A Stochastic Optimization Model for Consecutive Promotion

Nowadays in business environment, marketing competitiveness is as demanding as ever. To survive under keen competitions, industries must keep acquiring customers and make them loyal while maximizing profit from their service subscription or product purchasing. Intensive research works have been done in answering when and what kind of promotions should be used under limited marketing communication resources to maintain a perpetual generation of revenue. In this paper, we investigate the advantages in consecutive promotion based on the framework of the model proposed in Ching et al. [1]. The customers’ behavior is modelled by using a Markov chain and we aim at maximizing the expected profit using stochastic dynamic programming. We find that a multi-period promotion strategy is better than the strategy of applying several single-period promotions in our tested examples.link_to_OA_fulltex

Cardinality of Binary Operations: A Remark on the Ubiquitous Sum

We establish the sufficient conditions to determine how many binary operations can possibly take place between any two arbitrary elements from a given set, provided that the operation is well defined. If we mark and collect each of such operations in another set S, we call the number �the cardinality of the set S of binary operations between any two elements for a given set of N elements. We find that such number �is closely related to the sum of consecutive numbers, the Ubiquitous Sum (Bezuszka and Kenney [2]). In particular, �is simply the combination of selecting from N distinct objects, two at a time. This idea can be generated to look for the cardinality of a set of ternary operations. We have verified that this cardinality is the same as the combination of selecting from N distinct objects, three at a time. The results can be generalized to derive the formulae of factorization for, when N ε N, Tn = 1n + 2n +3n + ... + Nn, n = 1, 2, 3, ... We also discuss how the formulae are applicable in mathematics pedagogy

A tandem queueing system with applications to pricing strategy

In this paper, we analyze a Markovian queueing system with multiple types of customers and two queues in tandem. All customers have to go through two stages of services. In Stage 1, the queueing system has multiple identical servers while in Stage 2, there is one single-server queue for each type of customers. The queueing discipline in the whole system is Blocked Customer Delayed (BCD). We first obtain the steady-state probability distribution of the queueing system and the expected waiting time for customers. We then apply the queueing model to solve an optimal pricing policy problem in assuming that the demand rate is dependent on the price. The objective is to minimize the number of servers in the first stage and also maximize the expected earnings by taking into account the demand and the prices. We also obtained some analytic results for the optimal pricing strategy.link_to_subscribed_fulltex

Recent research on geometry education: an ICME-13 survey team report

This survey on the theme of Geometry Education (including new technologies) focuses chiefly on the time span since 2008. Based on our review of the research literature published during this time span (in refereed journal articles, conference proceedings and edited books), we have jointly identified seven major threads of contributions as these relate to the early years of learning (pre-school and primary school) through to post-compulsory education and to the issue of mathematics teacher education for geometry. These themes are as follows: developments in and trends in the use of theories; advances in the understanding of spatial reasoning; the use and role of diagrams and gestures; advances in the understanding of the role of technologies; advances in the understanding of the teaching and learning of definitions; advances in the understanding of the teaching and learning of the proving process; and, moving beyond traditional Euclidean approaches. Within each theme, we identify relevant research and also offer commentary on future directions