Comparison of Work Scheduling Using Constraint Programming or Auctions

Business processes designers take into account the resources that the processes would need, but, due to the variable cost of certain parameters (like energy) or other circumstances, this scheduling must be done when business process enactment. In this report we formalize the energy aware resource cost, including time and usage dependent rates. We also present a constraint programming approach and an auction-based approach to solve the mentioned problem including a comparison of them and a comparison of the proposed algorithms for solving them

Mobile or fixed bearing for total knee arthroplasty? Ambulatory gait analysis results

Background: Mobile-bearing knee replacements have some theoretical advantages over fixed-bearing devices. However, very few randomized controlled clinical trials have been published to date, and studies showed little clinical and subjective advantages for the mobile-bearing using traditional systems of scoring. The choice of the ideal outcome measure to assess total joint replacement remains a complex issue. However, gait analysis provides objective and quantifying evidences of treatment evaluation. Significant methodological advances are currently made in gait analysis laboratories and ambulatory gait devices are now available. The goal of this study was to provide gait parameters as a new objective method to assess total knee arthroplasty outcome between patients with fixed- and mobile-bearing, using an ambulatory device with minimal sensor configuration. This randomized controlled double-blind study included to date 14 patients: the gait signatures of four patients with mobile-bearing were compared to the gait signatures of nine patients with fixed-bearing pre-operatively and post-operatively at 6 weeks, 3 months and 6 months. Each participant was asked to perform two walking trials of 30m long at his/her preferred speed and to complete a EQ-5D questionnaire, a WOMAC and Knee Society Score (KSS). Lower limbs rotations were measured by four miniature angular rate sensors mounted respectively, on each shank and thigh. A new method for a portable system for gait analysis has been developed with very encouraging results regarding the objective outcome of total knee arthroplasty using mobile- and fixed-bearings.

Reversed shoulder arthroplasty baseplate fixed according to the three major columns principle

Introduction: Glenoid bone volume and bone quality can render the fixation of a reversed shoulder arthroplasty (RSA) basis plate hazardous. Cadaveric study at our institution has demonstrated that optimal baseplate fixation could be achieved with screws in three major columns. Our aim is to review our early rate of aseptic glenoid loosening in a series of baseplates fixed according to this principle. Methods: Between 2005 and 2008, 48 consecutive RSA (Reversed Aequalis) were implanted in 48 patients with an average age of 74.4 years (range, 56 to 86 years). There were 37 women and 11 men. Twenty-seven primary RSAs were performed for cuff tear arthropathy, 3 after failed rotator cuff surgery, 6 for failed arthroplasties, 7 for acute fractures and 5 after failed ORIF. All baseplate fixations were done using a nonlocking posterior screw in the scapular spine, a nonlocking anterior screw in the glenoid body, a locking superior screw in the coracoid and a locking inferior screw in the pillar. All patients were reviewed with standardized radiographs. We reported the positions of the screws in relation to the scapular spine and the coracoid process in two different views. We defined screw positions as totally, partially or out of the target. Finally, we reported aseptic glenoid loosening which was defined as implant subsidence. Results: Four patients were lost to follow-up. Thus 44 shoulders could be reviewed after a mean follow-up of 16 months (range, 9 to 32 months). Thirty-seven (84%) screws were either partially or totally in the spine. Thus, 7 (16%) scapular spine screws were out of the target. No coracoid screw was out of the target. At final follow-up control, we reported no glenoid loosening. Conclusion: Early glenoid loosening occurred before the two years follow-up and is most of time related to technical problems and/or insufficient glenoid bone stock and bone quality. Our study demonstrate that baseplate fixation of a RSA according to the three columns principle is a reproducible technique and a valuable way to prevent early glenoid loosening.

