Data‐Driven Robust Optimization for Solving the Heterogeneous Vehicle Routing Problem with Customer Demand Uncertainty

ABSTRACTMost of the research on vehicle routing problems has focused on the operational or the tactical level. However, any decision made on a strategic level will affect the lower level decisions. One type of strategic decision that has been considered in the literature is to compose an appropriate fleet of different vehicles to perform transportation tasks, which yields the fleet size and mix vehicle routing problem (FSMVRP). This work defines a new variant of the FSMVRP where the customer demands may vary over a set of periods, for example by having different demands on each day of the week. The objective is to find the best fleet composition that can be used to repeatedly fulfil the customer demands, as well as the best routing with that fleet for each of the different periods in the planning horizon. Simple heuristics incorporating a tabu search are implemented to find the fleet composition. Computational results are reported on instances created from a set of standard FSMVRP test instances.

The vehicle routing problem is a traditional combinatorial problem with practical relevance for a wide range of industries. In the literature, several specificities have been tackled by dedicated methods in order to better reflect real-world situations. Following this trend, this article addresses the fleet size and mix vehicle routing problem with time windows in which companies hire a third-party logistics company. The shipping charges considered in this work are calculated using step cost functions, in which values are determined according to the type of vehicle and the total distance traveled, with fixed values for predefined distance ranges. A mixed integer linear programming model is introduced and two sequential insertion heuristics are proposed. The introduced methods are examined through a computational comparative analysis in small-sized instances with known optimal solution, 168 benchmark instances from the literature, and 3 instances based on a real-world problem from the civil construction industry. The numerical experiments show that the proposed methods are efficient and show good performance in different scenarios.

This paper introduces the Fleet Size and Mix Vehicle Routing Problem with Synchronized Visits (FSM-VRPS), an extension of the Vehicle Routing Problem with Synchronization (VRPS), where a mixed fleet composed of electric and conventional bikes, and passenger cars having different acquisition costs are considered. The problem consists of planning a set of different vehicle routes to serve a set of clients who may require more than one visit by different healthcare specialists, and some of these visits should be synchronized. Moreover, each client must be visited within a specified time window. In addition, the problem uses bikes to reduce Carbon Dioxide (CO2) emission for environmentally cleaner routing operations. This problem has many real-life applications, such as the scheduling of visits for homecare givers in the healthcare sector. We present a mixed integer linear-programming formulation and develop a Multi-Start Adaptive Large Neighborhood Search with Threshold Accepting algorithm. The results showed that our algorithm is highly effective on the FSM-VRPS, as well as on the heterogeneous VRPS. We also demonstrate the advantage of adopting different types of vehicles in terms of reducing the number of vehicles and costs. The analysis of the results also indicated that the new components added to the standard Adaptive Large Neighborhood Search algorithm enhanced intensification and diversification mechanisms during the search process.

In the well‐known vehicle routing problem (VRP), a set of identical vehicles located at a central depot is to be optimally routed to supply customers with known demands subject to vehicle capacity constraints. An important variant of the VRP arises when a mixed fleet of vehicles, characterized by different capacities and costs, is available for distribution activities. The problem is known as fleet size and mix VRP with fixed costs FSMF and has several practical applications. In this article, we present a new mixed integer programming formulation for FSMF based on a two‐commodity network flow approach. New valid inequalities are proposed to strengthen the linear programming relaxation of the mathematical formulation. The effectiveness of the proposed cuts is extensively tested on benchmark instances. © 2009 Wiley Periodicals, Inc. NETWORKS, 2009

Logistics activity is both a major energy consumption user and an important CO₂ emission source. As logistics service activity rises in the city, it is crucial to improve the efficiency of fuel usage, as well as decrease the CO₂ emission of unit shipment using vehicle routing optimization. Based on the analysis of the characteristics of energy consumption and emission factors of CO₂ in the vehicle routing problem with multiple vehicles, this paper investigates the problem of fleet size and mixed vehicle routing problem considering CO₂ emissions cost (Green Fleet Size and Mixed Vehicle Routing Problem, G-FSMVRP ). A heuristic algorithm based on a genetic algorithm is given. Finally, a numerical simulation example is given to illustrate the optimization model and its algorithm. The findings show that: (1) the shortest route does not necessarily produce the least energy consumption; (2) compared with the traditional vehicle routing (based on shortest path), vehicle routing considering CO₂ emissions has a lower total cost, but longer distance travelled; and, (3) the genetic algorithm is an effective algorithm to solve the green vehicle routing problem.

A robust optimization framework for energy management of CCHP users with integrated demand response in electricity market

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second objective is to minimize the shortage of products for all retailers. In order to get closer to a real-world situation, the uncertainty in the demand of retailers is applied using fuzzy numbers. Additionally, the volume of products is applied using robust parameters, because the possible value of this parameter is not distinct and belongs to a bounded uncertainty set. The fuzzy-robust counterpart model may be larger than the deterministic form or the uncertain model with one approach and it has with further complexity; however, it provides a better efficient solution for this problem. The proposed fuzzy approach is used to solve the bi-objective mixed-integer linear problem to find the most preferred solution. Moreover, it is impossible to improve one of the objective functions without considering deterioration in the other objective functions. In order to show the conflict between two objective functions in an excellent fashion, a Pareto-optimal solution with the e-constraint method is obtained. Some numerical test problems are used to demonstrate the efficiency and validity of the presented model.

