Branch-and-Cut for the split delivery vehicle routing problem with time windows

The split delivery vehicle routing problem with time windows (SDVRPTW) is a notoriously hard combinatorial optimization problem. First, it is hard to find a useful compact mixed-integer programming (MIP) formulation for the SDVRPTW. Standard modeling approaches either suffer from inherent symmetries (mixed-integer programs with a vehicle index) or cannot exactly capture all aspects of feasibility. Because of the possibility to visit customers more than once, the standard mechanisms to propagate load and time along the routes fail. Second, the lack of useful formulations has rendered any direct MIP-based approach impossible. Up to now, the most effective exact algorithms for the SDVRPTW have been branch-and-price-and-cut approaches using path-based formulations. In this paper, we propose a new and tailored branch-and-cut algorithm to solve the SDVRPTW. It is based on a new, relaxed compact model, in which some integer solutions are infeasible for the SDVRPTW. We use known and introduce some new classes of valid inequalities to cut off such infeasible solutions. One new class is path-matching constraints that generalize infeasible-path constraints. However, even with the valid inequalities, some integer solutions to the new compact formulation remain to be tested for feasibility. For a given integer solution, we build a generally sparse subnetwork of the original instance. On this subnetwork, all time-window-feasible routes can be enumerated, and a path-based residual problem then solved to decide on the selection of routes, the delivery quantities, and thereby the overall feasibility. All infeasible solutions need to be cut off. For this reason, we derive some strengthened feasibility cuts exploiting the fact that solutions often decompose into clusters. Computational experiments show that the new approach is able to prove optimality for several previously unsolved instances from the literature

The Split Delivery Vehicle Routing Problem with Time Windows and Customer Inconvenience Constraints

In classical routing problems, each customer is visited exactly once. By contrast, when allowing split deliveries, customers may be served through multiple visits. This potentially results in substantial savings in travel costs. Even if split deliveries are beneficial to the transport company, several visits may be undesirable on the customer side: at each visit the customer has to interrupt his primary activities and handle the goods receipt. The contribution of the present paper consists in a thorough analysis of the possibilities and limitations of split delivery distribution strategies. To this end, we investigate two different types of measures for limiting customer inconvenience (a maximum number of visits and the temporal synchronization of deliveries) and evaluate the impact of these measures on carrier efficiency by means of different objective functions (comprising variable routing costs, costs related to route durations, fixed fleet costs). We consider the vehicle routing problem with time windows in which split deliveries are allowed (SDVRPTW) and define the corresponding generalization that takes into account customer inconvenience constraints (SDVRPTW-IC). We design an extended branch-and-cut algorithm to solve the SDVRPTW-IC and report on experimental results showing the impact of customer inconvenience constraints. We finally draw useful insights for logistics managers on the basis of the experimental analysis carried out

A Branch-Price-and-Cut Algorithm for the Capacitated Multiple Vehicle Traveling Purchaser Problem with Unitary Demand

The multiple vehicle traveling purchaser problem (MVTPP) consists of simultaneously selecting suppliers and routing a fleet of homogeneous vehicles to purchase different products at the selected suppliers so that all product demands are fulfilled and traveling and purchasing costs are minimized. We consider variants of the MVTPP in which the capacity of the vehicles can become binding and the demand for each product is one unit. Corresponding solution algorithms from the literature are either branch-and-cut or branch-and-price algorithms, where in the latter case the route-generation subproblem is solved on an expanded graph by applying standard dynamic-programming techniques. Our branch-price-and-cut algorithm employs a novel labeling algorithm that works directly on the original network and postpones the purchasing decisions until the route has been completely defined. Moreover, we define a new branching rule generally applicable in case of unitary product demands, introduce a new family of valid inequalities to apply when suppliers can be visited at most once, and show how product incompatibilities can be handled without considering additional resources in the pricing problem. In comprehensive computational experiments with standard benchmark sets we prove that the new branch-price-and-cut approach is highly competitive

Acupuncture randomized trials (ART) in patients with chronic low back pain and osteoarthritis of the knee - Design and protocols