A polynomial algorithm for special case of the one-machine scheduling problem with time-lags

The standard one-machine scheduling problem consists in schedulinga set of jobs in one machine which can handle only one job at atime, minimizing the maximum lateness. Each job is available forprocessing at its release date, requires a known processing timeand after finishing the processing, it is delivery after a certaintime. There also can exists precedence constraints between pairsof jobs, requiring that the first jobs must be completed beforethe second job can start. An extension of this problem consistsin assigning a time interval between the processing of the jobsassociated with the precedence constrains, known by finish-starttime-lags. In presence of this constraints, the problem is NP-hardeven if preemption is allowed. In this work, we consider a specialcase of the one-machine preemption scheduling problem with time-lags, where the time-lags have a chain form, and propose apolynomial algorithm to solve it. The algorithm consist in apolynomial number of calls of the preemption version of the LongestTail Heuristic. One of the applicability of the method is to obtainlower bounds for NP-hard one-machine and job-shop schedulingproblems. We present some computational results of thisapplication, followed by some conclusions.

Dynamic price competition with fixed capacities

Many revenue management (RM) industries are characterized by (a) fixed capacities in theshort term (e.g., hotel rooms, seats on an airline flight), (b) homogeneous products (e.g., twoairline flights between the same cities at similar times), and (c) customer purchasing decisionslargely influenced by price. Competition in these industries is also very high even with just twoor three direct competitors in a market. However, RM competition is not well understood andpractically all known implementations of RM software and most published models of RM donot explicitly model competition. For this reason, there has been considerable recent interestand research activity to understand RM competition. In this paper we study price competitionfor an oligopoly in a dynamic setting, where each of the sellers has a fixed number of unitsavailable for sale over a fixed number of periods. Demand is stochastic, and depending on howit evolves, sellers may change their prices at any time. This reflects the fact that firms constantly,and almost costlessly, change their prices (alternately, allocations at a price in quantity-basedRM), reacting either to updates in their estimates of market demand, competitor prices, orinventory levels. We first prove existence of a unique subgame-perfect equilibrium for a duopoly.In equilibrium, in each state sellers engage in Bertrand competition, so that the seller withthe lowest reservation value ends up selling a unit at a price that is equal to the equilibriumreservation value of the competitor. This structure hence extends the marginal-value conceptof bid-price control, used in many RM implementations, to a competitive model. In addition,we show that the seller with the lowest capacity sells all its units first. Furthermore, we extendthe results transparently to n firms and perform a number of numerical comparative staticsexploiting the uniqueness of the subgame-perfect equilibrium.

Introducing systematic dispatcher-assisted cardiopulmonary resuscitation (telephone-CPR) in a non-Advanced Medical Priority Dispatch System (AMPDS): implementation process and costs.

OBJECTIVE: In order to improve the quality of our Emergency Medical Services (EMS), to raise bystander cardiopulmonary resuscitation rates and thereby meet what is becoming a universal standard in terms of quality of emergency services, we decided to implement systematic dispatcher-assisted or telephone-CPR (T-CPR) in our medical dispatch center, a non-Advanced Medical Priority Dispatch System. The aim of this article is to describe the implementation process, costs and results following the introduction of this new "quality" procedure. METHODS: This was a prospective study. Over an 8-week period, our EMS dispatchers were given new procedures to provide T-CPR. We then collected data on all non-traumatic cardiac arrests within our state (Vaud, Switzerland) for the following 12months. For each event, the dispatchers had to record in writing the reason they either ruled out cardiac arrest (CA) or did not propose T-CPR in the event they did suspect CA. All emergency call recordings were reviewed by the medical director of the EMS. The analysis of the recordings and the dispatchers' written explanations were then compared. RESULTS: During the 12-month study period, a total of 497 patients (both adults and children) were identified as having a non-traumatic cardiac arrest. Out of this total, 203 cases were excluded and 294 cases were eligible for T-CPR. Out of these eligible cases, dispatchers proposed T-CPR on 202 occasions (or 69% of eligible cases). They also erroneously proposed T-CPR on 17 occasions when a CA was wrongly identified (false positive). This represents 7.8% of all T-CPR. No costs were incurred to implement our study protocol and procedures. CONCLUSIONS: This study demonstrates it is possible, using a brief campaign of sensitization but without any specific training, to implement systematic dispatcher-assisted cardiopulmonary resuscitation in a non-Advanced Medical Priority Dispatch System such as our EMS that had no prior experience with systematic T-CPR. The results in terms of T-CPR delivery rate and false positive are similar to those found in previous studies. We found our results satisfying the given short time frame of this study. Our results demonstrate that it is possible to improve the quality of emergency services at moderate or even no additional costs and this should be of interest to all EMS that do not presently benefit from using T-CPR procedures. EMS that currently do not offer T-CPR should consider implementing this technique as soon as possible, and we expect our experience may provide answers to those planning to incorporate T-CPR in their daily practice.

