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 variable neighbourhood search algorithm for the open vehicle routing problem

In the open vehicle routing problem (OVRP), the objective is to minimise the number of vehicles and then minimise the total distance (or time) travelled. Each route starts at the depot and ends at a customer, visiting a number of customers, each once, en route, without returning to the depot. The demand of each customer must be completely fulfilled by a single vehicle. The total demand serviced by each vehicle must not exceed vehicle capacity. Additionally, in one variant of the problem, the travel time of each vehicle should not exceed an upper limit.     

A truck and drones model for last-mile delivery: A mathematical model and heuristic approach

We present a mathematical formulation and a heuristic solution approach for the optimal planning of delivery routes in a multi-modal system combining truck and Unmanned Aerial Vehicle (UAV) operations. In this system, truck and UAV operations are synchronized, i.e., one or more UAVs travel on a truck, which serves as a mobile depot. Deliveries can be made by both UAVs and the truck. While the truck follows a multi-stop route, each UAV delivers a single shipment per dispatch. The presented optimization model minimizes the waiting time of customers in the system. The model determines the optimal allocation of customers to truck and UAVs, the optimal route sequence of the truck, and the optimal launch and reconvene locations of the UAVs along the truck route. We formulate the problem as a Mixed-Integer Linear Programming (MILP) model and conduct a bound analysis to gauge the maximum potential of the proposed system to reduce customer waiting time compared to a traditional truck-only delivery system. To be able to solve real-world problem size instances, we propose an efficient Truck and Drone Routing Algorithm (TDRA). The solution quality and computational performance of the mathematical model and the TDRA are compared together and with the truck-only model based on a variety of problem instances. Further, we apply the TDRA to a real-world case study for e-commerce delivery in São Paulo, Brazil. Our numerical results suggest significant reductions in customer waiting time to be gained from the proposed multi-modal delivery model.     

A column generation algorithm for the vehicle routing problem with soft time windows

The Vehicle Routing Problem with Time Windows consists of computing a minimum cost set of routes for a fleet of vehicles of limited capacity visiting a given set of customers with known demand, with the additional constraint that each customer must be visited in a specified time window. We consider the case in which time window constraints are relaxed into “soft” constraints, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. We present a branch-and-price algorithm which is the first exact optimization algorithm for this problem.     

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。     

Waiting Time Distributions in the Preemptive Accumulating Priority Queue

We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.     

<Emphasis Type="Italic">GI</Emphasis>/<Emphasis Type="Italic">M</Emphasis>/1 type queueing-inventory systems with postponed work,reservation, cancellation and common life time

In this paper we analyze two single server queueing-inventory systems in which items in the inventory have a random common life time. On realization of common life time, all customers in the system are flushed out. Subsequently the inventory reaches its maximum level S through a (positive lead time) replenishment for the next cycle which follows an exponential distribution. Through cancellation of purchases, inventory gets added until their expiry time; where cancellation time follows exponential distribution. Customers arrive according to a Poisson process and service time is exponentially distributed. On arrival if a customer finds the server busy, then he joins a buffer of varying size. If there is no inventory, the arriving customer first try to queue up in a finite waiting room of capacity K. Finding that at full, he joins a pool of infinite capacity with probability γ (0 < γ < 1); else it is lost to the system forever. We discuss two models based on ‘transfer’ of customers from the pool to the waiting room / buffer. In Model 1 when, at a service completion epoch the waiting room size drops to preassigned number L ? 1 (1 < L < K) or below, a customer is transferred from pool to waiting room with probability p (0 < p < 1) and positioned as the last among the waiting customers. If at a departure epoch the waiting room turns out to be empty and there is at least one customer in the pool, then the one ahead of all waiting in the pool gets transferred to the waiting room with probability one. We introduce a totally different transfer mechanism in Model 2: when at a service completion epoch, the server turns idle with at least one item in the inventory, the pooled customer is immediately taken for service. At the time of a cancellation if the server is idle with none, one or more customers in the waiting room, then the head of the pooled customer go to the buffer directly for service. Also we assume that no customer joins the system when there is no item in the inventory. Several system performance measures are obtained. A cost function is discussed for each model and some numerical illustrations are presented. Finally a comparison of the two models are made.     