Background: We report on the study design and protocols of two randomized controlled trials (Acupuncture Randomized Trials = ART) that investigate the efficacy of acupuncture in the treatment of chronic low back pain and osteoarthritis of the knee, respectively. Objective: To investigate whether acupuncture is more efficacious than (a) no treatment or (b) minimal acupuncture in the treatment of low back pain and osteoarthritis. Design: Two randomized, controlled, multicenter trials with three treatment arms and a total follow-up time of 52 weeks. Setting: 30 practitioners and outpatient units in Germany specialized in acupuncture treatment. Patients: 300 patients will be included in each study. In the low back pain trial, patients will be included according to clinical diagnosis. In the osteoarthritis pain trial, patients will be included according to the American College of Rheumatology criteria. Interventions: Patients are randomly assigned to receive either (1) semi-standardized acupuncture (150 patients), (2) minimal acupuncture at non-acupuncture points (75 patients), or (3) no treatment for two months followed by semi-standardized acupuncture (75 patients, waiting list control). Acupuncture treatment consists of 12 sessions per patient over a period of 8 weeks. Main Outcome Measure: The main outcome measure is the difference between baseline and the end of the 8-week treatment period in the following parameters: pain intensity as measured by a visual analogue scale (VAS; 0-100 mm) in the low back pain trial and by the Western Ontario and McMaster Universities Osteoarthritis Score (WOMAC) in the osteoarthritis trial. Outlook: The results of these two studies (available in 2004) will provide health care providers and policy makers with the information needed to make scientifically sound assessments of acupuncture therapy

Acupuncture Point Localization Varies Among Acupuncturists

Background: Studies assessing the point-specific effect of acupuncture or the characteristics of acupuncture points (APs) tend to yield inconclusive results. In order to identify a possible confounding factor, we aimed to examine the variability in AP localization by means of a survey. Material and Methods: Attendees of the 14th ICMART (International Council of Medical Acupuncture and Related Techniques) congress as well as DAGfA (German Medical Society of Acupuncture) lecturers and students were asked to locate and mark the APs LI 10 and TH 5 on a research assistant's arm. Identified points were transferred into a coordinate system, and the respective bivariate distribution function was calculated. Additionally, participants filled out a questionnaire about their acupuncture education and experience, the acupuncture style and point localization techniques used most frequently, and their estimation of the size of an AP. Results: The areas of the ellipses, theoretically containing 95% of AP localizations, varied between 44.49 and 5.18 cm(2). The largest distance between 2 identified points was 8.45 cm for LI 10 and 5.3 cm for TH 5. Apart from being trained at the same school, no other factor could be identified that determined the variability in AP localization. Conclusion: Our results indicate that congruity of AP localization among experienced acupuncturists might be low. Although there are some limitations to our results, this possible bias should be taken into account when conducting acupuncture trials and interpreting results of previous acupuncture studies

Branch-and-Price-and-Cut for the Active-Passive Vehicle-Routing Problem

This paper presents a branch-And-price-And-cut algorithm for the exact solution of the active-passive vehicle-routing problem (APVRP). The APVRP covers a range of logistics applications where pickup-And-delivery requests necessitate a joint operation of active vehicles (e.g., trucks) and passive vehicles (e.g., loading devices such as containers or swap bodies). The objective is to minimize aweighted sum of the total distance traveled, the total completion time of the routes, and the number of unserved requests. To this end, the problem supports a flexible coupling and decoupling of active and passive vehicles at customer locations. Accordingly, the operations of the vehicles have to be synchronized carefully in the planning. The contribution of the paper is twofold: First, we present an exact branch-And-price-And-cut algorithm for this class of routing problems with synchronization constraints. To our knowledge, this algorithm is the first such approach that considers explicitly the temporal interdependencies between active and passive vehicles. The algorithm is based on a nontrivial network representation that models the logical relationships between the different transport tasks necessary to fulfill a request as well as the synchronization of the movements of active and passive vehicles. Second, we contribute to the development of branch-And-price methods in general, in that we solve, for the first time, an ng-path relaxation of a pricing problem with linear vertex costs by means of a bidirectional labeling algorithm. Computational experiments show that the proposed algorithm delivers improved bounds and solutions for a number of APVRP benchmark instances. It is able to solve instances with up to 76 tasks, four active, and eight passive vehicles to optimality within two hours of CPU time

Acupuncture for chronic neck pain: a pilot for a randomised controlled trial

Background: Acupuncture is increasingly being used for many conditions including chronic neck pain. However the evidence remains inconclusive, indicating the need for further well-designed research. The aim of this study was to conduct a pilot randomised controlled parallel arm trial, to establish key features required for the design and implementation of a large-scale trial on acupuncture for chronic neck pain. Methods: Patients whose GPs had diagnosed neck pain were recruited from one general practice, and randomised to receive usual GP care only, or acupuncture ( up to 10 treatments over 3 months) as an adjunctive treatment to usual GP care. The primary outcome measure was the Northwick Park Neck Pain Questionnaire (NPQ) at 3 months. The primary analysis was to determine the sample size for the full scale study. Results: Of the 227 patients with neck pain identified from the GP database, 28 (12.3%) consenting patients were eligible to participate in the pilot and 24 (10.5%) were recruited to the trial. Ten patients were randomised to acupuncture, receiving an average of eight treatments from one of four acupuncturists, and 14 were randomised to usual GP care alone. The sample size for the full scale trial was calculated from a clinically meaningful difference of 5% on the NPQ and, from this pilot, an adjusted standard deviation of 15.3%. Assuming 90% power at the 5% significance level, a sample size of 229 would be required in each arm in a large-scale trial when allowing for a loss to follow-up rate of 14%. In order to achieve this sample, one would need to identify patients from databases of GP practices with a total population of 230,000 patients, or approximately 15 GP practices roughly equal in size to the one involved in this study (i.e. 15,694 patients). Conclusion: This pilot study has allowed a number of recommendations to be made to facilitate the design of a large-scale trial, which in turn will help to clarify the existing evidence base on acupuncture for neck pain