The crew-scheduling module in the GIST system

The public transportation is gaining importance every year basically duethe population growth, environmental policies and, route and streetcongestion. Too able an efficient management of all the resources relatedto public transportation, several techniques from different areas are beingapplied and several projects in Transportation Planning Systems, indifferent countries, are being developed. In this work, we present theGIST Planning Transportation Systems, a Portuguese project involving twouniversities and six public transportation companies. We describe indetail one of the most relevant modules of this project, the crew-scheduling module. The crew-scheduling module is based on the application of meta-heuristics, in particular GRASP, tabu search and geneticalgorithm to solve the bus-driver-scheduling problem. The metaheuristicshave been successfully incorporated in the GIST Planning TransportationSystems and are actually used by several companies.

Fixed-term contracts and the duration distribution of unemployment

In the mid-1980s, many European countries introduced fixed-term contracts.Since then their labor markets have become more dynamic. This paper studiesthe implications of such reforms for the duration distribution ofunemployment, with particular emphasis on the changes in the durationdependence. I estimate a parametric duration model using cross-sectionaldata drawn from the Spanish Labor Force Survey from 1980 to 1994 to analyzethe chances of leaving unemployment before and after the introduction offixed-term contracts. I find that duration dependence has increased sincesuch reform. Semi-parametric estimation of the model also shows that forlong spells, the probability of leaving unemployment has decreased sincesuch reform.

Locating emergency services with different priorities: The priority queuing covering location problem

Previous covering models for emergency service consider all the calls to be of the sameimportance and impose the same waiting time constraints independently of the service's priority.This type of constraint is clearly inappropriate in many contexts. For example, in urban medicalemergency services, calls that involve danger to human life deserve higher priority over calls formore routine incidents. A realistic model in such a context should allow prioritizing the calls forservice.In this paper a covering model which considers different priority levels is formulated andsolved. The model heritages its formulation from previous research on Maximum CoverageModels and incorporates results from Queuing Theory, in particular Priority Queuing. Theadditional complexity incorporated in the model justifies the use of a heuristic procedure.

Restless bandits, partial conservation laws and indexability

We show that if performance measures in a stochastic scheduling problem satisfy a set of so-called partial conservation laws (PCL), which extend previously studied generalized conservation laws (GCL), then the problem is solved optimally by a priority-index policy for an appropriate range of linear performance objectives, where the optimal indices are computed by a one-pass adaptive-greedy algorithm, based on Klimov's. We further apply this framework to investigate the indexability property of restless bandits introduced by Whittle, obtaining the following results: (1) we identify a class of restless bandits (PCL-indexable) which are indexable; membership in this class is tested through a single run of the adaptive-greedy algorithm, which also computes the Whittle indices when the test is positive; this provides a tractable sufficient condition for indexability; (2) we further indentify the class of GCL-indexable bandits, which includes classical bandits, having the property that they are indexable under any linear reward objective. The analysis is based on the so-called achievable region method, as the results follow fromnew linear programming formulations for the problems investigated.

On the performance of small-area estimators: Fixed vs. random area parameters

Most methods for small-area estimation are based on composite estimators derived from design- or model-based methods. A composite estimator is a linear combination of a direct and an indirect estimator with weights that usually depend on unknown parameters which need to be estimated. Although model-based small-area estimators are usually based on random-effects models, the assumption of fixed effects is at face value more appropriate.Model-based estimators are justified by the assumption of random (interchangeable) area effects; in practice, however, areas are not interchangeable. In the present paper we empirically assess the quality of several small-area estimators in the setting in which the area effects are treated as fixed. We consider two settings: one that draws samples from a theoretical population, and another that draws samples from an empirical population of a labor force register maintained by the National Institute of Social Security (NISS) of Catalonia. We distinguish two types of composite estimators: a) those that use weights that involve area specific estimates of bias and variance; and, b) those that use weights that involve a common variance and a common squared bias estimate for all the areas. We assess their precision and discuss alternatives to optimizing composite estimation in applications.

