Reoptimization gaps versus model errors in online-dispatching of service units for ADAC

Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100-150 vehicles and 400 requests in about 10 s to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within 10 s. One way out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new models ShadowPrice and ZIBDIP_dummy can keep up with ZIBDIP.     

Approximation algorithms for a vehicle routing problem

In this paper we investigate a vehicle routing problem motivated by a real-world application in cooperation with the German Automobile Association (ADAC). The general task is to assign service requests to service units and to plan tours for the units such as to minimize the overall cost. The characteristics of this large-scale problem due to the data volume involve strict real-time requirements. We show that the problem of finding a feasible dispatch for service units starting at their current position and serving at most k requests is NP-complete for each fixed k ≥ 2. We also present a polynomial time (2k − 1)-approximation algorithm, where again k denotes the maximal number of requests served by a single service unit. For the boundary case when k equals the total number |E| of requests (and thus there are no limitations on the tour length), we provide a -approximation. Finally, we extend our approximation results to include linear and quadratic lateness costs.     

Real-time split-delivery pickup and delivery time window problems with transfers

In this research we present the design and implementation of heuristics for solving split-delivery pickup and delivery time window problems with transfer (SDPDTWP) of shipments between vehicles for both static and real-time data sets. In the SDPDTWP each shipment is constrained with the earliest possible pickup time from the origin and the latest acceptable delivery time to a destination. Split-deliveries occur when two or more vehicles service the same origin or destination. The proposed heuristics were applied to both static and real-time data sets. The heuristics computed a solution, in a few seconds, for a static problem from the literature, achieving an improvement of 60% in distance in comparison to the published solution. In the real-time SDPDTWP problems, requests for pickup and delivery of a package, breakdown of a truck or insertion of a truck can occur after the vehicle has left the origin and is enroute to service the customers. Thirty data sets, each consisting of one to seven real-time customer or truck events, were used to test the efficiency of the heuristics. The heuristics obtained solutions to real-time data sets in under five seconds of CPU time.      

Minimising average passenger waiting time in personal rapid transit systems

Personal Rapid Transit (PRT) is an emerging urban transport mode. A PRT system operates much like a conventional hackney taxi system, except that the vehicles are driven by computer (no human driver) between stations in a dedicated network of guideways. The world’s first two PRT systems began operating in 2010 and 2011. In both PRT and taxi systems, passengers request immediate service; they do not book ahead. Perfect information about future requests is therefore not available, but statistical information about future requests is available from historical data. If the system does not use this statistical information to position empty vehicles in anticipation of future requests, long passenger waiting times result, which makes the system less attractive to passengers, but using it gives rise to a difficult stochastic optimisation problem. This paper develops three lower bounds on achievable mean passenger waiting time, one based on queuing theory, one based on the static problem, in which it is assumed that perfect information is available, and one based on a Markov Decision Process model. An evaluation of these lower bounds, together with a practical heuristic developed previously, in simulation shows that these lower bounds can often be nearly attained, particularly when the fleet size is large. The results also show that low waiting times and high utilisation can be simultaneously obtained when the fleet size is large, which suggests important economies of scale.     

环形路网上带有服务时长的在线TSP问题

为了提高快递揽件的时效性,需要对快递车辆进行有效调度。针对环形路网上服务时长以及需求无法预知的揽件问题,本文提出了以服务总时间尽可能短为目标的环形路网上带有服务时长的在线旅行商问题。用在线算法分析了此问题竞争比的下界,设计了两个在线算法并分析了各自的竞争比,结果表明服务时长可以改善在线车的性能。最后通过简单算例对两个算法进行说明,本文研究结论可以为环形路网上的快递车辆实时调度提供指导。     