Chapter 4 - Data-driven robust stochastic optimization for power systems operations

This paper considers facility location, inventory pre‐positioning and vehicle routing as strategic and operational decisions corresponding to preparedness and response phases in disaster relief logistics planning. For balancing surpluses and shortages, an effective lateral transshipment strategy is proposed to evenly distribute the relief resources between warehouses after the disaster occurs. To handle ambiguity in the probability distribution of demand, we develop a risk‐averse two‐stage distributionally robust optimization (DRO) model for the disaster relief logistics planning problem, which specifies the worst‐case mean‐conditional value‐at‐risk (CVaR) as a risk measure. For computationally tractability, we transform the robust counterpart into its equivalent linear mixed‐integer programming model under the discrepancy‐based ambiguity set centered at the nominal (empirical) distributions on the observed demand from the historical data. We verify the effectiveness of the proposed DRO model and the value of lateral transshipment strategy by an illustrative small‐scale example. The numerical results show that the proposed DRO model has advantage on avoiding over‐conservative solutions compared to the classic robust optimization model. We also illustrate the applicability of the proposed DRO model by a real‐world case study of hurricanes in the southeastern United States. The computational results demonstrate that the proposed DRO model has superior out‐of‐sample performance and can mitigate the adverse effects of Optimizers' Curse compared with the traditional stochastic programming model.

This study presents a parameter coordination and robust optimization approach based on knowledge network modeling. The method allows multidisciplinary designer to synthetically coordinate and optimize parameter considering multidisciplinary knowledge. First, a knowledge network model is established, including design knowledge from assembly, manufacture, performance, and simulation. Second, the parameter coordination method is presented to solve the knowledge network model, monitor the potential conflicts due to engineering changes, and obtain the consistency solution space corresponding to the given knowledge. Finally, the robust parameter optimization model is established, and genetic arithmetic is used to obtain the robust optimization parameter. A design instance is introduced to show the validity of this method.

The economic and low‐carbon operation strategy of multi‐energy microgrids (MEM) has become an important research topic in smart grids. The operation of MEM is affected by uncertain factors from renewable energy and internal load. To handle uncertainties from both source and load sides, the authors propose a novel worst‐case‐and‐probability uncertainty sets and a novel worst‐expectation min‐max‐max‐min two‐stage four‐level robust optimisation (RO) model considering stepped carbon trading for MEM. This four‐level RO model is a more generalised model compared with the traditional two‐stage RO and distributionally robust optimisation based models. First, the unsolvable original four‐level model is decoupled into a master problem and a sub‐problem (SP). Second, Karush–Kuhn–Tucker condition is applied to convert SP into a solvable problem. Third, column and constraint generation (C&CG) algorithm is employed to solve the reformulated four‐level RO. Finally, the effectiveness of the proposed model and solution method is verified by case studies. The results indicate that the convergence behaviour of this solution method is excellent. The MEM operator can select appropriate robustness factors and comprehensive norms to control its conservatism level. Besides, MEM could reduce carbon emissions by participating in carbon trading and installing carbon capture devices.

In the introductory section of this paper there is a view of several types of stochastic vehicle routing problems. In the second section of the paper the vehicle routing problem with stochastic demands is described. The following modifications to the vehicle routing problem are required: Customers demand is a random variable with a known probability distribution. Routes must be designed before the actual demands become known.The presence of nonlinear constraints, caused by random demands, can complicate the solution. Under the specific presumptions it is possible to transfer a nonlinear constraint to a linear form. This transformation enables to use the known algorithms of the deterministic vehicle routing problem for solution of the stochastic vehicle routing problem.

A new heuristic for the fleet size and mix vehicle routing problem

As one of the most popular supply chain management problems, the Vehicle Routing Problem (VRP) has been thoroughly studied in the last decades, most of these studies focus on deterministic problem where the customer demands are known in advance. But the Vehicle Routing Problem with Stochastic Demands (VRPSD) has not received enough consideration. In the VRPSD, the vehicle does not know the customer demands until the vehicle arrive to them. This paper use a hybrid algorithm for solving VRPSD, the hybrid algorithm based on Particle Swarm Optimization (PSO) Algorithm, combines a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm, and Variable Neighborhood Search (VNS) algorithm. A real number encoding method is designed to build a suitable mapping between solutions of problem and particles in PSO. A number of computational studies, along with comparisons with other existing algorithms, showed that the proposed hybrid algorithm is a feasible and effective approach for Vehicle Routing Problem with Stochastic Demands.

A parallel implementation of the TSSP + 1 decomposition for the capacity-constrained vehicle routing problem