Joint Vehicle and Crew Routing and Scheduling

Traditional vehicle routing problems implicitly assume only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a Joint Vehicle and Crew Routing and Scheduling Problem, in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. It proposes a constraint programming model that overlays crew routing constraints over a standard vehicle routing problem. The constraint programming model uses a novel optimization constraint that detects infeasibility and bounds crew objectives. Experimental results demonstrate significant benefits of using constraint programming over mixed integer programming and a vehicle-then-crew sequential approach.

The periodic vehicle routing problem (PVRP) is an extension of the well-known vehicle routing problem. In this paper, the PVRP with time windows and time spread constraints (PVRP-TWTS) is addressed, which arises in the high-value shipment transportation area. In the PVRP-TWTS, period-specific demands of the customers must be delivered by a fleet of heterogeneous capacitated vehicles over the several planning periods. Additionally, the arrival times to a customer should be irregular within its time window over the planning periods, and the waiting time is not allowed for the vehicles due to the security concerns. This study, proposes novel mixed-integer linear programming (MILP) and constraint programming (CP) models for the PVRP-TWTS. Furthermore, we develop several valid inequalities to strengthen the proposed MILP and CP models as well as a lower bound. Even though CP has successful applications for various optimization problems, it is still not as well-known as MILP in the operations research field. This study aims to utilize the effectiveness of CP in solving the PVRP-TWTS. This study presents a CP model for PVRP-TWTS for the first time in the literature to the best of our knowledge. Having a comparison of the CP and MILP models can help in providing a baseline for the problem. We evaluate the performance of the proposed MILP and CP models by modifying the well-known benchmark set from the literature. The extensive computational results show that the CP model performs much better than the MILP model in terms of the solution quality.

In this paper we describe a procedure that automatically synthesizes a neighborhood from an ensemble of Mixed Integer Programming (MIP) and/or Constraint Programming (CP) models. We move on from a recent paper by Adamo et al. (2015) in which a neighborhood structure is automatically designed from a (single) MIP model through a three-step approach: (1) a semantic feature extraction from the MIP model; (2) the derivation of neighborhood design mechanisms based on these features; (3) an automatic configuration phase to find the “proper mix” of such mechanisms taking into account the instance distribution. Here, we extend the previous work in order to generate a suitable neighborhood from an ensemble of MIP and/or CP models of a given combinatorial optimization problem. Computational results show relevant improvements over the approach considering a single model.

