Reducing emissions through speed optimization in supply vessel operations

This paper examines how optimizing sailing speeds can reduce supply vessels emissions in the upstream supply chain to offshore installations. We introduce several speed optimization strategies to be used in construction of periodic vessel schedules. The strategies consider vessel waiting times before the start of service at installations and at supply base. Tests carried out on real instances from Statoil’s activities on the Norwegian continental shelf indicate that a 25% emissions and fuel cost reductions can be achieved without fleet size increase.     

Optimal planning of liquefied natural gas deliveries

We investigate the problem of designing an optimal annual delivery plan for Liquefied Natural Gas (LNG). This problem requires determining the long-term cargo delivery dates and the assignment of vessels to the cargoes while accommodating several constraints, including berth availability, liquefaction terminal inventory, planned maintenance, and bunkering requirements. We describe a novel mixed-integer programming formulation that captures important industry requirements and constraints with the objective of minimizing the vessel fleet size. A peculiar property of the proposed formulation is that it includes a polynomial number of variables and constraints and is, in our experience, computationally tractable for large problem instances using a commercial solver. Extensive computational runs demonstrate the efficacy of the proposed model for real instances provided by a major energy company that involve up to 118 cargoes and a 373-day planning horizon.     

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.     

The fleet size and mix pollution-routing problem

This paper introduces the fleet size and mix pollution-routing problem which extends the pollution-routing problem by considering a heterogeneous vehicle fleet. The main objective is to minimize the sum of vehicle fixed costs and routing cost, where the latter can be defined with respect to the cost of fuel and CO₂ emissions, and driver cost. Solving this problem poses several methodological challenges. To this end, we have developed a powerful metaheuristic which was successfully applied to a large pool of realistic benchmark instances. Several analyses were conducted to shed light on the trade-offs between various performance indicators, including capacity utilization, fuel and emissions and costs pertaining to vehicle acquisition, fuel consumption and drivers. The analyses also quantify the benefits of using a heterogeneous fleet over a homogeneous one.     

Weather impact on containership routing in closed seas: A chance-constraint optimization approach

Weather conditions have a strong effect on the operation of vessels and unavoidably influence total time at sea and associated transportation costs. The velocity and direction of the wind in particular may considerably affect travel speed of vessels and therefore the reliability of scheduled maritime services. This paper considers weather effects in containership routing; a stochastic model is developed for determining optimal routes for a homogeneous fleet performing pick-ups and deliveries of containers between a hub and several spoke ports, while incorporating travel time uncertainties attributed to the weather. The problem is originally formulated as a chance-constrained variant of the vehicle routing problem with simultaneous pick-ups and deliveries and time constraints and solved using a genetic algorithm. The model is implemented to a network of island ports of the Aegean Sea. Results on the application of algorithm reveal that a small fleet is sufficient enough to serve network’s islands, under the influence of minor delays. A sensitivity analysis based on alternative scenarios in the problem’s parameters, leads to encouraging conclusions with respect to the efficiency and robustness of the algorithm.     

Inter-city bus routing and timetable setting under stochastic demands

Vehicle fleet routing and timetable setting are essential to the enhancement of an inter-city bus carrier’s operating cost, profit, level of service and competitiveness in the market. In past research the average passenger demand has usually served as input in the production of the final fleet routes and timetables, meaning that stochastic disturbances arising from variations in daily passenger demand in actual operations are neglected. To incorporate the stochastic disturbances of daily passenger demands that occur in actual operations, in this research, we established a stochastic-demand scheduling model. We applied a simulation technique, coupled with link-based and path-based routing strategies, to develop two heuristic algorithms to solve the model. To evaluate the performance of the proposed model and the two solution algorithms, we developed an evaluation method. The test results, regarding a major Taiwan inter-city bus operation, were good, showing that the model and the solution algorithms could be useful in practice.     