Emergency Logistics Planning in Natural Disasters

Logistics planning in emergency situations involves dispatching commodities (e.g., medical materials and personnel, specialised rescue equipment and rescue teams, food, etc.) to distribution centres in affected areas as soon as possible so that relief operations are accelerated. In this study, a planning model that is to be integrated into a natural disaster logistics Decision Support System is developed. The model addresses the dynamic time-dependent transportation problem that needs to be solved repetitively at given time intervals during ongoing aid delivery. The model regenerates plans incorporating new requests for aid materials, new supplies and transportation means that become available during the current planning time horizon. The plan indicates the optimal mixed pick up and delivery schedules for vehicles within the considered planning time horizon as well as the optimal quantities and types of loads picked up and delivered on these routes. In emergency logistics context, supply is available in limited quantities at the current time period and on specified future dates. Commodity demand is known with certainty at the current date, but can be forecasted for future dates. Unlike commercial environments, vehicles do not have to return to depots, because the next time the plan is re-generated, a node receiving commodities may become a depot or a former depot may have no supplies at all. As a result, there are no closed loop tours, and vehicles wait at their last stop until they receive the next order from the logistics coordination centre. Hence, dispatch orders for vehicles consist of sets of “broken” routes that are generated in response to time-dependent supply/demand. The mathematical model describes a setting that is considerably different than the conventional vehicle routing problem. In fact, the problem is a hybrid that integrates the multi-commodity network flow problem and the vehicle routing problem. In this setting, vehicles are also treated as commodities. The model is readily decomposed into two multi-commodity network flow problems, the first one being linear (for conventional commodities) and the second integer (for vehicle flows). In the solution approach, these sub-models are coupled with relaxed arc capacity constraints using Lagrangean relaxation. The convergence of the proposed algorithm is tested on small test instances as well as on an earthquake scenario of realistic size.     

Alternative metrics to measure EMS system performance

In the development of strategy for the response to emergent incidents, emergency medical services (EMS) organizations must properly manage their resources while also adhering to response time mandates established by contractual agreements. Performance of an EMS system is typically measured by focusing on the response time of its first responders. However, given that some incidents require the response of multiple emergency vehicles, investigating only the initial response to incidents is inadequate. In this research, we propose two new metrics, in addition to the first response metric, to evaluate the performance of EMS operations: total response time and last responder response time. We develop three mixed integer programming formulations, each one focused on minimizing one of the three metrics, to model the assignment of emergency vehicles to incidents. We also propose a fourth model that combines the metrics via a weighted objective function. This model allows for the simultaneous consideration of the response metrics when evaluating the effectiveness of an emergency response dispatch policy. Experimental results, from comparisons of the models against a greedy dispatch policy, suggest the consideration of multiple response metrics leads to a more robust and effective dispatch policy. Finally, analysis using the models has potential to shape improved strategic and operational policies of EMS organizations. Journal of the Operational Research Society advance online publication, 29 June 2016; doi:10.1057/jors.2016.39     

Online-optimization of multi-elevator transport systems with reoptimization algorithms based on set-partitioning models

We develop and experimentally compare policies for the control of a system of k elevators with capacity one in a transport environment with ? floors, an idealized version of a pallet elevator system in a large distribution center of the Herlitz PBS AG in Falkensee. Each elevator in the idealized system has an individual waiting queue of infinite capacity. On each floor, requests arrive over time in global waiting queues of infinite capacity. The goal is to find a policy that, without any knowledge about future requests, assigns an elevator to each request and a schedule to each elevator so that certain expected cost functions (e.g., the average or the maximal flow times) are minimized. We show that a reoptimization policy for minimizing average squared waiting times can be implemented to run in real-time (1 s) using dynamic column generation. Moreover, in discrete event simulations with Poisson input it outperforms other commonly used policies like multi-server variants of greedy and nearest neighbor.     

Alternate risk measures for emergency medical service system design

The stochastic nature of emergency service requests and the unavailability of emergency vehicles when requested to serve demands are critical issues in constructing valid models representing real life emergency medical service (EMS) systems. We consider an EMS system design problem with stochastic demand and locate the emergency response facilities and vehicles in order to ensure target levels of coverage, which are quantified using risk measures on random unmet demand. The target service levels for each demand site and also for the entire service area are specified. In order to increase the possibility of representing a wider range of risk preferences we develop two types of stochastic optimization models involving alternate risk measures. The first type of the model includes integrated chance constraints (ICCs ), whereas the second type incorporates ICCs  and a stochastic dominance constraint. We develop solution methods for the proposed single-stage stochastic optimization problems and present extensive numerical results demonstrating their computational effectiveness.     

