Stochastic Customer Research Articles

Bi-Objective Mixed Integer Nonlinear Programming Model for Low Carbon Location-Inventory-Routing Problem with Time Windows and Customer Satisfaction

In order to support a low-carbon economy and manage market competition, location–inventory–routing logistics management must play a crucial role to minimize carbon emissions while maximizing customer satisfaction. This paper proposes a bi-objective mixed-integer nonlinear programming model with time window constraints that satisfies the normal distribution of stochastic customer demand. The proposed model aims to find Pareto optimal solutions for total cost minimization and customer satisfaction maximization. An improved non-dominated sorting genetic algorithm II (IMNSGA-II) with an elite strategy is developed to solve the model. The model considers cost factors, ensuring that out-of-stock inventory is not allowed. Factors such as a carbon trading mechanism and random variables to address customer needs are also included. An entropy weight method is used to derive the total cost, which is comprised of fixed costs, transportation costs, inventory costs, punishment costs, and the weight of carbon emissions costs. The IMNSGA-II produces the Pareto optimal solution set, and an entropy–TOPSIS method is used to generate an objective ranking of the solution set for decision-makers. Additionally, a sensitivity analysis is performed to evaluate the influence of carbon pricing on carbon emissions and customer satisfaction.

Integrated operations strategies for shared and privately-owned autonomous vehicles: A deep reinforcement learning framework

The shared autonomous vehicle (SAV), combining shared mobility and vehicle automation, will play a pivotal role in urban transportation. Effectively matching SAVs to stochastic customer demand poses a significant challenge, particularly when addressing microscopic multi-AV coordination to prevent conflicts and congestion within a network. To tackle this issue, we propose a novel traffic control scheme called the Integrated Operation Framework for Order Matching and AV Coordination (I-OFOMAC). This scheme introduces a third-party coordinator responsible for integrating online order matching for the SAV platform and real-time AV coordination for the road manager. Our approach utilizes an offline deep reinforcement learning method to train a state value neural network, which facilitates strategic order matching. Additionally, a neural network approximating bisimulation metrics is trained to enhance exploration and accelerate learning. To achieve scalability in network-level AV coordination, we adopt a scheduled transportation scheme. The coordinator solves the I-OFOMAC during each decision epoch, optimizing order matching and AV coordination. The I-OFOMAC aims to balance the goals of minimizing AV travel delay and maximizing SAV service revenue. We conduct extensive simulation studies in the realistic Wangjing network to evaluate the proposed I-OFOMAC scheme. Compared to two-step benchmark frameworks that implement order matching and AV coordination sequentially, the I-OFOMAC achieves an average increase of 13.28% in platform revenue (ranging from 2% to 22.53%) and a 4.48% reduction in average PAV travel delay (ranging from −6.55% to 20.17%).

Balancing resources for dynamic vehicle routing with stochastic customer requests

We consider a service provider performing pre-planned service for initially known customers with a fleet of vehicles, e.g., parcel delivery. During execution, new dynamic service requests occur, e.g., for parcel pickup. The goal of the service provider is to serve as many dynamic requests as possible while ensuring service of all initial customers. The allocation of initial services impacts the potential of serving dynamic requests. An allocation aiming on a time-efficient initial routing leads to minimal overall workload regarding the initial solution but may congest some vehicles that are unable to serve additional requests along their routes. An even workload division is less efficient but grants all vehicles flexibility for additional services. In this paper, we investigate the balance between efficiency and flexibility. For the initial customers, we modify a routing algorithm to allow a shift between efficient initial routing and evenly balanced workloads. For effective dynamic decision making with respect to the dynamic requests, we present value function approximations with different feature sets capturing vehicle workload in different levels of detail. We show that sacrificing some initial routing efficiency in favor of a balanced vehicle workload is a key factor for a flexible integration of later customer requests that leads to an average improvement of 10.75%. Further, we show when explicitly depicting heterogeneity in the vehicle workload by features of the value function approximation provides benefits and that the best choice of features leads to an average improvement of 5.71% compared to the worst feature choice.

