Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

Discrete Conditional Phase-type models utilising classification trees: Application to modelling health service capacities

Discrete Conditional Phase-type (DC-Ph) models consist of a process component (survival distribution) preceded by a set of related conditional discrete variables. This paper introduces a DC-Ph model where the conditional component is a classification tree. The approach is utilised for modelling health service capacities by better predicting service times, as captured by Coxian Phase-type distributions, interfaced with results from a classification tree algorithm. To illustrate the approach, a case-study within the healthcare delivery domain is given, namely that of maternity services. The classification analysis is shown to give good predictors for complications during childbirth. Based on the classification tree predictions, the duration of childbirth on the labour ward is then modelled as either a two or three-phase Coxian distribution. The resulting DC-Ph model is used to calculate the number of patients and associated bed occupancies, patient turnover, and to model the consequences of changes to risk status.

Using simulation to assess cardiac first-responder schemes exhibiting stochastic and spatial complexities

A Monte-Carlo simulation-based model has been constructed to assess a public health scheme involving mobile-volunteer cardiac First-Responders. The scheme being assessed aims to improve survival of Sudden-Cardiac-Arrest (SCA) patients, through reducing the time until administration of life-saving defibrillation treatment, with volunteers being paged to respond to possible SCA incidents alongside the Emergency Medical Services. The need for a model, for example, to assess the impact of the scheme in different geographical regions, was apparent upon collection of observational trial data (given it exhibited stochastic and spatial complexities). The simulation-based model developed has been validated and then used to assess the scheme's benefits in an alternative rural region (not a part of the original trial). These illustrative results conclude that the scheme may not be the most efficient use of National Health Service resources in this geographical region, thus demonstrating the importance and usefulness of simulation modelling in aiding decision making.

”Bricks vs. Clicks”: The impact of manufacturer encroachment with a dealer leasing and selling of durable goods

In durable goods markets, many brand name manufacturers, including IBM, HP, Epson, and Lenovo, have adopted dual-channel supply chains to market their products. There is scant literature, however, addressing the product durability and its impact on players’ optimal strategies in a dual-channel supply chain. To fill this void, we consider a two-period dual-channel model in which a manufacturer sells a durable product directly through both a manufacturer-owned e-channel and an independent dealer who adopts a mix of selling and leasing to consumers. Our results show that the manufacturer begins encroaching into the market in Period 1, but the dealer starts withdrawing from the retail channel in Period 2. Moreover, as the direct selling cost decreases, the equilibrium quantities and wholesale prices become quite angular and often nonmonotonic. Among other results, we find that both the dealer and the supply chain may benefit from the manufacturer’s encroachment. Our results also indicate that both the market structure and the nature of competition have an important impact on the player’s (dealer’s) optimal choice of leasing and selling.

Threshold effects in the Teaching Space Allocation Problem with Splitting

Universities aim for good “Space Management” so as to use the teaching space efficiently. Part of this task is to assign rooms and time-slots to teaching activities with limited numbers and capacities of lecture theaters, seminar rooms, etc. It is also common that some teaching activities require splitting into multiple events. For example, lectures can be too large to fit in one room or good teaching practice requires that seminars/tutorials are taught in small groups. Then, space management involves decisions on splitting as well as the assignments to rooms and time-slots. These decisions must be made whilst satisfying the pedagogic requirements of the institution and constraints on space resources. The efficiency of such management can be measured by the “utilisation”: the percentage of available seat-hours actually used. In many institutions, the observed utilisation is unacceptably low, and this provides our underlying motivation: to study the factors that affect teaching space utilisation, with the goal of improving it. We give a brief introduction to our work in this area, and then introduce a specific model for splitting. We present experimental results that show threshold phenomena and associated easy-hard-easy patterns of computational difficulty. We discuss why such behaviour is of importance for space management.

Evaluating Train Protection Systems

This paper arose from the work carried out for the Cullen/Uff Joint Inquiry into Train Protection Systems. It is concerned with the problem of evaluating the benefits of safety enhancements in order to avoid rare, but catastrophic accidents, and the role of Operations Research in the process. The problems include both input values and representation of outcomes. A key input is the value of life. This paper briefly discusses why the value of life might vary from incident to incident and reviews alternative estimates before producing a 'best estimate' for rail. When the occurrence of an event is uncertain, the normal method is to apply a single 'expected' value. This paper argues that a more effective method of representing such situations is through Monte-Carlo simulation and demonstrates the use of the methodology on a case study of the decision as to whether or not advanced train protection (ATP) should have been installed on a route to the west of London. This paper suggests that the output is more informative than traditional cost-benefit appraisals or engineering event tree approaches. It also shows that, unlike the results from utilizing the traditional approach, the value of ATP on this route would be positive over 50% of the time.

