Solving the bicriterion routing and scheduling problem for hazardous materials distribution

Hazardous materials routing and scheduling decisions involve the determination of the minimum cost and/or risk routes for servicing the demand of a given set of customers. This paper addresses the bicriterion routing and scheduling problem arising in hazardous materials distribution planning. Under the assumption that the cost and risk attributes of each arc of the underlying transportation network are time-dependent, the proposed routing and scheduling problem pertains to the determination of the non-dominated time-dependent paths for servicing a given and fixed sequence of customers (intermediate stops) within specified time windows. Due to the heavy computational burden for solving this bicriterion problem, an alternative algorithm is proposed that determines the k-shortest time-dependent paths. Moreover an algorithm is provided for solving the bicriterion problem. The proximity of the solutions of the k-shortest time-dependent path problem with the non-dominated solutions is assessed on a set of problems developed by the authors.     

Closed-loop Inventory Routing Problem for returnable transport items

Increasing concerns on supply chain sustainability have given birth to the concept of closed-loop supply chain. Closed-loop supply chains include the return processes besides forward flows to recover the value from the customers or end-users. Vendor Managed Inventory (VMI) systems ensure collaborative relationships between a vendor and a set of customers. In such systems, the vendor takes on the responsibility of product deliveries and inventory management at customers. Product deliveries also include reverse flows of returnable transport items. The execution of the VMI policy requires vendor to deal with a Closed-loop Inventory Routing Problem (CIRP) consisting of its own forward and backward routing decisions, and inventory decisions of customers. In CIRP literature, traditional assumptions of disregarding reverse logistic operations, knowing beforehand distribution costs between nodes and customers demand, and managing single product restrict the usage of the proposed models in current food logistics systems. From this point of view, the aim of this research is to enhance the traditional models for the CIRP to make them more useful for the decision makers in closed-loop supply chains. Therefore, we propose a probabilistic mixed-integer linear programming model for the CIRP that accounts for forward and reverse logistics operations, explicit fuel consumption, demand uncertainty and multiple products. A case study on the distribution operations of a soft drink company shows the applicability of the model to a real-life problem. The results suggest that the proposed model can achieve significant savings in total cost and thus offers better support to decision makers.     

Integrated scheduling of m-truck,m-drone,and m-depot constrained by time-window,drop-pickup,and m-visit using constraint programming

The idea of deploying unmanned aerial vehicles, also known as drones, for final-mile delivery in logistics operations has vitalized this new research stream. One conceivable scenario of using a drone in conjunction with a traditional delivery truck to distribute parcels is discussed in earlier literature and termed the parallel drone scheduling traveling salesman problem (PDSTSP). This study extends the problem by considering two different types of drone tasks: drop and pickup. After a drone completes a drop, the drone can either fly back to depot to deliver the next parcels or fly directly to another customer for pickup. Integrated scheduling of multiple depots hosting a fleet of trucks and a fleet of drones is further studied to achieve an operational excellence. A vehicle that travels near the boundary of the coverage area might be more effective to serve customers that belong to the neighboring depot. This problem is uniquely modeled as an unrelated parallel machine scheduling with sequence dependent setup, precedence-relationship, and reentrant, which gives us a framework to effectively consider those operational challenges. A constraint programming approach is proposed and tested with problem instances of m-truck, m-drone, m-depot, and hundred-customer distributed across an 8-mile square region.     

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and meta-heuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective.     

A lamda-optimal based heuristic for the berth scheduling problem

Berth scheduling aims to optimally schedule vessels to berthing areas along a quay and is a complex optimization problem. In this paper we propose a lamda-optimal based heuristic as a resolution approach for the discrete space berth scheduling problem. The proposed heuristic can also be applied to validate optimality, in the case where other (meta)heuristics are applied as resolution approaches. A second internal Genetic Algorithms based heuristic is also proposed to reduce the computational time required for medium to large scale instances. Numerical experiments performed show that the proposed heuristic is adequate to produce near-optimal results within acceptable computational times.     

