A multi-visit flexible-docking vehicle routing problem with drones for simultaneous pickup and delivery services

This study investigates a multi-visit flexible-docking vehicle routing problem that uses a truck and drone fleet to fulfill pickup and delivery requests in rural areas. In this collaborative truck–drone system, each drone may serve multiple customers per trip (multi-visit services), dock to the same or different truck from where it launched (flexible docking), and perform simultaneous pickup and delivery. These characteristics complicate the temporal, spatial, and loading synchronization for trucks and drones, making the decisions of order allocation and vehicle routing highly interdependent and intractable. This problem is formulated as a mixed-integer linear programming model and solved by a tailored adaptive large neighborhood search metaheuristic. Numerical experiments are conducted on sparse rural networks to demonstrate the efficiency of the proposed method. We observe that the proposed truck–drone system shows an average cost saving of 34% compared to the truck-only case. Moreover, deep insights into the impacts of multi-visit services, flexible docking, and simultaneous pickup and delivery on the performance of the truck–drone system are discussed.     

An adaptive guidance meta-heuristic for the vehicle routing problem with splits and clustered backhauls

This paper presents the case study of an Italian carrier, Grendi Trasporti Marittimi, which provides freight transportation services by trucks and containers. Its trucks deliver container loads from a port to import customers and collect container loads from export customers to the same port. In this case study, all import customers in a route must be serviced before all export customers, each customer can be visited more than once and containers are never unloaded or reloaded from the truck chassis along any route. We model the problem using an Integer Linear Programming formulation and propose an Adaptive Guidance metaheuristic. Our extensive computational experiments show that the adaptive guidance algorithm is capable of determining good-quality solutions in many instances of practical or potential interest for the carrier within 10?min of computing time, whereas the mathematical formulation often fails to provide the first feasible solution within 3?h of computing time.     

General solutions to the single vehicle routing problem with pickups and deliveries

The single vehicle routing problem with pickups and deliveries (SVRPPD) is defined on a graph in which pickup and delivery demands are associated with the customer vertices. The problem consists of designing a least cost route for a vehicle of capacity Q. Each customer is allowed to be visited once for a combined pickup and delivery, or twice if these two operations are performed separately. This article proposes a mixed integer linear programming model for the SVRPPD. It introduces the concept of general solution which encompasses known solution shapes such as Hamiltonian, double-path and lasso. Classical construction and improvement heuristics, as well as a tabu search heuristic, are developed and tested over several instances. Computational results show that the best solutions generated by the heuristics are frequently non-Hamiltonian and may contain up to two customers visited twice.     

Expected Distances in Distribution Problems

In many problems in distribution management it is necessary to take account of the expected distances that result from dispatching vehicles to meet customer demand. For example, in mathematical models for determining the optimal location of depots, the sum of radial distances (between customers and the depot), or the sum of the weighted distances, is used as a measure of the delivery "costs". Since actual delivery operations from the depot usually consist of truck-routes with each truck delivering to more than one customer at a time, it is important to know to what extent the above simplification is valid, namely to find a relationship between the actual route-distances and the sum of the radial distances.This paper makes use of an algorithm which plans optimal or near optimal routes to estimate this relationship by solving a large number of randomly generated problems. The discrepancies between the two methods are shown to be significant under certain circumstances.     

智能制造环境下的备件生产与运输协同调度问题研究

智能制造和即时配送环境下的备件生产与运输协同调度问题是目前国内研究的一大热点,这是因为备件供应链响应速度已成为当前备件制造企业赢得客户的关键因素。为了提高客户满意度,尽可能缩短从客户下达定制化生产订单到订单配送完成的时间,本文建立了以所有客户总等待时间最短为目标的混合整数规划模型和集合覆盖模型,推导了最优解性质,并设计改进的分支定价算法求得最优解。通过将小规模算例结果与CPLEX进行对比,验证了模型和算法的有效性。多组算例测试结果表明,所提出的模型和算法可以有效提升智能制造环境下的备件供应链运作效率。     