A hybrid ant colony optimization algorithm to solve a transport problem with stochastic customer demands and electric vehicles of limited load capacity

A hybrid ant colony optimization algorithm to solve a transport problem with stochastic customer demands and electric vehicles of limited load capacity

GRASP‐based request allocation and MDP‐based vehicle routing in home pick‐up service with service continuity consideration

AbstractService continuity (SC) plays an important role in service industry. In this paper, a daily home parcel pick‐up scheduling and routing problem is studied with SC consideration. In this context, a fixed group of couriers is assigned to provide services exclusively within a specific region. Each day, customers within this region either have pre‐scheduled services in advance or stochastically make service requests during the couriers' shifts. Pre‐scheduled service request can be serviced by any courier serving the region, while stochastic service request can only be serviced by the courier most familiar with the corresponding customer. Consequently, the study problem is divided into two distinct sub‐problems: (i) the allocation of pre‐scheduled requests to couriers before their tours start and (ii) routing each courier independently to service both its allocated customers and its potential stochastic customers. The sub‐problem (ii) is formulated as a Markov decision process and an existing dynamic programming method is applied to solve it exactly. For the sub‐problem (i), Greedy Randomized Adaptive Search Procedure‐based meta‐heuristics is proposed. Finally, these meta‐heuristics are evaluated through computational experiments, yielding valuable application insights.

Request acceptance with overbooking in dynamic and collaborative vehicle routing

We consider the problem setting of a less-than-truckload carrier serving stochastic customer requests. Each request must be answered dynamically by accepting or rejecting it immediately. On the next day, accepted requests are served in routes using a set of vehicles with limited load capacity and route duration. After the request acceptance phase and before the fulfillment, multiple carriers participate in a combinatorial auction to exchange requests. An auctioneer allocates the bundles of requests to carriers according to their bids in a cost-minimizing way and distributes the auction profits. This type of horizontal collaboration provides cost savings and contributes to reducing negative impacts of transportation. We describe the carrier’s optimization problem of maximizing profit as a Markov decision process that comprises the sequential decisions in all phases, i.e., request acceptance, request selection for the auction, bidding, and routing. For solving a version of the vehicle routing problem with pickups and deliveries, heuristic approaches are proposed that achieve efficient and balanced routes. We design overbooking policies for strategically accepting more requests bearing in mind the options provided by the auction. Computational results show that – by trading requests in an auction – carriers can accept more requests than they could serve on their own. The carriers’ request acceptance decisions impact their individual profits and the overall collaboration savings. The largest benefits can be achieved with an overbooking policy that prescribes which requests should be accepted by all carriers, based on the locations of both the request and the carriers’ depots.

A branch-and-regret algorithm for the same-day delivery problem

We study a dynamic vehicle routing problem where stochastic customers request urgent deliveries characterized by restricted time windows. The aim is to use a fleet of vehicles to maximize the number of served requests and minimize the traveled distance. The problem is known in the literature as the same-day delivery problem, and it is of high importance because it models a number of real-world applications, including the delivery of online purchases. We solve the same-day delivery problem by proposing a novel branch-and-regret algorithm in which sampled scenarios are used to anticipate future events and an adaptive large neighborhood search is iteratively invoked to optimize routing plans. The branch-and-regret is equipped with four innovation elements: a new way to model the subproblem, a new policy to generate scenarios, new consensus functions, and a new branching scheme Extensive computational experiments on a large variety of instances prove the outstanding performance of the branch-and-regret, also in comparison with recent literature, in terms of served requests, traveled distance, and computational effort.

The Traveling Salesman Problem with Stochastic and Correlated Customers

It is well-known that the cost of parcel delivery can be reduced by designing routes that take into account the uncertainty surrounding customers’ presences. Thus far, routing problems with stochastic customer presences have relied on the assumption that all customer presences are independent from each other. However, the notion that demographic factors retain predictive power for parcel-delivery efficiency suggests that shared characteristics can be exploited to map dependencies between customer presences. This paper introduces the correlated probabilistic traveling salesman problem (CPTSP). The CPTSP generalizes the traveling salesman problem with stochastic customer presences, also known as the probabilistic traveling salesman problem (PTSP), to account for potential correlations between customer presences. I propose a generic and flexible model formulation for the CPTSP using copulas that maintains computational and mathematical tractability in high-dimensional settings. I also present several adaptations of existing exact and heuristic frameworks to solve the CPTSP effectively. Computational experiments on real-world parcel-delivery data reveal that correlations between stochastic customer presences do not always affect route decisions, but could have a considerable impact on route cost estimates. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2022.0005 .