Optimal scheduling of a taxi fleet with mixed electric and gasoline vehicles to service advance reservations

This study addresses the problem of scheduling a fleet of taxis that are appointed to solely service customers with advance reservations. In contrast to previous studies that have dealt with the planning and operations of a taxi fleet with only electric vehicles (EVs), we consider that most taxi companies may have to operate with fleets comprised of both gasoline vehicles (GVs) and plug-in EVs during the transition from GV to (complete) EV taxi fleets. This paper presents an innovative multi-layer taxi-flow time-space network which effectively describes the movements of the taxis in the dimensions of space and time. An optimization model is then developed based on the time-space network to determine an optimal schedule for the taxi fleet. The objective is to minimize the total operating cost of the fleet, with a set of operating constraints for the EVs and GVs included in the model. Given that the model is formulated as an integer multi-commodity network flow problem, which is characterized as NP-hard, we propose two simple but effective decomposition-based heuristics to efficiently solve the problem with practical sizes. Test instances generated based on the data provided by a Taiwan taxi company are solved to evaluate the solution algorithms. The results show that the gaps between the objective values of the heuristic solutions and those of the optimal solutions are less than 3%, and the heuristics require much less time to obtain the good quality solutions. As a result, it is shown that the model, coupled with the algorithms, can be an effective planning tool to assist the company in routing and scheduling its fleet to service reservation customers.     

Scheduling railway freight delivery appointments using a bid price approach

This paper proposes a method for establishing aggressive but achievable delivery appointment times for railroad shipments, taking into account individual customer needs and forecasted available train capacity. The concept of scheduling appointment times is directly patterned after current motor carrier industry practice, so that customers can plan for rail or truck deliveries in the same way.A shipment routing problem is decomposed into a deterministic “dynamic car scheduling” (DCS) process for shipments already accepted and a stochastic “train segment pricing” (TSP) process for forecasting future demands which have not yet called in and for which delivery appointments have yet to be scheduled. Both are formulated as multi-commodity network flow (MCNF) problems, where each shipment is treated as a separate commodity. Gain coefficients represent recapture probabilities that a specific customer will accept a carrier’s service offer.A comparison with a widely used revenue management formulation is given. A Lagrangian heuristic for obtaining a primal solution is also described. The problem is solved within a 1% gap using the subgradient algorithm.     

The time-dependent vehicle routing problem with soft time windows and stochastic travel times

This paper studies a vehicle routing problem with time-dependent and stochastic travel times. In our problem setting, customers have soft time windows. A mathematical model is used in which both efficiency for service as well as reliability for customers are taken into account. Depending on whether service times are included or not, we consider two versions of this problem. Two metaheuristics are built: a Tabu Search and an Adaptive Large Neighborhood Search. We carry out our experiments for well-known problem instances and perform comprehensive analyses on the numerical results in terms of the computational time and the solution quality. Experiments confirm that the proposed procedure is effective to obtain very good solutions to be performed in real-life environment.     

Train routing and timetabling problem for heterogeneous train traffic with switchable scheduling rules

This paper proposes a mathematical model for the train routing and timetabling problem that allows a train to occasionally switch to the opposite track when it is not occupied, which we define it as switchable scheduling rule. The layouts of stations are taken into account in the proposed mathematical model to avoid head-on and rear-end collisions in stations. In this paper, train timetable could be scheduled by three different scheduling rules, i.e., no switchable scheduling rule (No-SSR) which allows trains switching track neither at stations and segments, incomplete switchable scheduling rule (In-SSR) which allows trains switching track at stations but not at segments, and complete switchable scheduling rule (Co-SSR) which allows trains switching track both at stations and segments. Numerical experiments are carried out on a small-scale railway corridor and a large-scale railway corridor based on Beijing–Shanghai high-speed railway (HSR) corridor respectively. The results of case studies indicate that Co-SSR outperforms the other two scheduling rules. It is also found that the proposed model can improve train operational efficiency.     

A differential evolution approach for the vehicle routing problem with backhauls and time windows

This paper presents a differential evolution algorithm (DEA) to solve a vehicle routing problem with backhauls and time windows (VRPBTW) and applied for a catering firm. VRPBTW is an extension of the vehicle routing problem, which includes capacity and time window constraints. In this problem, customers are divided into two subsets: linehaul and backhaul. Each vehicle starts from a depot and goods are delivered from the depot to the linehaul customers. Goods are subsequently brought back to the depot from the backhaul customers. The objective is to minimize the total distance that satisfies all of the constraints. The problem is formulated using mixed integer programming and solved using DEA. Proposed algorithm is tested with several benchmark problems to demonstrate effectiveness and efficiency of the algorithm and results show that our proposed algorithm can find superior solutions for most of the problems in comparison with the best known solutions. Hence, DEA was carried out for catering firm to minimize total transportation costs. Copyright © 2013 John Wiley & Sons, Ltd.     