A two-queue model with Bernoulli service schedule and switching times

In this paper, we present a detailed analysis of a cyclic-service queueing system consisting of two parallel queues, and a single server. The server serves the two queues with a Bernoulli service schedule described as follows. At the beginning of each visit to a queue, the server always serves a customer. At each epoch of service completion in the ith queue at which the queue is not empty, the server makes a random decision: with probability p_i, it serves the next customer; with probability 1-p_i, it switches to the other queue. The server takes switching times in its transition from one queue to the other. We derive the generating functions of the joint stationary queue-length distribution at service completion instants, by using the approach of the boundary value problem for complex variables. We also determine the Laplace-Stieltjes transforms of waiting time distributions for both queues, and obtain their mean waiting times. This revised version was published online in June 2006 with corrections to the Cover Date.     

A goal programming approach to vehicle routing problems with soft time windows

The classical vehicle routing problem involves designing a set of routes for a fleet of vehicles based at one central depot that is required to serve a number of geographically dispersed customers, while minimizing the total travel distance or the total distribution cost. Each route originates and terminates at the central depot and customers demands are known. In many practical distribution problems, besides a hard time window associated with each customer, defining a time interval in which the customer should be served, managers establish multiple objectives to be considered, like avoiding underutilization of labor and vehicle capacity, while meeting the preferences of customers regarding the time of the day in which they would like to be served (soft time windows). This work investigates the use of goal programming to model these problems. To solve the model, an enumeration-followed-by-optimization approach is proposed which first computes feasible routes and then selects the set of best ones. Computational results show that this approach is adequate for medium-sized delivery problems.     

Lowest priority waiting time distribution in an accumulating priority Lévy queue

We derive the waiting time distribution of the lowest class in an accumulating priority (AP) queue with positive Lévy input. The priority of an infinitesimal customer (particle) is a function of their class and waiting time in the system, and the particles with the highest AP are the next to be processed. To this end we introduce a new method that relies on the construction of a workload overtaking process and solving a first-passage problem using an appropriate stopping time.     

Product form solution for exponential G-networks with dependent service and completion of service of killed customers

Queueing networks with negative customers (G-networks), Poisson flow of positive customers, multi-server exponential nodes, and dependent service at the different nodes are studied. Every customer arriving at the network is defined by a set of random parameters: customer route, the length of customer route, customer volume and his service time at each route stage as well. A killed positive customer is removed at the last place in the queue and quits the network just after his remaining service time will be elaborated. For such G-networks, the multidimensional stationary distribution of the network state probabilities is shown to be representable in product form.     

Dynamic scheduling of a GI/GI/1+GI queue with multiple customer classes

We consider a dynamic control problem for a GI/GI/1+GI queue with multiclass customers. The customer classes are distinguished by their interarrival time, service time, and abandonment time distributions. There is a cost c _k >0 for every class k∈{1,2,…,N} customer that abandons the queue before receiving service. The objective is to minimize average cost by dynamically choosing which customer class the server should next serve each time the server becomes available (and there are waiting customers from at least two classes). It is not possible to solve this control problem exactly, and so we formulate an approximating Brownian control problem. The Brownian control problem incorporates the entire abandonment distribution of each customer class. We solve the Brownian control problem under the assumption that the abandonment distribution for each customer class has an increasing failure rate. We then interpret the solution to the Brownian control problem as a control for the original dynamic scheduling problem. Finally, we perform a simulation study to demonstrate the effectiveness of our proposed control.     

Queues with waiting time dependent service

Motivated by service levels in terms of the waiting-time distribution seen, for instance, in call centers, we consider two models for systems with a service discipline that depends on the waiting time. The first model deals with a single server that continuously adapts its service rate based on the waiting time of the first customer in line. In the second model, one queue is served by a primary server which is supplemented by a secondary server when the waiting of the first customer in line exceeds a threshold. Using level crossings for the waiting-time process of the first customer in line, we derive steady-state waiting-time distributions for both models. The results are illustrated with numerical examples.     

线形网络上单台车辆分群调度问题

本文研究线形网络上单台车辆分群调度问题:若干客户分布在一条直线上,它们被划分成若干个连续子集,其中每个子集称为一个群;每个客户有一个释放时间和一个服务时间;一台机器服务所有客户,且要求每个群内的客户连续服务;目标为极小化时间表长。该问题分两种形式:返回型和不返回型。返回型的时间表长定义为机器服务完所有客户后返回其初始位置的时间;不返回型的时间表长则定义为所有客户的最大完工时间。我们的结果是:对每个客户服务时间为零的情形,证明了两种形式均可在O(n²) 时间内解决;对每个客户服务时间任意的情形,就返回型和不返回型,分别给出了16/9和13/7近似算法。     

