An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation called SDCP that is based on segment-level consideration sets, we add a class of constraints called product constraints (σPC), that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ESDCPκ, and compare the performance of both methods on the benchmark data sets in the literature. In our computational testing on the benchmark data sets in the literature, 2PC achieves the CDLP value at a fraction of the CPU time taken by column generation. For a large network our 2PC procedure runs under 70 seconds to come within 0.02% of the CDLP value, while column generation takes around 1 hour; for an even larger network with 68 legs, column generation does not converge even in 10 hours for most of the scenarios while 2PC runs under 9 minutes. Thus we believe our approach is very promising for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small

An enhanced concave program relaxation for choice network revenue management

The network choice revenue management problem models customers as choosing from an offer-set, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of constraints called product constraints, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called ?SDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product constraints and the ?SDCP method are very simple and easy to implement and are applicable to the case of overlapping segment consideration sets. In our computational testing on the benchmark data sets in the literature, SDCP with product constraints achieves the CDLP value at a fraction of the CPU time taken by column generation and we believe is a very promising approach for quickly approximating CDLP when segment consideration sets overlap and the consideration sets themselves are relatively small.discrete-choice models, network revenue management, optimization

An Enhanced Concave Program Relaxation for Choice Network Revenue Management

The network choice revenue management problem models customers as choosing from an offerset, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of valid inequalities called product cuts, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called kSDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product cuts and the kSDCP method are very simple and easy to implement, work with general discrete choice models and are applicable to the case of overlapping segment consideration sets. In our computational testing SDCP with product cuts achieves the CDLP value at a fraction of the CPU time taken by column generation and hence has the potential to be scalable to industrial-size problems

Dynamically accepting and scheduling patients for home healthcare

The importance of home healthcare is growing rapidly since populations of developed and even developing countries are getting older and the number of hospitals, retirement homes, and medical staff do not increase at the same rate. We consider the Home Healthcare Nurse Scheduling Problem where patients arrive dynamically over time and acceptance and appointment time decisions have to be made as soon as patients arrive. The objective is to maximise the average number of daily visits for a single nurse. For the sake of service continuity, patients have to be visited at the same day and time each week during their episode of care. We propose a new heuristic based on generating several scenarios which include randomly generated and actual requests in the schedule, scheduling new customers with a simple but fast heuristic, and analysing results to decide whether to accept the new patient and at which appointment day/time. We compare our approach with two greedy heuristics from the literature, and empirically demonstrate that it achieves significantly better results compared to these other two methods

Home healthcare routing and scheduling of multiple nurses in a dynamic environment

Human resource planning in home healthcare is gaining importance day by day since companies in developed and developing countries face serious nurse and caregiver shortages. In the problem considered in this paper, the decision of patient assignment must be made immediately when the patient request arrives. Once patients have been accepted, they are serviced at the same days, times and by same nurse during their episode of care. The objective is to maximise the number of patient visits for a set of nurses during the planning horizon. We propose a new heuristic based on generating several scenarios which include current schedules of nurses, the new request under consideration, as well as randomly generated future requests to solve three decision problems: first, do we accept the patient? If so, which nurse services the patient? Finally, which days and times are weekly visits of the patient assigned to? We compare our approach with a greedy heuristic from the literature by considering some real-life aspects such as clustered service areas and skill requirements, and empirically demonstrate that it achieves significantly higher average daily visits and shorter travel times compared to the greedy method

A review of choice-based revenue management : theory and methods

Over the last fifteen years, the theory and practice of revenue management has experienced significant developments due to the need to incorporate customer choice behavior. In this paper, we portray these developments by reviewing the key literature on choice-based revenue management, specifically focusing on methodological publications of availability control over the years 2004–2017. For this purpose, we first state the choice-based network revenue management problem by formulating the underlying dynamic program, and structure the review according to its components and the resulting inherent challenges. In particular, we first focus on the demand modeling by giving an overview of popular choice models, discussing their properties, and describing estimation procedures relevant to choice-based revenue management. Second, we elaborate on assortment optimization, which is a fundamental component of the problem. Third, we describe recent developments on tackling the entire control problem. We also discuss the relation to dynamic pricing. Finally, we give directions for future research