A zero-inventory production and distribution problem with a fixed customer sequence

In this paper, we study the zero-inventory production and distribution problem with a single transporter and a fixed sequence of customers. The production facility has a limited production rate, and the delivery truck has non-negligible traveling times between locations. The order in which customers may receive deliveries is fixed. Each customer requests a delivery quantity and a time window for receiving the delivery. The lifespan of the product starts as soon as the production for a customer’s order is finished, which makes the product expire in a constant time. Since the production facility and the shipping truck are limited resources, not all the customers may receive the delivery within their specified time windows and/or within product lifespan. The problem is then to choose a subset of customers from the given sequence to receive the deliveries to maximize the total demand satisfied, without violating the product lifespan, the production/distribution capacity, and the delivery time window constraints. We analyze several fundamental properties of the problem and show that these properties can lead to a fast branch and bound search procedure for practical problems. A heuristic lower bound on the optimal solution is developed to accelerate the search. Empirical studies on the computational effort required by the proposed search procedure comparing to that required by CPLEX on randomly generated test cases are reported.     

A model for rational abandonments from invisible queues

We propose a model for abandonments from a queue, due to excessive wait, assuming that waiting customers act rationally but without being able to observe the queue length. Customers are allowed to be heterogeneous in their preferences and consequent behavior. Our goal is to characterize customers' patience via more basic primitives, specifically waiting costs and service benefits: these two are optimally balanced by waiting customers, based on their individual cost parameters and anticipated waiting time. The waiting time distribution and patience profile then emerge as an equilibrium point of the system. The problem formulation is motivated by teleservices, prevalently telephone- and Internet-based. In such services, customers and servers are remote and queues are typically associated with the servers, hence queues are invisible to waiting customers. Our base model is the M/M/m queue, where it is shown that a unique equilibrium exists, in which rational abandonments can occur only upon arrival (zero or infinite patience for each customer). As such a behavior fails to capture the essence of abandonments, the base model is modified to account for unusual congestion or failure conditions. This indeed facilitates abandonments in finite time, leading to a nontrivial, customer dependent patience profile. Our analysis shows, quite surprisingly, that the equilibrium is unique in this case as well, and amenable to explicit calculation. This revised version was published online in June 2006 with corrections to the Cover Date.     

A branch-and-cut algorithm for the plant-cycle location problem

The Plant-Cycle Location Problem (PCLP) is defined on a graph G=(I∪J, E), where I is the set of customers and J is the set of plants. Each customer must be served by one plant, and the plant must be opened to serve customers. The number of customers that a plant can serve is limited. There is a cost of opening a plant, and of serving a customer from an open plant. All customers served by a plant are in a cycle containing the plant, and there is a routing cost associated to each edge of the cycle. The PCLP consists in determining which plants to open, the assignment of customers to plants, and the cycles containing each open plant and its customers, minimizing the total cost. It is an NP-hard optimization problem arising in routing and telecommunications. In this article, the PCLP is formulated as an integer linear program, a branch-and-cut algorithm is developed, and computational results on real-world data and randomly generated instances are presented. The proposed approach is able to find optimal solutions of random instances with up to 100 customers and 100 potential plants, and of instances on real-world data with up to 120 customers and 16 potential plants.     

A queueing model for crowdsourcing

Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c-server queueing system. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a server soon after getting a service or by one of c servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability \(p, 0 \le p \le 1\). With probability \(q = 1 - p\), a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon completion of a service a free server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented.     