Design framework of large-scale one-way electric vehicle sharing systems: A continuum approximation model

This paper proposes a Continuum Approximation (CA) model for design of a one-way Electrical Vehicle (EV) sharing system that serves a metropolitan area. This model determines the optimal EV sharing station locations and the corresponding EV fleet sizes to minimize the comprehensive system cost, including station construction investment, vehicle charging, transportation and vehicle balancing, under stochastic and dynamic trip demands. This is a very complex problem due to the NP-hard nature of location design, the large number of individual users, and the stochasticity and dynamics of generated trips. Further, the considerable charging time required by EVs distinguishes this problem from traditional car sharing problems where a vehicle is immediately available for pickup after being dropped at a station. We find that the CA approach can overcome these modeling challenges by decomposing the studied area into a number of small neighborhoods that each can be approximated by an Infinite Homogeneous Plane (IHP). We find that the system cost of an IHP is a unimodal function of the station service area size and can be efficiently solved in a sub-linear time by the bisection algorithm. Then integrating the solutions of all IHPs yields an approximate solution to the original heterogeneous area. With numerical experiments, we show that the CA solution is able to estimate the total system cost of the discrete counterpart solution efficiently with good accuracy, even for large-scale heterogeneous problems. This implies that the proposed CA approach is capable of providing a near-optimum solution to the comprehensive design of a practical large-scale EV sharing system. With this model, we also conduct sensitivity analysis to reveal insights into how cost components and system design vary with key parameter values. As far as the author’s knowledge, this study is the first work that addresses design of an EV sharing system considering both longer-term location and fleet size planning and daily vehicle operations. The proposed CA model also extends the CA methodology literature from traditional location problems with stationary demand, single-facility based service to EV sharing problems considering dynamic demands, OD trips, and nonlinear vehicle charging times.     

Developing green fleet management strategies: Repair/retrofit/replacement decisions under environmental regulation

The considerable cost of maintaining large fleets has generated interest in cost minimization strategies. With many related decisions, numerous constraints, and significant sources of uncertainty (e.g. vehicle breakdowns), fleet managers face complex dynamic optimization problems. Existing methodologies frequently make simplifying assumptions or fail to converge quickly for large problems. This paper presents an approximate dynamic programming approach for making vehicle purchase, resale, and retrofit decisions in a fleet setting with stochastic vehicle breakdowns. Value iteration is informed by dual variables from linear programs, as well as other bounds on vehicle shadow prices. Sample problems are based on a government fleet seeking to comply with emissions regulation. The model predicts the expected cost of compliance, the rules the fleet manager will use in deciding how to comply, and the regulation’s impact on the value of vehicles in the fleet. Stricter regulation lowers the value of some vehicle categories while raising the value of others. Such insights can help guide regulators, as well as the fleet managers they oversee. The methodologies developed could be applied more broadly to general multi-asset replacement problems, many of which have similar structures.     

Integrated airline planning: Robust update of scheduling and fleet balancing under demand uncertainty

The airline schedule planning problem is defined as the sequence of decisions that need to be made to obtain a fully operational flight schedule. Historically, the airline scheduling problem has been sequentially solved. However, there have already been many attempts in order to obtain airline schedules in an integrated way. But due to tractability issues it is nowadays impossible to determine a fully operative and optimal schedule with an integrated model which accounts for all the key airline related aspects such as competitive effects, stochastic demand figures and uncertain operating conditions. Airlines usually develop base schedules, which are obtained much time in advance to the day of operations and not accounting for all the related uncertainty. This paper proposes a mathematical model in order to update base schedules in terms of timetable and fleet assignments while considering stochastic demand figures and uncertain operating conditions, and where robust itineraries are introduced in order to ameliorate miss-connected passengers. The proposed model leads to a large-scale problem which is difficult to be solved. Therefore, a novel improved and accelerated Benders decomposition approach is proposed. The analytical work is supported with case studies involving the Spanish legacy airline, IBERIA. The presented approach shows that the number of miss-connected passengers may be reduced when robust planning is applied.     