An Enhanced Concave Program Relaxation for Choice Network Revenue Management

The network choice revenue management problem models customers as choosing from an offerset, and the firm decides the best subset to offer at any given moment to maximize expected revenue. The resulting dynamic program for the firm is intractable and approximated by a deterministic linear program called the CDLP which has an exponential number of columns. However, under the choice-set paradigm when the segment consideration sets overlap, the CDLP is difficult to solve. Column generation has been proposed but finding an entering column has been shown to be NP-hard. In this paper, starting with a concave program formulation based on segment-level consideration sets called SDCP, we add a class of valid inequalities called product cuts, that project onto subsets of intersections. In addition we propose a natural direct tightening of the SDCP called kSDCP, and compare the performance of both methods on the benchmark data sets in the literature. Both the product cuts and the kSDCP method are very simple and easy to implement, work with general discrete choice models and are applicable to the case of overlapping segment consideration sets. In our computational testing SDCP with product cuts achieves the CDLP value at a fraction of the CPU time taken by column generation and hence has the potential to be scalable to industrial-size problems.operations research, marketing, bid prices, yield management, heuristics, discrete-choice, network revenue management

Air traffic flow management slot allocation to minimize propagated delay and improve airport slot adherence

In Europe, one of the instruments at the Network Manager’s (NM) disposal to tackle demand-capacity imbalance is to impose ground, i.e. Air Traffic Flow Management (ATFM), delays to flights. To compensate for anticipated delays and improve on-time performance, Aircraft Operators usually embed a buffer time in their schedules. The current practice for allocating ATFM delays does not take into account if flights have any remaining schedule buffer to absorb ATFM delay and reduce delay propagation to subsequent flights. Furthermore, the policy presently employed is to minimize ATFM delays, an order of magnitude of half a minute per flight, while propagated delays are approximately ten times higher. In this paper, we explore the possibility to control ATFM delay distribution in a way so as to minimize delay propagated to subsequent flights, but also to increase flights’ adherence to airport slots at coordinated airports. To this aim, we propose a two-level mixed-integer optimization model to solve en-route demand-capacity imbalance problem and further improve airport slot adherence. The rationales behind the research are drawn from practical experience, while the model proposed is compatible with the one currently being used by the NM, making it easy to implement. We test the model on two real-world case studies and conduct ex post analysis to test the effects of violation of model assumptions on results. The results show that it is possible to use the proposed methodology to lower delay propagated to subsequent flights and at the same time to improve airport slot adherence. In addition, they suggest that the current regulatory settings aiming to minimize ATFM delay minutes, as well as operational implementation thereof, are neither necessarily fully aligned with the desires and operating goals of Aircraft Operators, nor they improve the predictability of operations in the network

Unconstraining methods for revenue management systems under small demand

Sales data often only represents a part of the demand for a service product owing to constraints such as capacity or booking limits. Unconstraining methods are concerned with estimating the true demand from such constrained sales data. This paper addresses the frequently encountered situation of observing only a few sales events at the individual product level and proposes variants of small demand forecasting methods to be used for unconstraining. The usual procedure is to aggregate data; however, in that case we lose information on when restrictions were imposed or lifted within a given booking profile. Our proposed methods exploit this information and are able to approximate convex, concave or homogeneous booking curves. Furthermore, they are numerically robust due to our proposed group-based parameter optimization. Empirical results on accuracy and revenue performance based on data from a major car rental company indicate revenue improvements over a best practice benchmark by statistically significant 0.5%–1.4% in typical scenarios

Unconstraining methods for revenue management systems under small demand

Sales data often only represents a part of the demand for a service product owing to constraints such as capacity or booking limits. Unconstraining methods are concerned with estimating the true demand from such constrained sales data. This paper addresses the frequently encountered situation of observing only a few sales events at the individual product level and proposes variants of small demand forecasting methods to be used for unconstraining. The usual procedure is to aggregate data; however, in that case we lose information on when restrictions were imposed or lifted within a given booking profile. Our proposed methods exploit this information and are able to approximate convex, concave or homogeneous booking curves. Furthermore, they are numerically robust due to our proposed group-based parameter optimization. Empirical results on accuracy and revenue performance based on data from a major car rental company indicate revenue improvements over a best practice benchmark by statistically significant 0.5%-1.4% in typical scenarios