The distribution of goods to a set of geographically dispersed customers is a common problem faced by carrier companies, well-known as the Vehicle Routing Problem (VRP). The VRP consists of finding an optimal set of routes that minimizes total travel times for a given number of vehicles with a fixed capacity. Given the demand of each customer and a depot, the optimal set of routes should adhere to the following conditions: ?? Each customer is visited exactly once by exactly one vehicle. ?? All vehicle routes start and end at the depot. ?? Every route has a total demand not exceeding the vehicle capacity. The travel times between any two potential locations are given as input to the problem. Consequently, the total travel is computed by summing up the travel time over the chosen routes. In reality, carrier companies are faced with a number of other issues not conveyed in the VRP. The research in this thesis introduces a number of realistic variants of the VRP. These variants consider the VRP as a core component and incorporate additional features. By definition the VRP is NP-hard. Throughout the years a vast amount of research was aimed at developing both exact and heuristic solution procedures. Building on this established literature, solution procedures are developed to fit the variants proposed in this thesis. The standard VRP considers that the travel time between any pair of locations is constant throughout the day. However, congestion is present in most road networks. Considering traffic congestion results in time-dependent travel times, where the travel time between two location depends not only on the distance between them but also on the time of day one chooses to traverse this distance. Time-dependent travel times are considered in Chapters 2 and 3 of this thesis. Thus, in these Chapters we incorporate the time dimension into the VRP. The standard VRP does not take into account any customer service aspect. The customers are presumed to be available to receive their goods upon arrival of the vehicles. However, a number of carrier companies quote their expected arrival time to their customers. We introduce the concept of self-imposed time windows (SITW). SITW reflect the fact that the carrier company decides on when to visit the customer and communicates this to the customer. Once a time window is quoted to a customer the carrier company strives to provide service within this time window. SITW differ from time windows in the widely studied VRP with time windows (VRPTW), as the latter are exogenous constraints. In Chapters 4 and 5 SITW are endogenous decisions in stochastic environments. Thus, in addition to the sequencings decisions required by the VRP further timing decisions are needed. This thesis extends the VRP in two major dimensions: time-dependent travel times and self-imposed time windows. In reality carrier companies are faced with various uncertainties. The presented models incorporated some of these uncertainties by addressing three stochastic aspects: (I) In Chapter 3 stochastic service times are considered. (II) In Chapter 4, stochasticity in travel time is modeled to describes variability caused by random events such as car accidents or vehicle break down. (III) Finally, in Chapter 5 the objective was to construct a long term plan for providing consistent service to reoccurring customers. Stochasticity in this thesis is treated in an a priori manner. The plan, consisting of routes and timing decisions where necessary, is determined beforehand and is not modified according to the realization of the random events. Chapter 2 addresses environmental concerns by studying CO2 emissions in a timedependent vehicle routing problem environment. In addition to the decisions required for the assignment and scheduling of customers to vehicles, the vehicle speed limit is considered. The emissions per kilometer as a function of speed, is a function with a unique minimum speed v*. However, we show that limiting vehicle speed to this v* might be sub-optimal, in terms of total emissions. We adapted a Tabu search procedure for the proposed model. Furthermore, upper and lower bounds on the total amount of emissions that may be saved are presented. Quantifying the tradeoff between minimizing travel time as opposed to CO2 emissions is an important contribution. Another important contribution lies in incorporating fuel costs in the optimization. As fuel costs are correlated with CO2 emissions, Chapter 2 shows that even in today’s cost structure limiting vehicle speeds is beneficial. Chapter 3 defines the perturbed time-dependent VRP (P-TDVRP) model which is designed to handle unexpected delays at the various customer locations. A solution method that combines disruptions in a Tabu Search procedure is proposed. In Chapter 3 we identify situations capable of absorbing delays. i.e. where inserting a delay will lead to an increase in travel time that is less than the delay length itself. Based on this, assumptions with respect to the solution structure of P-TDVRP are formulated and validated. Furthermore, most experiments showed that the additional travel time required by the P-TDVRP, when compared to the travel time required by the TDVRP, was justified. In Chapter 4 the notion of self imposed time windows is defined and embedded in the VRP-SITW model. The objective of this problem is to minimize delay costs (caused by late arrivals at customers) as well as traveling time. The problem is optimized under various disruptions in travel times. The basic mechanism of dealing with these disruptions is allocating time buffers throughout the routes. Thus, additional timing decisions are taken. The time buffers attempt to reduce potential damage of disruptions. The solution approach combines a linear programming model with a local search heuristic. In Chapter 4, two main types of experiments were conducted: one compares the VRP with VRP-SITW while the other compares VRPTW with VRPSITW. The first set of experiments assessed the increase in operational costs caused by incorporating SITW in the VRP. The second set of experiments enabled evaluating the savings in operational costs by using flexible time windows, when compared to the VRPTW. Chapter 5 extends the customer service dimension by considering the consistent vehicle routing problem. Consistency is defined by having the same driver visiting the same customers at roughly the same time. As such, two main dimensions of consistency are identified in the literature, driver- and temporal consistency. In Chapter 5, driver consistency is imposed by having the same driver visit the same customers. Furthermore, we impose temporal consistency by SITW. A stochastic programming formulation is presented for the consistent VRP with stochastic customers. An exact solution method is proposed by adapting the 0-1 integer L- shaped algorithm to the problem. The method was able to solve the majority of test instances to optimality.