A decomposition approach to determining fleet size and structure with network flow effects and demand uncertainty

This paper presents a new methodology to determine fleet size and structure for those airlines operating on hub‐and‐spoke networks. The methodology highlights the impact of stochastic traffic network flow effects on fleet planning process and is employed to construct an enhanced revenue model by incorporating the expected revenue optimization model into fleet planning process. The objective of the model is to find a feasible allocation of aircraft fleet types to route legs using minimum fleet purchasing cost, thus ensuring that the expected fleet profit is maximized subject to several critical resource constraints. By using a linear approximation to the total network revenue function, the fleet planning model with enhanced revenue modeling is decomposed into the nonlinear aspects of expected revenue optimization and the linear aspects of determining fleet size and structure by optimal allocation of aircraft fleet types to route legs. To illustrate this methodology and its economic benefits, an example consisting of 6 chosen aircraft fleet types, 12 route legs, and 57 path‐specific origin‐destination markets is presented and compared with the results found using revenue prorated fleet planning formulation. The results show that the fleet size and structure of the methodology proposed in this paper gain 211.4% improvement in fleet profit over the use of the revenue prorated fleet planning approach. In addition, comparison with the deterministic model reveals that the fleet size and structure of this proposed methodology are more adaptable to the fluctuations of passenger demands. Copyright © 2016 John Wiley & Sons, Ltd.     

A bi-objective approach to routing and scheduling maritime transportation of crude oil

Maritime transportation, the primary mode for intercontinental movement of crude oil, accounts for 1.7 billion tons annually – bulk of which are carried via a fleet of large crude oil tankers. Although spectacular episodes such as Exxon Valdez underline the significant risk and tremendous cost associated with marine shipments of hazardous materials, maritime literature has focused only on the cost-effective scheduling of these tankers. It is important that oil transport companies consider risk, since the insurance premiums is contingent on the expected claim. Hence through this work, we present a mixed-integer optimization program – with operating cost and transport risk objectives, which could be used to prepare routes and schedules for a heterogeneous fleet of crude oil tankers. The bi-objective model was tested on a number of problem instances of realistic size, which were further analyzed to conclude that the cheapest route may not necessarily yield the lowest insurance premiums, and that larger vessels should be used if risk is more important as it enables better exploitation of the risk structure.     

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.     

Short-term planning of liquefied natural gas deliveries

The ability of a supplier of liquefied natural gas (LNG) to deliver cargoes at desired times, while effectively managing a fleet of cryogenic vessels can significantly impact its profits. We investigate in this paper an LNG short-term delivery planning problem by considering mandatory cargoes as well as optional cargoes to select, along with the scheduling of a heterogeneous vessel fleet with controllable cruising speeds. Several technical constraints are accommodated including time windows, berth availability, bunkering restrictions, inventory, liquefaction terminal storage capacity, maximum waiting time, and planned maintenance restrictions. The objective is to maximize the net profit.We propose a mixed-integer programming formulation that includes a polynomial number of variables and constraints and accommodates all of the problem features. Also, we describe an optimization-based variable neighborhood search procedure that embeds the proposed compact formulation. To assess the quality of the generated solutions, we propose a second valid formulation with an exponential number of decision variables and we solve its linear programming relaxation using column generation. We provide the results of extensive computational results that were carried out on a set of large-scale set of realistic instances, with up to 62 vessels and 160 cargoes, provided by a major LNG producer. These results provide evidence that the proposed improvement procedure yields high-quality solutions.     