Discrepancy between prevalence and perceived effectiveness of treatment methods in myofascial pain syndrome: Results of a cross-sectional, nationwide survey

Background: Myofascial pain is a common dysfunction with a lifetime prevalence affecting up to 85% of the general population. Current guidelines for the management of myofascial pain are not available. In this study we investigated how physicians on the basis of prescription behaviour evaluate the effectiveness of treatment options in their management of myofascial pain. Methods: We conducted a cross-sectional, nationwide survey with a standardized questionnaire among 332 physicians (79.8% male, 25.6% female, 47.5 +/- 9.6 years) experienced in treating patients with myofascial pain. Recruitment of physicians took place at three German meetings of pain therapists, rheumatologists and orthopaedists, respectively. Physicians estimated the prevalence of myofascial pain amongst patients in their practices, stated what treatments they used routinely and then rated the perceived treatment effectiveness on a six-point scale (with 1 being excellent). Data are expressed as mean +/- standard deviation. Results: The estimated overall prevalence of active myofascial trigger points is 46.1 +/- 27.4%. Frequently prescribed treatments are analgesics, mainly metamizol/paracetamol (91.6%), non-steroidal anti-inflammatory drugs/coxibs (87.0%) or weak opioids (81.8%), and physical therapies, mainly manual therapy (81.1%), TENS (72.9%) or acupuncture (60.2%). Overall effectiveness ratings for analgesics (2.9 +/- 0.7) and physical therapies were moderate (2.5 +/- 0.8). Effectiveness ratings of the various treatment options between specialities were widely variant. 54.3% of all physicians characterized the available treatment options as insufficient. Conclusions: Myofascial pain was estimated a prevalent condition. Despite a variety of commonly prescribed treatments, the moderate effectiveness ratings and the frequent characterizations of the available treatments as insufficient suggest an urgent need for clinical research to establish evidence-based guidelines for the treatment of myofascial pain syndrome

Deqi sensations without cutaneous sensory input: results of an RCT

<p>Abstract</p> <p>Background</p> <p>Deqi is defined in relation to acupuncture needling as a sensory perception of varying character. In a recently published sham laser validation study, we found that subjects in the verum and the sham laser group experienced deqi sensations. Therefore, we aim to further analyze whether the perceptions reported in the two study arms were distinguishable and whether expectancy effects exhibited considerable impact on our results.</p> <p>Methods</p> <p>A detailed re-analysis focusing on deqi sensations was performed from data collected in a previously published placebo-controlled, double-blind, clinical cross-over trial for a sham laser evaluation. Thirty-four healthy volunteers (28 ± 10.7 years; 16 women, 18 men) received two laser acupuncture treatments at three acupuncture points LI4 (hégu), LU7 (liéque), and LR3 (táichong); once by verum laser and once using a sham device containing an inactive laser in randomized order. Outcome measures were frequency, intensity (evaluated by visual analogue scale; VAS), and quality of the subjects' sensations perceived during treatments (assessed with the "acupuncture sensation scale").</p> <p>Results</p> <p>Both, verum and the sham laser acupuncture result in similar deqi sensations with regard to frequency (p-value = 0.67), intensity (p-value = 0.71) and quality (p-values between 0.15 - 0.98). In both groups the most frequently used adjectives to describe these perceptions were "spreading", "radiating", "tingling", "tugging", "pulsing", "warm", "dull", and "electric". Sensations reported were consistent with the perception of deqi as previously defined in literature. Subjects' conviction regarding the effectiveness of laser acupuncture or the history of having received acupuncture treatments before did not correlate with the frequency or intensity of sensations reported.</p> <p>Conclusions</p> <p>Since deqi sensations, described as sensory perceptions, were elicited without any cutaneous sensory input, we assume that they are a product of non-specific effects from the overall treatment procedure. Expectancy-effects due to previous acupuncture experience and belief in laser acupuncture do not seem to play a major role in elicitation of deqi sensations. Our results give hints that deqi might be a central phenomenon of awareness and consciousness, and that its relevance should be taken into account, even in clinical trials. However, further research is required to understand mechanisms underlying deqi.</p