An efficient mixed integer programming model for pairing containers in inland transportation based on the assignment of orders

The inland transportation takes a significant portion of the total cost that arises from intermodal transportation. In addition, there are many parties (shipping lines, haulage companies, customers) who share this operation as well as many restrictions that increase the complexity of this problem and make it NP-hard. Therefore, it is important to create an efficient strategy to manage this process in a way to ensure all parties are satisfied. This paper investigates the pairing of containers/orders in drayage transportation from the perspective of delivering paired containers on 40-ft truck and/or individual containers on 20-ft truck, between a single port and a list of customer locations. An assignment mixed integer linear programming model is formulated, which solves the problem of how to combine orders in delivery to save the total transportation cost when orders with both single and multiple destinations exist. In opposition to the traditional models relying on the vehicle routing problem with simultaneous pickups and deliveries and time windows formulation, this model falls into the assignment problem category which is more efficient to solve on large size instances. Another merit for the proposed model is that it can be implemented on different variants of the container drayage problem: import only, import–inland and import–inland–export. Results show that in all cases the pairing of containers yields less cost compared to the individual delivery and decreases empty tours. The proposed model can be solved to optimality efficiently (within half hour) for over 300 orders.     

Defining order picking policy: A storage assignment model and a simulated annealing solution in AS/RS systems

Improving technology, variable customer demands, variety of products and increasing improvement of production systems has brought storage facilities, which has an important role on business operations, to a critical point. This circumstance has revealed the necessity on activating of storage systems and operations. In this study, mathematical model, which minimizes simultaneously storage allocation, storage retrieval and storage keeping costs, is generated for an AS/RS system of an enterprise. The mathematical model has run for small solution space and optimal solution is obtained. The problem in this study is an NP hard problem that is why optimal solution cannot be obtained for large solution spaces. So the problem in existing system is solved by using simulated annealing and an optimal order policy is proposed.     

带时间窗偏好的同时配集货且需求可拆分车辆路径问题

针对带时间窗偏好的同时配集货且需求可拆分车辆路径问题,最小化派遣成本、理货成本、时间窗惩罚成本以及油耗成本之和,建立数学模型。设计混合遗传变邻域搜索算法求解问题,在算法中引入时空距离的理念,首先用最近邻插入法和Logistic映射方程生成初始种群;然后利用变邻域搜索算法的深度搜索能力优化算法;提出自适应搜索策略,平衡种群进化所需的广度和深度;设计拆分准则,为各客户设置不同的拆分服务量;提出确定车辆最优出发时间的时差推移法,减少车辆在客户处的等待时间;最后通过多组算例验证本文模型和算法的有效性。     

A heuristic algorithm for the truckload and less-than-truckload problem

The delivery of goods from a warehouse to local customers is an important and practical problem of a logistics manager. In reality, we are facing the fluctuation of demand. When the total demand is greater than the whole capacity of owned trucks, the logistics managers may consider using an outsider carrier.Logistics managers can make a selection between a truckload (a private truck) and a less-than-truckload carrier (an outsider carrier). Selecting the right mode to transport a shipment may bring significant cost savings to the company.In this paper, we address the problem of routing a fixed number of trucks with limited capacity from a central warehouse to customers with known demand. The objective of this paper is developing a heuristic algorithm to route the private trucks and to make a selection of less-than-truckload carriers by minimizing a total cost function. Both the mathematical model and the heuristic algorithm are developed. Finally, some computational results and suggestions for future research are presented.     

A game theoretic model for two types of customers competing for service

Two types of customers arrive at a single server station and demand service. If a customer finds the server busy upon arrival (or retrial) he immediately departs and conducts a retrial after an exponential period of time and persists this way until he gets served. Both types of customers face linear costs for waiting and conducting retrials and wish to find optimal retrial rates which will minimize these costs. This problem is analysed as a two-person nonzero sum game. Both noncooperative strategies are studied.     

基于两阶段求解策略的动态电动车辆路径优化研究

由于政府对新能源汽车的补贴政策和市区对燃油车限行政策的实时,越来越多的物流公司在城市配送中广泛采用电动汽车。然而,电动车续航里程受限,需要在途充电或者换电,同时客户需求的动态性以及充/换电设施的排队等现实因素也应该被考虑。为此,提出了分阶段策略求解动态电动车辆路径优化问题,并建立了两阶段的EVRP模型。其中第一阶段针对静态客户建立了静态EVRP模型,第二阶段在设计了换电站及动态客户插入策略的基础上,建立了动态EVRP模型以路径更新策略。最后,设计改进的CW-TS混合启发式算法来求解静态模型,设计贪婪算法求解动态模型。实验结果表明,模型与算法具有较好的适用性和有效性。     