Robust supply vessel routing and scheduling

We solve the problem of tactical supply vessel planning arising in the upstream offshore petroleum logistics. Supply vessels deliver all the necessary materials and equipment to offshore installations from an onshore supply base according to a delivery schedule. The planning of supply vessels should be done so that their number is minimized and at the same time provide a reliable flow of supplies from the base. The execution of a weekly sailing plan is affected by weather conditions, especially in winter time. Harsh weather conditions increase the number of vessels required to perform the operations as well as the service times at the installations, and thus disrupt the schedule, leading to additional costs and reduced service level. We present a methodology for robust supply vessel planning enabling a trade-off analysis to be made between the schedules’ service level and vessels’ cost. The methodology involves the generation of multiple vessel schedules with different level of robustness using an adaptive large neighbourhood search metaheuristic and a subsequent discrete event simulation procedure for the assessment of the service level. To control the level of robustness we developed a concept of slacks and incorporated it into the metaheuristic algorithm.     

Free-floating bike sharing: Solving real-life large-scale static rebalancing problems

Free-floating bike sharing (FFBS) is an innovative bike sharing model. FFBS saves on start-up cost, in comparison to station-based bike sharing (SBBS), by avoiding construction of expensive docking stations and kiosk machines. FFBS prevents bike theft and offers significant opportunities for smart management by tracking bikes in real-time with built-in GPS. However, like SBBS, the success of FFBS depends on the efficiency of its rebalancing operations to serve the maximal demand as possible.Bicycle rebalancing refers to the reestablishment of the number of bikes at sites to desired quantities by using a fleet of vehicles transporting the bicycles. Static rebalancing for SBBS is a challenging combinatorial optimization problem. FFBS takes it a step further, with an increase in the scale of the problem. This article is the first effort in a series of studies of FFBS planning and management, tackling static rebalancing with single and multiple vehicles. We present a Novel Mixed Integer Linear Program for solving the Static Complete Rebalancing Problem. The proposed formulation, can not only handle single as well as multiple vehicles, but also allows for multiple visits to a node by the same vehicle. We present a hybrid nested large neighborhood search with variable neighborhood descent algorithm, which is both effective and efficient in solving static complete rebalancing problems for large-scale bike sharing programs.Computational experiments were carried out on the 1 Commodity Pickup and Delivery Traveling Salesman Problem (1-PDTSP) instances used previously in the literature and on three new sets of instances, two (one real-life and one general) based on Share-A-Bull Bikes (SABB) FFBS program recently launched at the Tampa campus of University of South Florida and the other based on Divvy SBBS in Chicago. Computational experiments on the 1-PDTSP instances demonstrate that the proposed algorithm outperforms a tabu search algorithm and is highly competitive with exact algorithms previously reported in the literature for solving static rebalancing problems in SBSS. Computational experiments on the SABB and Divvy instances, demonstrate that the proposed algorithm is able to deal with the increase in scale of the static rebalancing problem pertaining to both FFBS and SBBS, while deriving high-quality solutions in a reasonable amount of CPU time.     

A fuzzy-stochastic optimization model for the intermodal fleet management problem of an international transportation company

ABSTRACT

In this paper, a fuzzy-stochastic optimization model is developed for an intermodal fleet management system of a large international transportation company. The proposed model integrates various strategic, tactical and operational level decisions simultaneously. Since real-life fleet planning problems may involve different types of uncertainty jointly such as randomness and fuzziness, a hybrid chance-constrained programming and fuzzy interactive resolution-based approach is employed. Therefore, stochastic import/export freight demand and fuzzy transit times, truck/trailer availabilities, the transport capacity of Ro-Ro vessels, bounds on block train services, etc. can also be taken into account concurrently. In addition to minimize overall transportation costs, optimization of total transit times and CO₂ emission values are also incorporated in order to provide sustainable fleet plans by maximizing customer satisfaction and environmental considerations. Computational results show that effective and efficient fleet plans can be produced by making use of the proposed optimization model.     