Heuristic approaches for solving large-scale bus transit vehicle scheduling problem with route time constraints

This paper presents new models for multiple depot vehicle scheduling problem (MDVS) and multiple depot vehicle scheduling problem with route time constraints (MDVSRTC). The route time constraints are added to the MDVS problem to account for the real world operational restrictions such as fuel consumption. Compared to existing formulations, this formulation decreases the size of the problem by about 40% without eliminating any feasible solution. It also presents an exact and two heuristic solution procedures for solving the MDVSRTC problem. Although these methods can be used to solve medium size problems in reasonable time, real world applications in large cities require that the MDVSRTC problem size be reduced. Two techniques are proposed to decrease the size of the real world problems. For real-world application, the problem of bus transit vehicle scheduling at the mass transit administration (MTA) in Baltimore is studied. The final results of model implementation are compared to the MTA's schedules in January 1998. The comparison indicates that, the proposed model improves upon the MTA schedules in all respects. The improvements are 7.9% in the number of vehicles, 4.66% in the operational time and 5.77% in the total cost.     

Reducing carbon emission of pickup and delivery using integrated scheduling

Integrated scheduling is a powerful way to reduce carbon emission of pickup and delivery because the vehicle loading efficiency can be improved. Our study investigates theoretically the potential carbon emission reduction brought by integrated scheduling, and develops the upper and lower bounds. To demonstrate the practical advantage of carbon emission reduction brought by integrated scheduling, we use the real application of pickup and delivery, i.e., “picking up and delivering customers to airport” (PDCA). Using based-on-set-partitioning formulation, we accurately obtain the minimal carbon emissions of non-integrated scheduling and integrated scheduling. We conclude that integrated scheduling reduces carbon emission by approximate 10.8%. However, the cost in integrated scheduling may be more than before, which causes a company unwilling to accept integrated scheduling. The acceptable integrated scheduling is proposed. We identify the situations under which carbon emission can be efficiently reduced in acceptable integrated scheduling based on the extensive experiments of PDCA.     

Scheduling of airport runway operations using stochastic branch and bound methods

In this paper we present a solution methodology based on the stochastic branch and bound algorithm to find optimal, or close to optimal, solutions to the stochastic airport runway scheduling problem. The objective of the scheduling problem is to find a sequence of aircraft operations on one or several runways that minimizes the total makespan, given uncertain aircraft availability at the runway. Enhancements to the general stochastic branch and bound algorithm are proposed and we give the specific details pertaining to runway scheduling. We show how the algorithm can be terminated early with solutions that are close to optimal, and investigate the impact of the uncertainty level. The computational experiment indicates that the sequences obtained using the stochastic branch and bound algorithm have, on average, 5–7% shorter makespans than sequences obtained using deterministic sequencing models. In addition, the proposed algorithm is able to solve instances with 14 aircraft using less than 1 min of computation time.     

A network equilibrium approach for modelling activity-travel pattern scheduling problems in multi-modal transit networks with uncertainty

An understanding of the interaction between individuals’ activities and travel choice behaviour plays an important role in long-term transit service planning. In this paper, an activity-based network equilibrium model for scheduling daily activity-travel patterns (DATPs) in multi-modal transit networks under uncertainty is presented. In the proposed model, the DATP choice problem is transformed into a static traffic assignment problem by constructing a new super-network platform. With the use of the new super-network platform, individuals’ activity and travel choices such as time and space coordination, activity location, activity sequence and duration, and route/mode choices, can be simultaneously considered. In order to capture the stochastic characteristics of different activities, activity utilities are assumed in this study to be time-dependent and stochastic in relation to the activity types. A concept of DATP budget utility is proposed for modelling the uncertainty of activity utility. An efficient solution algorithm without prior enumeration of DATPs is developed for solving the DATP scheduling problem in multi-modal transit networks. Numerical examples are used to illustrate the application of the proposed model and the solution algorithm.     

Integrated optimization on train scheduling and preventive maintenance time slots planning

We address the problem of simultaneously scheduling trains and planning preventive maintenance time slots (PMTSs) on a general railway network. Based on network cumulative flow variables, a novel integrated mixed-integer linear programming (MILP) model is proposed to simultaneously optimize train routes, orders and passing times at each station, as well as work-time of preventive maintenance tasks (PMTSs). In order to provide an easy decomposition mechanism, the limited capacity of complex tracks is modelled as side constraints and a PMTS is modelled as a virtual train. A Lagrangian relaxation solution framework is proposed, in which the difficult track capacity constraints are relaxed, to decompose the original complex integrated train scheduling and PMTSs planning problem into a sequence of single train-based sub-problems. For each sub-problem, a standard label correcting algorithm is employed for finding the time-dependent least cost path on a time-space network. The resulting dual solutions can be transformed to feasible solutions through priority rules. Numerical experiments are conducted on a small artificial network and a real-world network adapted from a Chinese railway network, to evaluate the effectiveness and computational efficiency of the integrated optimization model and the proposed Lagrangian relaxation solution framework. The benefits of simultaneously scheduling trains and planning PMTSs are demonstrated, compared with a commonly-used sequential scheduling method.     