The sustainable hybrid truck-drone delivery model with stochastic customer existence

Drone delivery is a fast delivery mode that has gained tremendous attention from academia and various companies in recent years. However, due to limited battery and payload capacities which may reduce the system's efficiency, it is better to coordinate ground vehicles and drones to take advantage of both trucks' large capacity and the drone's high speed. As a restriction for realistic parcel delivery systems, customer presence is only sometimes deterministic. For instance, a customer makes an order from an e-retailer, but due to various probable reasons, he cannot be present at home to get service. In this paper, we have introduced a sustainable hybrid truck-drone delivery model with stochastic customer presence. We have modeled the system with the Markov chain and proposed a linear mathematical model. This work processes with a heuristic and a Branch-and-Bound algorithm. Also, we have carried out numerous computational experiments to evaluate the proposed solution methods' performance, where the results show the efficiency of the proposed algorithms. Finally, we performed a detailed sensitivity analysis on a case study and studied various aspects of the problem. The results highlight that truck and drone coordination reduces completion time, operational costs, truck emissions, and social penalties.

A hybrid large-neighborhood search for a truck and drone delivery system with stochastic customer existence and time windows

In recent years, e-commerce has become increasingly popular, and consumers expect quick and affordable delivery, placing additional pressure on city logistics activities. An innovative approach is proposed to coordinate ground vehicles and drones for delivery services, which has gained tremendous attention from academia and logistic service providers. This paper introduces a variant of this problem: the two-echelon truck and drone routing problem, characterized by stochastic demand existence and soft time windows. A Markov chain is used to model the problem, and a linear mathematical model is presented. This work employs a hybrid large-neighborhood search approach. Numerous computational experiments are conducted to evaluate the performance of the proposed solution method, and the results demonstrate its efficacy.

An Adaptive Large Neighborhood Search heuristic for last-mile deliveries under stochastic customer availability and multiple visits

Attended Home Delivery, where customer attendance at home is required, is an essential last-mile delivery challenge, e.g., for valuable, perishable, or oversized items. Logistics service providers are often faced no-show customers. In this paper, we consider the delivery problem in which customers can be revisited on the same day by a courier in the case of a failed first delivery attempt. Specifically, customer presence uncertainty is considered in a two-stage stochastic program, where penalties are introduced as recourse actions for failed deliveries. We build on the notion of a customer availability profile defined as a profile containing historical time-varying probability information of successful deliveries. We tackle this stochastic program by developing an efficient parallelized Adaptive Large Neighborhood Search algorithm. Our results show that by achieving a right balance between increasing the hit rate and reducing travel cost, logistics service providers can realize costs savings as high as 32% if they plan for second visits on the same day.

An Adaptive Tabu Search Algorithm for Solving the Two-Dimensional Loading Constrained Vehicle Routing Problem with Stochastic Customers

In practical logistic distributions, uncertainties may exist in each distribution process, and sometimes suppliers have to take undesirable measures to deal with the subsequent schedule variances. In light of the uncertainty of customers in logistics distribution and the widely applied two-dimensional loading patterns in transportation, we propose and formulate a two-dimensional loading-constrained vehicle routing problem with stochastic customers (2L-VRPSC), where each customer has a known probability of presence and customers’ demands are a set of non-stackable items. A stochastic modeling platform of 2L-VRPSC is established based on a Monte Carlo simulation and scenario analysis to minimize the expected total transportation cost. To achieve this, an enhanced adaptive tabu search (EATS) algorithm incorporating the multi-order bottom-fill-skyline (MOBFS) packing heuristic is proposed, where the EATS algorithm searches for the optimal routing combination and the MOBFS checks the feasibility of each route and guides the EATS to search for feasible solutions. The widely used two-dimensional loading-constrained vehicle routing problem (2L-VRP) benchmarks under different loading configurations considering items’ sequential and rotation constraints are applied for experiments, which demonstrates the comparable efficiency of the proposed EATS-MOBFS for solving 2L-VRP. Furthermore, the results and analysis of experiments based on the new 2L-VRPSC instances verify the versatility of the proposed solving approach, which is capable of providing more practical solutions to some real-life scenarios with customers’ uncertain information.