Dynamic demand fulfillment in spare parts networks with multiple customer classes

We study real-time demand fulfillment for networks consisting of multiple local warehouses, where spare parts of expensive technical systems are kept on stock for customers with different service contracts. Each service contract specifies a maximum response time in case of a failure and hourly penalty costs for contract violations. Part requests can be fulfilled from multiple local warehouses via a regular delivery, or from an external source with ample capacity via an expensive emergency delivery. The objective is to minimize delivery cost and penalty cost by smartly allocating items from the available network stock to arriving part requests. We propose a dynamic allocation rule that belongs to the class of one-step lookahead policies. To approximate the optimal relative cost, we develop an iterative calculation scheme that estimates the expected total cost over an infinite time horizon, assuming that future demands are fulfilled according to a simple static allocation rule. In a series of numerical experiments, we compare our dynamic allocation rule with the optimal allocation rule, and a simple but widely used static allocation rule. We show that the dynamic allocation rule has a small optimality gap and that it achieves an average cost reduction of 7.9% compared to the static allocation rule on a large test bed containing problem instances of real-life size.     

A dynamic vehicle routing problem with multiple delivery routes

This paper considers a vehicle routing problem where each vehicle performs delivery operations over multiple routes during its workday and where new customer requests occur dynamically. The proposed methodology for addressing the problem is based on an adaptive large neighborhood search heuristic, previously developed for the static version of the problem. In the dynamic case, multiple possible scenarios for the occurrence of future requests are considered to decide about the opportunity to include a new request into the current solution. It is worth noting that the real-time decision is about the acceptance of the new request, not about its service which can only take place in some future routes (a delivery route being closed as soon as a vehicle departs from the depot). In the computational results, a comparison is provided with a myopic approach which does not consider scenarios of future requests.     

Solving (large scale) matching problems combinatorially

In this paper we describe computational results for a modification of the shortest augmenting path approach for solving large scale matching problems. Using a new assignment start procedure and the two-phase strategy, where first the problem is solved on a sparse subgraph and then reoptimization is used, matching problems on complete graphs with 1000 nodes are solved in about 10–15 seconds on an IBM 4361.This work was partially supported by Sonderforschungsbereich 303, University of Bonn, and a special grant from the Deutsche Forschungsgemeinschaft.     

Telecommunication Link Restoration Planning with Multiple Facility Types

To ensure uninterrupted service, telecommunication networks contain excess (spare) capacity for rerouting (restoring) traffic in the event of a link failure. We study the NP-hard capacity planning problem of economically installing spare capacity on a network to permit link restoration of steady-state traffic. We present a planning model that incorporates multiple facility types, and develop optimization-based heuristic solution methods based on solving a linear programming relaxation and minimum cost network flow subproblems. We establish bounds on the performance of the algorithms, and discuss problem instances that nearly achieve these worst-case bounds. In tests on three real-world problems and numerous randomly-generated problems containing up to 50 nodes and 150 edges, the heuristics provide good solutions (often within 0.5% of optimality) to problems with single facility type, in equivalent or less time than methods from the literature. For multi-facility problems, the gap between our heuristic solution values and the linear programming bounds are larger. However, for small graphs, we show that the optimal linear programming value does not provide a tight bound on the optimal integer value, and our heuristic solutions are closer to optimality than implied by the gaps.     

A two-stage model for a day-ahead paratransit planning problem

We consider a dynamic planning problem for paratransit transportation. The focus is on a decision to take one day ahead: which requests to serve with own vehicles, and which requests to subcontract to taxis? We call this problem the day-ahead paratransit planning problem. The developed model is a non-standard two-stage integer recourse model. Both stages consist of two consecutive optimization problems: the clustering of requests into routes, and the assignment of these routes to vehicles. To solve this model, a genetic algorithm approach is used. Computational results are presented for randomly generated data sets.     