A column generation algorithm for the bus driver scheduling problem

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.     

An activity-based approach for scheduling multimodal transit services

This paper proposes a new activity-based transit assignment model for investigating the scheduling (or timetabling) problem of transit services in multi-modal transit networks. The proposed model can be used to generate the short-term and long-term timetables of multimodal transit lines for transit operations and service planning purposes. The interaction between transit timetables and passenger activity-travel scheduling behaviors is captured by the proposed model, as the activity and travel choices of transit passengers are considered explicitly in terms of departure time choice, activity/trip chain choices, activity duration choice, transit line and mode choices. A heuristic solution algorithm which combines the Hooke–Jeeves method and an iterative supply–demand equilibrium approach is developed to solve the proposed model. Two numerical examples are presented to illustrate the differences between the activity-based approach and the traditional trip-based method, together with comparison on the effects of optimal timetables with even and uneven headways. It is shown that the passenger travel scheduling pattern derived from the activity-based approach is significantly different from that obtained by the trip-based method, and that a demand-sensitive (with uneven headway) timetable is more efficient than an even-headway timetable.     

A subway planning bi-objective multi-period optimization model integrating timetabling and vehicle scheduling: a case study of Tehran

Due to the interaction among different planning levels and various travel demands during a day, the transit network planning is of great importance. In this paper, a bi-objective multi-period planning model is proposed for the synchronization of timetabling and vehicle scheduling. The main aim of the problem is to minimize the weighted transfer waiting time in the interchange stations along with the operational costs of vehicles. In order to demonstrate the effectiveness of the proposed integrated model, a real case study of Tehran subway is considered. The proposed model is solved by the ε-constraint method and some outstanding results are achieved.

     

An integrated modelling approach for the bicriterion vehicle routing and scheduling problem with environmental considerations

The consideration of pollution in routing decisions gives rise to a new routing framework where measures of the environmental implications are traded off with business performance measures. To address this type of routing decisions, we formulate and solve a bi-objective time, load and path-dependent vehicle routing problem with time windows (BTL-VRPTW). The proposed formulation incorporates a travel time model representing realistically time varying traffic conditions. A key feature of the problem under consideration is the need to address simultaneously routing and path finding decisions. To cope with the computational burden arising from this property of the problem we propose a network reduction approach. Computational tests on the effect of the network reduction approach on determining non-dominated solutions are reported. A generic solution framework is proposed to address the BTL-VRPTW. The proposed framework combines any technique that creates capacity-feasible routes with a routing and scheduling method that aims to convert the identified routes to problem solutions. We show that transforming a set of routes to BTL-VRPTW solutions is equivalent to solving a bi-objective time dependent shortest path problem on a specially structured graph. We propose a backward label setting technique to solve the emerging problem that takes advantage of the special structure of the graph. The proposed generic solution framework is implemented by integrating the routing and scheduling method into an Ant Colony System algorithm. The accuracy of the proposed algorithm was assessed on the basis of its capability to determine minimum travel time and fuel consumption solutions. Although the computational results are encouraging, there is ample room for future research in algorithmic advances on addressing the proposed problem.     

Multi-objective bilevel construction material transportation scheduling in large-scale construction projects under a fuzzy random environment

Abstract

This paper investigates a transportation scheduling problem in large-scale construction projects under a fuzzy random environment. The problem is formulated as a fuzzy, random multi-objective bilevel optimization model where the construction company decides the transportation quantities from every source to every destination according to the criterion of minimizing total transportation cost and transportation time on the upper level, while the transportation agencies choose their transportation routes such that the total travel cost is minimized on the lower level. Specifically, we model both travel time and travel cost as triangular fuzzy random variables. Then the multi-objective bilevel adaptive particle swarm optimization algorithm is proposed to solve the model. Finally, a case study of transportation scheduling for the Shuibuya Hydropower Project in China is used as a real world example to demonstrate the practicality and efficiency of the optimization model and algorithm.