Stochastic optimization of multi-capacitated vehicle routing problem with pickup and delivery using saving matrix algorithm

The Multi-Capacitated Problem is an optimization problem. To reduce the overall distance, the optimization problem seeks out vehicle routes that connect every customer to a storage facility. This article uses a saving matrix approach to propose an extended Vehicle Routing Problem that considers a stochastic environment and multiple capacitors. Stochastic customers are an essential element of the problem. A computational analysis also supports the suggested approach to obtain the best route.

A Chance-Constrained Two-Echelon Vehicle Routing Problem with Stochastic Demands

Two-echelon distribution systems are often considered in city logistics to maintain economies of scale and satisfy the emission zone requirements in the cities. In this work, we formulate the two-echelon vehicle routing problem with stochastic demands as a chance-constrained stochastic optimization problem, where the total demand of the customers in each second-echelon route should fit within the second-echelon vehicle capacity with a high probability. We propose two efficient solution procedures based on column generation. Key to the efficiency of these procedures is the underlying labeling algorithm to generate new columns. We propose a novel labeling algorithm based on simultaneous construction of second-echelon routes and a labeling algorithm that builds second-echelon routes sequentially. To further enhance the performance of the solution procedure, we use statistical inference tests to ensure that the chance constraints are met. We reduce the number of customer combinations for which the chance constraint needs to be verified by imposing feasibility bounds on the stochastic customer demands. With these bounds, the runtimes of the labeling algorithms are reduced significantly. The novel labeling algorithm, statistical inference, and feasibility bounds can also be applied to dependent, correlated, and data-driven (scenario-based) demand distributions. Finally, we show the value of the stochastic formulation in terms of improved solution cost and guaranteed feasibility of second-echelon routes. Funding: This work was funded by the Dutch Research Council (NWO) DAREFUL project [Grant 629.002.211] and was carried out on the Dutch national e-infrastructure with the support of SURF Cooperative. Supplemental Material: The online appendices are available at https://doi.org/10.1287/trsc.2022.1162 .

Multiperiod integrated spare parts and tour planning for on-site maintenance activities with stochastic repair requests

Motivated by the problem facing many home-attended maintenance service providers, this paper considers the joint optimization problem of spare parts planning and the scheduling of a single technician to visit geographically distributed customers for on-site maintenance activities. We present and formulate the problem using stochastic mixed-integer programs, encompassing many important real-life characteristics, such as stochastic spare parts demand, stochastic customer requests, and return visits. We also propose an anticipatory solution method, which uses a look-ahead procedure to integrate stochastic information into the planning process and compare this with two myopic planning approaches. With a detailed numerical study, we show that anticipation can lead to cost reductions and service level improvements, especially when customers are sparely distributed. Furthermore, our results reveal that the repair kit and technician tour integrated planning helps to substantially reduce penalty costs for late service. We also provide insights into the value of having perfect information about spare part demand and future request locations.

Resource-controlled stochastic customer order scheduling via particle swarm optimization with bound information

PurposeCycle time reduction is important for order fulling process but often subject to resource constraints. This study considers an unrelated parallel machine environment where orders with random demands arrive dynamically. Processing speeds are controlled by resource allocation and subject to diminishing marginal returns. The objective is to minimize long-run expected order cycle time via order schedule and resource allocation decisions.Design/methodology/approachA stochastic optimization algorithm named CAP is proposed based on particle swarm optimization framework. It takes advantage of derived bound information to improve local search efficiency. Parameter impacts including demand variance, product type number, machine speed and resource coefficient are also analyzed through theoretic studies. The algorithm is evaluated and benchmarked with four well-known algorithms via extensive numerical experiments.FindingsFirst, cycle time can be significantly improved when demand randomness is reduced via better forecasting. Second, achieving processing balance should be of top priority when considering resource allocation. Third, given marginal returns on resource consumption, it is advisable to allocate more resources to resource-sensitive machines.Originality/valueA novel PSO-based optimization algorithm is proposed to jointly optimize order schedule and resource allocation decisions in a dynamic environment with random demands and stochastic arrivals. A general quadratic resource consumption function is adopted to better capture diminishing marginal returns.