Dynamic pricing for used products in remanufacturing with back orders(ABS 3* Journal, Accepted with Revision on 2nd December 2011).

In remanufacturing, the supply of used products and the demand for remanufactured products are usually mismatched because of the great uncertainties on both sides. In this paper, we propose a dynamic pricing policy to balance this uncertain supply and demand. Specifically, we study a remanufacturer’s problem of pricing a single class of cores with random price-dependent returns and random demand for the remanufactured products with backlogs. We model this pricing task as a continuous-time Markov decision process, which addresses both the finite and infinite horizon problems, and provide managerial insights by analyzing the structural properties of the optimal policy. We then use several computational examples to illustrate the impacts of particular system parameters on pricing policy.

Adaptive linear combination of heuristic orderings in constructing examination timetables

In this paper, we investigate adaptive linear combinations of graph coloring heuristics with a heuristic modifier to address the examination timetabling problem. We invoke a normalisation strategy for each parameter in order to generalise the specific problem data. Two graph coloring heuristics were used in this study (largest degree and saturation degree). A score for the difficulty of assigning each examination was obtained from an adaptive linear combination of these two heuristics and examinations in the list were ordered based on this value. The examinations with the score value representing the higher difficulty were chosen for scheduling based on two strategies. We tested for single and multiple heuristics with and without a heuristic modifier with different combinations of weight values for each parameter on the Toronto and ITC2007 benchmark data sets. We observed that the combination of multiple heuristics with a heuristic modifier offers an effective way to obtain good solution quality. Experimental results demonstrate that our approach delivers promising results. We conclude that this adaptive linear combination of heuristics is a highly effective method and simple to implement.

Bricks vs. clicks: Which is better for marketing remanufactured products?

The economical and environmental benefits are the central issues for remanufacturing. Whereas extant remanufacturing research focuses primarily on such issues in remanufacturing technologies, production planning, inventory control and competitive strategies, we provide an alternative yet somewhat complementary approach to consider both issues related to different channels structures for marketing remanufactured products. Specifically, based on observations from current practice, we consider a manufacturer sells new units through an independent retailer but with two options for marketing remanufactured products: (1) marketing through its own e-channel (Model M) or (2) subcontracting the marketing activity to a third party (Model 3P). A central result we obtain is that although Model M is always greener than Model 3P, firms have less incentive to adopt it because both the manufacturer and retailer may be worse off when the manufacturer sells remanufactured products through its own e-channel rather than subcontracting to a third party. Extending both models to cases in which the manufacturer interacts with multiple retailers further reveals that the more retailers in the market, the greener Model M relative to Model 3P.

A solution concept for network games: The role of multilateral interactions

We propose an allocation rule that takes into account the importance of both players and their links and characterize it for a fixed network. Our characterization is along the lines of the characterization of the Position value for Network games by van den Nouweland and Slikker (2012). The allocation rule so defined admits multilateral interactions among the players through their links which distinguishes it from the other existing rules. Next, we extend our allocation rule to flexible networks à la Jackson (2005).

Determination of (0,2)-regular sets in graphs and applications

In this paper, relevant results about the determination of (k,t)-regular sets, using the main eigenvalues of a graph, are reviewed and some results about the determination of (0,2)-regular sets are introduced. An algorithm for that purpose is also described. As an illustration, this algorithm is applied to the determination of maximum matchings in arbitrary graphs.

A review of dynamic Bayesian network techniques with applications in healthcare risk modelling

Coping with an ageing population is a major concern for healthcare organisations around the world. The average cost of hospital care is higher than social care for older and terminally ill patients. Moreover, the average cost of social care increases with the age of the patient. Therefore, it is important to make efficient and fair capacity planning which also incorporates patient centred outcomes. Predictive models can provide predictions which their accuracy can be understood and quantified. Predictive modelling can help patients and carers to get the appropriate support services, and allow clinical decision-makers to improve care quality and reduce the cost of inappropriate hospital and Accident and Emergency admissions. The aim of this study is to provide a review of modelling techniques and frameworks for predictive risk modelling of patients in hospital, based on routinely collected data such as the Hospital Episode Statistics database. A number of sub-problems can be considered such as Length-of-Stay and End-of-Life predictive modelling. The methodologies in the literature are mainly focused on addressing the problems using regression methods and Markov models, and the majority lack generalisability. In some cases, the robustness, accuracy and re-usability of predictive risk models have been shown to be improved using Machine Learning methods. Dynamic Bayesian Network techniques can represent complex correlations models and include small probabilities into the solution. The main focus of this study is to provide a review of major time-varying Dynamic Bayesian Network techniques with applications in healthcare predictive risk modelling.