A new constraint programming model and a linear programming-based adaptive large neighborhood search for the vehicle routing problem with synchronization constraints

In this study, the open vehicle routing problem with heterogeneous vehicle fleet (HFOVRP) is addressed. Unlike the standard vehicle routing problems, vehicles do not return to the depot after their customer visits in the open vehicle routing problems. In the HFOVRP, demands of customers must be served by a heterogeneous vehicle fleet, where the tour length of each vehicle is limited by a maximum allowed tour length. The aim of the studied HFOVRP is to minimize the total fixed cost of used vehicles. In this study, a constraint programming (CP) model is developed for the HFOVRP. A mixed-integer linear programming (MILP) formulation of the HFOVRP is also provided to make a comparison with the CP model. Then, the performances of the CP and MILP models are assessed on a set of small-sized instances with varying number of customers. The computational results show that the CP model is effective for providing good-quality solutions for small-sized instances of the HFOVRP in short computational times. KeywordsVehicle routingOpen vehicle routing problemHeterogeneous vehicle fleetConstraint programmingMathematical modelling

This paper studies a simultaneous vehicle and crew routing and scheduling problem arising in long-distance road transport in Europe: Pickup-and-delivery requests have to be fulfilled over a multi-period planning horizon by a heterogeneous fleet of trucks and drivers. Typically, in the vehicle routing literature, a fixed assignment of a driver to a truck is assumed. In our approach, we abandon this assumption and allow truck/driver changes at geographically dispersed relay stations. This offers greater planning flexibility and allows a better utilization of trucks, but also creates intricate interdependencies between trucks and drivers and requires the synchronization of their routes. A solution heuristic based on a two-stage decomposition of the problem is developed, taking into account European Union social legislation for drivers, and computational experiments using real-world data provided by a major German forwarder are presented and analyzed. The obtained results suggest that for the vehicle and driver cost structure prevalent in Western Europe and for transport requests that are not systematically acquired to complement one another, no cost savings are possible through simultaneous vehicle and crew routing and scheduling, although no formal proof of this fact is possible.

In the literature, line balancing is mostly investigated in deterministic environments. But production systems inevitably contain stochastic situations. In this study, the stochastic type-II assembly line balancing problem (ALBP) is considered. Firstly, a chance-constrained nonlinear mixed integer programming (MIP) formulation is developed from the well-known deterministic form. Then, a new linearized stochastic model is proposed by using some transformation approaches to reduce model complexity, and the model is solved. Finally, constraint programming (CP) models for deterministic ALBPs, nonlinear chance-constrained stochastic ALBPs and linearized chance-constrained stochastic ALBPs are developed, respectively. Problems from the literature are utilized to test the effectiveness of the proposed models and the results are compared with a bidirectional heuristic algorithm. The numerical results show that the CP models are more effective and successful for solving the stochastic ALBP. Some managerial implications are also suggested for industrial environments that consistently face ALBPs.

This paper schedules capacitated parallel machines of a real production system by considering different quantities of production and processing times required to complete customer orders. A new mixed linear programming model is developed according to the concept of constrained vehicle routing problems to have a complete schedule for machines by determining the sequence of both jobs and idle times for each machine. The optimisation model minimises the total cost of the production system, including tardiness, earliness and sequence-dependent setup costs. A constraint programming (CP) model and a meta-heuristic hybrid algorithm are also developed to compare their results with the mixed linear programming model. The numerical findings show that the total cost estimated by the mixed integer programming model is 10%-13% better (lower) than the ones estimated by the CP model and the meta-heuristic algorithm when small instances of the scheduling problem are solved. By increasing the size of the scheduling problem, the meta-heuristic algorithm shows the best computational performance estimating 11% better (lower) total cost compared with the CP model. [Received: 14 April 2020; Accepted: 26 October 2020]