Solving large-scale dynamic vehicle routing problems with stochastic requests

Dynamic vehicle routing problems (DVRPs) arise in several applications such as technician routing, meal delivery, and parcel shipping. We consider the DVRP with stochastic customer requests (DVRPSR), in which vehicles must be routed dynamically with the goal of maximizing the number of served requests. We model the DVRPSR as a multi-stage optimization problem, where the first-stage decision defines route plans for serving scheduled requests. Our main contributions are knapsack-based linear models to approximate accurately the expected reward-to-go, measured as the number of accepted requests, at any state of the stochastic system. These approximations are based on representing each vehicle as a knapsack with a capacity given by the remaining service time available along the vehicle’s route. We combine these approximations with optimal acceptance and assignment decision rules and derive efficient and high-performing online scheduling policies. We further leverage good predictions of the expected reward-to-go to design initial route plans that facilitate serving dynamic requests. Computational experiments on very large instances based on a real street network demonstrate the effectiveness of the proposed methods in prescribing high-quality offline route plans and online scheduling decisions.

Backup Agreement as a Coordination Mechanism in a Decentralized Fruit Chain in a Developing Country

This paper aims to analyze the impacts of a backup agreement contract on the performance of a small agricultural producers’ citrus supply chain. A backup agreement contract, which ensures for each echelon that a quantity of products will be bought independently of real demand, is proposed to coordinate a three-echelon supply chain, aimed at improving income. After presenting an overview of the literature that shows various coordination mechanisms but no backup agreement proposals for supply chain coordination, this paper develops a decentralized three-echelon supply chain facing stochastic customer demand and includes the backup agreement as a coordination mechanism to guarantee a balanced relationship between the chain members. The model is tested in a real case study in Colombia, and a sensitivity analysis is provided. Results show that a backup agreement contract coordinates the small agricultural producers’ supply chain and improves income for each echelon, especially for the small producer. However, the economic mechanism complexity can limit coordination among echelons, mainly because of a lack of trust and consolidated supply capacity from small farmers. The foregoing requires the development of an associative structure by small producers, which is proposed as future research work.

Instant customer base analysis in the financial services sector

This study empirically validates the performance of stochastic customer base models in noncontract settings where the time at which a customer becomes dormant is not observable. We collaborate with a nationwide financial services company in Korea and analyze the complete transaction data of 373,031 retail customers from 2015 to 2018. We implement the following four buy-'til-you-die (BTYD) models: a) the original Pareto/NBD model, b) the Pareto/GGG model, c) the BG/CNBD-k model, and d) the MBG/CNBD-k model. The four BTYD models perform well in classifying active customers, with an area under the receiver operating characteristic curve of 0.82 ∼ 0.86 for each of the one-month, two-month, …, and twelve-month forecasting horizons. The results demonstrate that the BTYD framework can be used for customer base analysis as an instant heuristic approach that can complement existing customer relationship management tools.

Revenue Management of Group Service Considering Different Quality Levels and Stochastic Customer Patience

We consider a service that provides different quality levels to customers who are served in groups (referred to as “group service” (GS)). We consider stochastic customer patience and build a multitype service model to maximize service profit. First, we consider a fixed number of service personnel and decompose the model into several subproblems. We then transform the model into a service personnel allocation problem that can be efficiently solved. Furthermore, we use the water-filling theory, together with a dichotomy approach, to design the numerical algorithm to conduct a numerical test based on actual data. The main contributions of this study are as follows. First, we provide the service provider with a service capacity allocation mechanism that can determine the optimal choice of service quality levels, number of service groups of different quality levels, time length of the service registration period, and service prices. Second, we find that under scarce service capacity, the single-type service can be more profitable than the multitype service, and low-quality services have higher marginal profits than high-quality services. However, when service capacity increases to a certain level, the multitype service can be more profitable than the single-type service. Third, we construct a service capacity decision mechanism and demonstrate the influence of service quality on the total number of service personnel and service groups. The conclusions are potentially useful to GS service providers to effectively make better managerial decisions and improve service profits.