) with stochastic demands and weight-related cost is an extension of the VRP. Although some researchers have studied the VRP with either stochastic demands or weight-related cost, the literature on this problem is quite limited. We adopt the a priori optimization to tackle this problem and propose a dynamic programming to compute the expected cost of each route. We develop the adaptive large neighborhood search heuristics equipped with several approximate methods for the problem. To evaluate our heuristics, we generate 84 test instances. Computational results demonstrate the performance of our heuristics and can serve as benchmarks for future researchers.