应急管理中车辆受限的生产_库存及配送整合模型

针对突发事件发生后,救灾物资不足、车辆数量及容量有限的情况,本文考虑了制造商生产、包装新的救灾物资,构造了车辆返回制造商需要等待订单完成生产的时间函数,建立了一个生产、库存及配送整合的混合整数规划模型。该模型由原材料供应商、制造商、配送中心及客户需求点四部分构成,以完成原材料的运输、制造商中的订单生产并运送到需求点及配送中心的库存订单运送到需求点的总花费时间最短为目标。本文将模型分为两层子模型进行求解:第一层模型采用改进的遗传算法求解;第二层模型采用隐枚举法求解。最后给出一个具体的案例以验证模型的合理性及算法的有效性。     

Branch-and-price-and-cut for the multiple traveling repairman problem with distance constraints

In this paper, we extend the multiple traveling repairman problem by considering a limitation on the total distance that a vehicle can travel; the resulting problem is called the multiple traveling repairmen problem with distance constraints (MTRPD). In the MTRPD, a fleet of identical vehicles is dispatched to serve a set of customers. Each vehicle that starts from and ends at the depot is not allowed to travel a distance longer than a predetermined limit and each customer must be visited exactly once. The objective is to minimize the total waiting time of all customers after the vehicles leave the depot. To optimally solve the MTRPD, we propose a new exact branch-and-price-and-cut algorithm, where the column generation pricing subproblem is a resource-constrained elementary shortest-path problem with cumulative costs. An ad hoc label-setting algorithm armed with bidirectional search strategy is developed to solve the pricing subproblem. Computational results show the effectiveness of the proposed method. The optimal solutions to 179 out of 180 test instances are reported in this paper. Our computational results serve as benchmarks for future researchers on the problem.     

Questionnaire design improvement and missing item scores estimation for rapid and efficient decision making

In this paper we consider a single-server, cyclic polling system with switch-over times and Poisson arrivals. The service disciplines that are discussed, are exhaustive and gated service. The novel contribution of the present paper is that we consider the reneging of customers at polling instants. In more detail, whenever the server starts or ends a visit to a queue, some of the customers waiting in each queue leave the system before having received service. The probability that a certain customer leaves the queue, depends on the queue in which the customer is waiting, and on the location of the server. We show that this system can be analysed by introducing customer subtypes, depending on their arrival periods, and keeping track of the moment when they abandon the system. In order to determine waiting time distributions, we regard the system as a polling model with varying arrival rates, and apply a generalised version of the distributional form of Little??s law. The marginal queue length distribution can be found by conditioning on the state of the system (position of the server, and whether it is serving or switching).     

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.     

A four-input three-stage queuing network approach to model an industrial system

An industrial system is represented as a four-input, three-stage queuing network in this paper. The four-input queuing network receives orders from clients, and the orders are waiting to be served. Each order comprises (i) time of occurrence of the orders, and (ii) quantity of items to be delivered in each order. The objective of this paper is to compute the optimal path which produces the least response time for the delivery of items to the final destination along the three stages of the network. The average number of items that can be delivered with this minimum response time constitute the optimum capacity of the queuing network. After getting serviced by the last node (a queue and its server) in each stage of the queuing network, a decision is made to route the items to the appropriate node in the next stage which can produce the least response time. Performance measures such as average queue lengths, average response times, average waiting times of the jobs in the four-input network are derived and plotted. Closed-form expressions for the equivalent service rate, equivalent average queue lengths, equivalent response and waiting times of a single equivalent queue with a server representing the entire four-input queuing network are also derived and plotted.     

The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service

Customers arriving according to a Markovian arrival process are served at a single server facility. Waiting customers generate priority at a constant rate γ$\gamma$; such a customer waits in a waiting space of capacity 1 if this waiting space is not already occupied by a priority generated customer; else it leaves the system. A customer in service will be completely served before the priority generated customer is taken for service (non-preemptive service discipline). Only one priority generated customer can wait at a time and a customer generating into priority at that time will have to leave the system in search of emergency service elsewhere. The service times of ordinary and priority generated customers follow PH-distributions. The matrix analytic method is used to compute the steady state distribution. Performance measures such as the probability of n consecutive services of priority generated customers, the probability of the same for ordinary customers, and the mean waiting time of a tagged customer are found by approximating them by their corresponding values in a truncated system. All these results are supported numerically.