Supply chain scheduling with receiving deadlines and non-linear penalty

We study the operations scheduling problem with delivery deadlines in a three-stage supply chain process consisting of (1) heterogeneous suppliers, (2) capacitated processing centres (PCs), and (3) a network of business customers. The suppliers make and ship semi-finished products to the PCs where products are finalized and packaged before they are shipped to customers. Each business customer has an order quantity to fulfil and a specified delivery date, and the customer network has a required service level so that if the total quantity delivered to the network falls below a given targeted fill rate, a non-linear penalty will apply. Since the PCs are capacitated and both shipping and production operations are non-instantaneous, not all the customer orders may be fulfilled on time. The optimization problem is therefore to select a subset of customers whose orders can be fulfilled on time and a subset of suppliers to ensure the supplies to minimize the total cost, which includes processing cost, shipping cost, cost of unfilled orders (if any), and a non-linear penalty if the target service level is not met. The general version of this problem is difficult because of its combinatorial nature. In this paper, we solve a special case of this problem when the number of PCs equals one, and develop a dynamic programming-based algorithm that identifies the optimal subset of customer orders to be fulfilled under each given utilization level of the PC capacity. We then construct a cost function of a recursive form, and prove that the resulting search algorithm always converges to the optimal solution within pseudo-polynomial time. Two numerical examples are presented to test the computational performance of the proposed algorithm.     

A tandem network with a sharing buffer

In this paper, we consider a two-stage tandem network. The customers waiting in these two stages share one finite buffer. By constructing a Markov process, we derive the stationary probability distribution of the system and the sojourn time distribution. Given some constraints on the minimum loss probability and the maximum waiting time, we also derive the optimal buffer size and the shared-buffer size by minimizing the total buffer costs. Numerical results show that, by adopting the buffer-sharing policy, the customer acceptance fraction and the delivery reliability are more sensitive to buffer size comparing with the buffer-allocation policy.     

Integrated production and allocation policies with one direct shipping option

We consider a single period inventory problem in which a supplier faces stochastic demands and customer specific waiting costs from multiple customers. The objective is to develop integrated production, allocation, and distribution policies so that the total production and customer waiting costs are minimized. We present an optimal policy for the two customer problem and derive a heuristic for a general problem based on the structural results of the two customer case. We show, numerically, that the heuristic performs very well with error bounds of less than 2% on average, while typical approximations may lead to significant sub-optimality.     

Large scale stochastic inventory routing problems with?split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer??s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly generated instances of the problem with up to 200 customers and 5 periods and about 400 thousands decision variables where half of them are integer are examined by numerical experiments. Our approach can obtain high quality near optimal solutions within a reasonable amount of computation time on an ordinary PC.     

A general variable neighborhood search for the one-commodity pickup-and-delivery travelling salesman problem

We present a variable neighborhood search approach for solving the one-commodity pickup-and-delivery travelling salesman problem. It is characterized by a set of customers such that each of the customers either supplies (pickup customers) or demands (delivery customers) a given amount of a single product, and by a vehicle, whose given capacity must not be exceeded, that starts at the depot and must visit each customer only once. The objective is to minimize the total length of the tour. Thus, the considered problem includes checking the existence of a feasible travelling salesman’s tour and designing the optimal travelling salesman’s tour, which are both NP-hard problems. We adapt a collection of neighborhood structures, k-opt, double-bridge and insertion operators mainly used for solving the classical travelling salesman problem. A binary indexed tree data structure is used, which enables efficient feasibility checking and updating of solutions in these neighborhoods. Our extensive computational analysis shows that the proposed variable neighborhood search based heuristics outperforms the best-known algorithms in terms of both the solution quality and computational efforts. Moreover, we improve the best-known solutions of all benchmark instances from the literature (with 200 to 500 customers). We are also able to solve instances with up to 1000 customers.