Driver scheduling problem modelling

The Drivers Scheduling Problem (DSP) consists of selecting a set of duties for vehicle drivers, for example buses, trains, plane or boat drivers or pilots, for the transportation of passengers or goods. This is a complex problem because it involves several constraints related to labour and company rules and can also present different evaluation criteria and objectives. Being able to develop an adequate model for this problem that can represent the real problem as close as possible is an important research area.The main objective of this research work is to present new mathematical models to the DSP problem that represent all the complexity of the drivers scheduling problem, and also demonstrate that the solutions of these models can be easily implemented in real situations. This issue has been recognized by several authors and as important problem in Public Transportation. The most well-known and general formulation for the DSP is a Set Partition/Set Covering Model (SPP/SCP). However, to a large extend these models simplify some of the specific business aspects and issues of real problems. This makes it difficult to use these models as automatic planning systems because the schedules obtained must be modified manually to be implemented in real situations. Based on extensive passenger transportation experience in bus companies in Portugal, we propose new alternative models to formulate the DSP problem. These models are also based on Set Partitioning/Covering Models; however, they take into account the bus operator issues and the perspective opinions and environment of the user.We follow the steps of the Operations Research Methodology which consist of: Identify the Problem; Understand the System; Formulate a Mathematical Model; Verify the Model; Select the Best Alternative; Present the Results of theAnalysis and Implement and Evaluate. All the processes are done with close participation and involvement of the final users from different transportation companies. The planner s opinion and main criticisms are used to improve the proposed model in a continuous enrichment process. The final objective is to have a model that can be incorporated into an information system to be used as an automatic tool to produce driver schedules. Therefore, the criteria for evaluating the models is the capacity to generate real and useful schedules that can be implemented without many manual adjustments or modifications. We have considered the following as measures of the quality of the model: simplicity, solution quality and applicability. We tested the alternative models with a set of real data obtained from several different transportation companies and analyzed the optimal schedules obtained with respect to the applicability of the solution to the real situation. To do this, the schedules were analyzed by the planners to determine their quality and applicability. The main result of this work is the proposition of new mathematical models for the DSP that better represent the realities of the passenger transportation operators and lead to better schedules that can be implemented directly in real situations.

Minimum price variations, time priority and quotes dynamics

We analyze the impact of a minimum price variation (tick) and timepriority on the dynamics of quotes and the trading costs when competitionfor the order flow is dynamic. We find that convergence to competitiveoutcomes can take time and that the speed of convergence is influencedby the tick size, the priority rule and the characteristics of the orderarrival process. We show also that a zero minimum price variation is neveroptimal when competition for the order flow is dynamic. We compare thetrading outcomes with and without time priority. Time priority is shownto guarantee that uncompetitive spreads cannot be sustained over time.However it can sometimes result in higher trading costs. Empiricalimplications are proposed. In particular, we relate the size of thetrading costs to the frequency of new offers and the dynamics of theinside spread to the state of the book.

Restless bandits, linear programming relaxations and a primal-dual index heuristic

We develop a mathematical programming approach for the classicalPSPACE - hard restless bandit problem in stochastic optimization.We introduce a hierarchy of n (where n is the number of bandits)increasingly stronger linear programming relaxations, the lastof which is exact and corresponds to the (exponential size)formulation of the problem as a Markov decision chain, while theother relaxations provide bounds and are efficiently computed. Wealso propose a priority-index heuristic scheduling policy fromthe solution to the first-order relaxation, where the indices aredefined in terms of optimal dual variables. In this way wepropose a policy and a suboptimality guarantee. We report resultsof computational experiments that suggest that the proposedheuristic policy is nearly optimal. Moreover, the second-orderrelaxation is found to provide strong bounds on the optimalvalue.