This thesis presents an investigation into the hybridisation of metaheuristic approaches to tackle the classical vehicle routing problem (VRP) and its adaptation to other useful and practical routing problems including the cumulative capacitated VRP (CCVRP) and the dynamic VRP (DVRP). Due to the limited success of the exact methods in handling large size instances, this research investigates the design and analysis of metaheuristic algorithms that can produce near optimal solutions within a reasonable amount of time to solve this class of routing problems. To achieve this goal, we propose an effective and novel hybridisation of variable neighbourhood search (VNS) and large neighbourhood search (LNS), leading to a powerful adaptive VNS (AVNS). Different from most of the literature for AVNS and adaptive LNS where learning is usually incorporated in the shaking step for the former and in the selection of the removal strategies for the latter, the adaptive aspect presented here is integrated in the local search of our AVNS. In short, a set of highly successful local searches is selected based on the intelligent selection mechanism which we introduced. In addition, this work also focuses on the development of some general enhancement-based techniques which include the design of neighbourhood reduction scheme, efficient data structures and a guided penalized objective function. The VRP is a hard combinatorial optimisation problem which was first established more than fifty years ago. Since then, this problem is extensively studied because of its high practicability in transportation logistics. Given the rising price of global oil, reducing the transportation cost provides a great impact in stabilizing the global economic system and adds a competitive advantage. The classical VRP focuses on this line of research. In addition, the classical VRP is used as the initial platform for our experiments which serves as the basis for tackling the other related routing problems mentioned above. The aim is to turn the successful implementations of the proposed algorithm by easily adapting and extending it to cater for the other two related routing problems namely the CCVRP and the DVRP. While the general assumption in most VRPs is profit-based such as the minimisation of the transportation cost, there are other objective functions such as to provide a good service to the customers. Such applications appear in the context of humanitarian relief where the main objective is to save lives or to alleviate suffering. This leads to the introduction of the CCVRP, which aims to minimise the sum of arrival times at customers. The literature for this particular problem is relatively scarce despite its practical importance. We therefore intend to investigate this new and interesting variant. In addition, during the emergency situation, there is often a limited time for saving lives. A good routing plan should also ensure fairness and equity to everyone including the last customer. Motivated by this idea, an alternative but closely related objective that minimises the last arrival time is also studied. We refer to this variant as the min-max CCVRP. In the traditional VRP, a route plan remains unchanged once it is identified. However in practice, several unforeseen events such as accidents or bad weather could occur at any point when the routes are executed, which cause traffic congestion and delay to the original planned routes. Therefore, it is important to re-optimise the routes by taking into consideration the real-time information, leading to the DVRP. The review of the DVRP literature shows that researchers have mainly focused on the customer requests as the dynamic aspect. Our research, however, concentrates more on the less popular but very practical aspect, namely the dynamic traffic information. Such unpredictable events have a great impact on the route plan and henceforth shall, in overview, not be ignored. The contributions of this thesis are fourfold: (i) To propose an effective hybridisation of the VNS and the LNS in addition to some new and powerful data structures and neighbourhood reduction scheme integrated in the algorithm, (ii) To adapt the AVNS algorithm for the CCVRP with extra features added and to present new best results, (iii) To demonstrate the flexibility and effectiveness of the AVNS algorithm to solve the min-max CCVRP and to explore the managerial insights for decision making when considering the min-sum and the min-max CCVRP objective functions, (iv) To adapt the AVNS algorithm as a re-optimisation procedure for the DVRP, where we introduce the concept of critical points which are used as the turning points for the vehicle.

A general heuristic for vehicle routing problems

Despite the success of constraint programming (CP ) for scheduling, the much wider penetration of mixed integer programming (MIP ) technology into business applications means that many practical scheduling problems are being addressed with MIP, at least as an initial approach. Furthermore, there has been impressive and well-documented improvements in the power of generic MIP solvers over the past decade. We empirically demonstrate that on an existing set of resource allocation and scheduling problems standard MIP and CP models are now competitive with the state-of-the-art manual decomposition approach. Motivated by this result, we formulate two tightly coupled hybrid models based on constraint integer programming (CIP ) and demonstrate that these models, which embody advances in CP and MIP, are able to out-perform the CP, MIP, and decomposition models. We conclude that both MIP and CIP are technologies that should be considered along with CP for solving scheduling problems.

CP methods for scheduling and routing with time-dependent task costs

NoC technology is composed of packet-based interconnections, where the communication resources are distributed across the network. Therefore, the optimal resource utilization is a crucial consideration for efficient architectural designs. This paper studies the practicality of the Constraint Programming (CP) models for NoC architecture designs that effectively use a regular mesh with wormhole switching and the XY routing. The complexity of the CP models is compared with the earlier Mixed Integer Programming (MIP) models. Practical CP-based mapping and scheduling models are developed and results are reported on the benchmark datasets. Results indicate that mapping and scheduling problems can be solved at near optimality even under relatively shorter run-time limits as compared to those required by the MIP models.

Integrating distributed disassembly line balancing and vehicle routing problem in supply chain: Integer programming, constraint programming, and heuristic algorithms