An optimal aircraft fleet management decision model under uncertainty

Decision planning for an efficient fleet management is crucial for airlines to ensure a profit while maintaining a good level of service. Fleet management involves acquisition and leasing of aircraft to meet travelers' demand. Accordingly, the methods used in modeling travelers' demand are crucial as they could affect the robustness and accuracy of the solutions. Compared with most of the existing studies that consider deterministic demand, this study proposes a new methodology to find optimal solutions for a fleet management decision model by considering stochastic demand. The proposed methodology comes in threefold. First, a five‐step modeling framework, which is incorporated with a stochastic demand index (SDI), is proposed to capture the occurrence of uncertain events that could affect the travelers' demand. Second, a probabilistic dynamic programming model is developed to optimize the fleet management model. Third, a probable phenomenon indicator is defined to capture the targeted level of service that could be achieved satisfactorily by the airlines under uncertainty. An illustrative case study is presented to evaluate the applicability of the proposed methodology. The results show that it is viable to provide optimal solutions for the aircraft fleet management model. Copyright © 2013 John Wiley & Sons, Ltd.     

A multiobjective model for maximizing fleet availability under the presence of flight and maintenance requirements

Every aircraft, military or civilian, must be grounded for maintenance after it has completed a certain number of flight hours since its last maintenance check. In this paper, we address the problem of deciding which available aircraft should fly and for how long, and which grounded aircraft should perform maintenance operations, in a group of aircraft that comprise a combat unit. The objective is to achieve maximum availability of the unit over the planning horizon. We develop a multiobjective optimization model for this problem, and we illustrate its application and solution on a real life instance drawn from the Hellenic Air Force. We also propose two heuristic approaches for solving large scale instances of the problem. We conclude with a discussion that gives insight into the behavior of the model and of the heuristics, based on the analysis of the results obtained.     

A hybrid optimization-simulation approach for robust weekly aircraft routing and retiming

We address the robust weekly aircraft routing and retiming problem, which requires determining weekly schedules for a heterogeneous fleet that maximizes the aircraft on-time performance, minimizes the total delay, and minimizes the number of delayed passengers. The fleet is required to serve a set of flights having known departure time windows while satisfying maintenance constraints. All flights are subject to random delays that may propagate through the network. We propose to solve this problem using a hybrid optimization-simulation approach based on a novel mixed-integer nonlinear programming model for the robust weekly aircraft maintenance routing problem. For this model, we provide an equivalent mixed-integer linear programming formulation that can be solved using a commercial solver. Furthermore, we describe a Monte-Carlo-based procedure for sequentially adjusting the flight departure times. We perform an extensive computational study using instances obtained from a major international airline, having up to 3387 flights and 164 aircraft, which demonstrates the efficacy of the proposed approach. Using the simulation software SimAir to assess the robustness of the solutions produced by our approach in comparison with that for the original solutions implemented by the airline, we found that on-time performance was improved by 9.8–16.0%, cumulative delay was reduced by 25.4–33.1%, and the number of delayed passengers was reduced by 8.2–51.6%.     

Sustainable cold supply chain management under demand uncertainty and carbon tax regulation

Increasing awareness of sustainability in supply chain management has prompted organizations and individuals to consider environmental impacts when managing supply chains. The issues concerning environmental impacts are significant in cold supply chains due to substantial carbon emissions from storage and distribution of temperature-sensitive product. This paper investigates the impact of carbon emissions arising from storage and transportation in the cold supply chain in the presence of carbon tax regulation, and under uncertain demand. A two-stage stochastic programming model is developed to determine optimal replenishment policies and transportation schedules to minimize both operational and emissions costs. A matheuristic algorithm based on the Iterated Local Search (ILS) algorithm and a mixed integer programming is developed to solve the problem in realistic sizes. The performance and robustness of the matheuristic algorithm are analyzed using test instances in various sizes. A real-world case study in Queensland, Australia is used to demonstrate the application of the model. The results highlight that higher emissions price does not always contribute to the efficiency of the cold supply chain system. Furthermore, the analyses indicate that using heterogeneous fleet including light duty and medium duty vehicles can lead to further cost saving and emissions reduction.