Using different response-time requirements to smooth time-varying demand for service

Many service systems have demand that varies significantly by time of day, making it costly to provide sufficient capacity to be able to respond very quickly to each service request. Fortunately, however, different service requests often have very different response-time requirements. Some service requests may need immediate response, while others can tolerate substantial delays. Thus it is often possible to smooth demand by partitioning the service requests into separate priority classes according to their response-time requirements. Classes with more stringent performance requirements are given higher priority for service. Lower capacity may be required if lower-priority-class demand can be met during off-peak periods. We show how the priority classes can be defined and the resulting required fixed capacity can be determined, directly accounting for the time-dependent behavior. For this purpose, we exploit relatively simple analytical models, in particular, M_t/G/∞ and deterministic offered-load models. The analysis also provides an estimate of the capacity savings that can be obtained from partitioning time-varying demand into priority classes.     

Single line queue with repeated demands

We analyze a model of a queueing system in which customers can only call in to request service: if the server is free, the customer enters service immediately, but if the service system is occupied, the unsatisfied customer must break contact and reinitiate his request later. Such a customer is said to be in “orbit”. In this paper we consider three models characterized by the discipline governing the order of re-request of service from orbit. First, all customers in orbit can reapply, but are discouraged and reduce their rate of demand as more customers join the orbit. Secondly, the FCFS discipline operates for the unsatisfied customers in orbit. Finally, the LCFS discipline governs the customers in orbit and the server takes an exponentially distributed vacation after each service is completed. We calculate several characteristics quantities of such systems, assuming a general service-time distribution and different exponential distributions for the times between arrivals of first and repeat requests.     

Queueing analysis of a mobile trunked system with mixed traffic and finite population

In trunk mobile systems, telephone lines are interfaced with the radio system at the repeaters which serve dispatch type mobile subscribers and telephone line users. We study a trunked mobile system which serves two different types of communication traffic (i) dispatch traffic which has short average service time and (ii) interconnect traffic of telephone line users. Both types of users are assumed to arrive from finite population. The dispatch users are allowed to access all repeaters while interconnect users can occupy only a fixed number of repeaters. A sharing service algorithm to derive blocking probabilities of dispatch and interconnect users and average dispatch delay is proposed.     

A GRASP and Path Relinking Heuristic for Rural Road Network Development

This paper presents a model for rural road network design that involves two objectives: maximize all season road connectivity among villages in a region and maximize route efficiency, while allocating a fix budget among a number of possible road projects. The problem is modeled as a bicriterion optimization problem and solved heuristically through a greedy randomized adaptive search procedure (GRASP) in conjunction with a path relinking procedure. The implementation of GRASP and path relinking includes two novel modifications, a new form of reactive GRASP and a new form of path relinking. Overall, the heuristic approach is streamlined through the incorporation of advanced network flow reoptimization techniques. Results indicate that this implementation outperforms both GRASP as well as a straightforward form of GRASP with path relinking. For small problem instances, for which optimality could be verified, this new, modified form of GRASP with path relinking solved all but one known instance optimally.     

Constrained Extremum Problems and Image Space Analysis—Part III: Generalized Systems

In Part I, sufficient and necessary optimality conditions and the image regularity conditions of constrained scalar and vector extremum problems are reviewed for Image Space Analysis. Part II presents the main feature of the duality and penalization of constrained scalar and vector extremum problems by virtue of Image Space Analysis. In the light, as said in Part I and Part II, to describe the state of Image Space Analysis for constrained optimization, and to stress that it allows us to unify and generalize the several topics of Optimization, in this Part III, we continue to give an exhaustive literature review on separation functions, gap functions and error bounds for generalized systems. Part III also throws light on some research gaps and concludes with the scope of future research in this area.     

A linear programming approach for linear programs with probabilistic constraints

We study a class of mixed-integer programs for solving linear programs with joint probabilistic constraints from random right-hand side vectors with finite distributions. We present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs. We provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed-integer formulation of Luedtke et al. (2010) [13] as well as via lower bounds produced by their cutting plane method. While we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics, we also prove that the theoretical worst-case solution quality for these algorithms is arbitrarily far from optimal. Our computational study compares our heuristics against both the extended mixed-integer programming formulation and the cutting plane method of Luedtke et al. (2010) [13]. Our heuristics efficiently and consistently produce solutions with small optimality gaps, while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5%.