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 ANZIAM JournalJournal Prestige (SJR): 0.216 Number of Followers: 1     Open Access journal ISSN (Print) 1446-1811 - ISSN (Online) 1446-8735 Published by Cambridge University Press  [387 journals]
• ANZ VOLUME 62 ISSUE 1 COVER AND FRONT MATTER

• PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S1446181119000178
Issue No: Vol. 62, No. 1 (2020)

• ANZ VOLUME 62 ISSUE 1 COVER AND BACK MATTER

• PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S144618111900018X
Issue No: Vol. 62, No. 1 (2020)

• EDITORIAL

• Authors: ANDREW BASSOM; GRAEME HOCKING
Pages: 1 - 2
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S1446181120000139
Issue No: Vol. 62, No. 1 (2020)

• CRITICAL LENGTH FOR THE SPREADING–VANISHING DICHOTOMY IN HIGHER
DIMENSIONS

• Authors: MATTHEW J. SIMPSON
Pages: 3 - 17
Abstract: We consider an extension of the classical Fisher–Kolmogorov equation, called the “Fisher–Stefan” model, which is a moving boundary problem on $0 PubDate: 2020-01-01T00:00:00.000Z DOI: 10.1017/S1446181120000103 Issue No: Vol. 62, No. 1 (2020) • STREAMLINED SOLUTIONS TO MULTILEVEL SPARSE MATRIX PROBLEMS • Authors: TUI H. NOLAN; MATT P. WAND Pages: 18 - 41 Abstract: We define and solve classes of sparse matrix problems that arise in multilevel modelling and data analysis. The classes are indexed by the number of nested units, with two-level problems corresponding to the common situation, in which data on level-1 units are grouped within a two-level structure. We provide full solutions for two-level and three-level problems, and their derivations provide blueprints for the challenging, albeit rarer in applications, higher-level versions of the problem. While our linear system solutions are a concise recasting of existing results, our matrix inverse sub-block results are novel and facilitate streamlined computation of standard errors in frequentist inference as well as allowing streamlined mean field variational Bayesian inference for models containing higher-level random effects. PubDate: 2020-01-01T00:00:00.000Z DOI: 10.1017/S1446181120000061 Issue No: Vol. 62, No. 1 (2020) • A MODIFIED IMMERSED FINITE VOLUME ELEMENT METHOD FOR ELLIPTIC INTERFACE PROBLEMS • Authors: Q. WANG; Z. ZHANG Pages: 42 - 61 Abstract: This paper presents a new immersed finite volume element method for solving second-order elliptic problems with discontinuous diffusion coefficient on a Cartesian mesh. The new method possesses the local conservation property of classic finite volume element method, and it can overcome the oscillating behaviour of the classic immersed finite volume element method. The idea of this method is to reconstruct the control volume according to the interface, which makes it easy to implement. Optimal error estimates can be derived with respect to an energy norm under piecewise$H^{2}$regularity. Numerical results show that the new method significantly outperforms the classic immersed finite volume element method, and has second-order convergence in$L^{\infty }\$ norm.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S1446181120000073
Issue No: Vol. 62, No. 1 (2020)

• GAME MODEL FOR ONLINE AND OFFLINE RETAILERS UNDER BUY-ONLINE AND
PICK-UP-IN-STORE MODE WITH DELIVERY COST AND RANDOM DEMAND

• Authors: YING OUYANG; ZHAOMAN WAN, ZHONG WAN
Pages: 62 - 88
Abstract: Online retailers are increasingly adding buy-online and pick-up-in-store (BOPS) modes to order fulfilment. In this paper, we study a system of BOPS by developing a stochastic Nash equilibrium model with incentive compatibility constraints, where the online retailer seeks optimal online sale prices and an optimal delivery schedule in an order cycle, and the offline retailer pursues a maximal rate of sharing the profit owing to the consignment from the online retailer. By an expectation method and optimality conditions, the equilibrium model is first transformed into a system of constrained nonlinear equations. Then, by a case study and sensitivity analysis, the model is validated and the following practical insights are revealed. (I) Our method can reliably provide an equilibrium strategy for the online and offline retailers under BOPS mode, including the optimal online selling price, the optimal delivery schedule, the optimal inventory and the optimal allocation of profits. (II) Different model parameters, such as operational cost, price sensitivity coefficient, cross-sale factor, opportunity loss ratio and loss ratio of unsold goods, generate distinct impacts on the equilibrium solution and the profits of the BOPS system. (III) Optimization of the delivery schedule can generate greater consumer surplus, and makes the offline retailer share less sale profit from the online retailer, even if the total profit of the BOPS system becomes higher. (IV) Inventory subsidy is an indispensable factor to improve the applicability of the game model in BOPS mode.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S1446181120000127
Issue No: Vol. 62, No. 1 (2020)

• STRATEGIC CUSTOMERS IN MARKOVIAN QUEUES WITH VACATIONS AND SYNCHRONIZED
ABANDONMENT

• Authors: GOPINATH PANDA; VEENA GOSWAMI
Pages: 89 - 120
Abstract: We study impatient customers’ joining strategies in a single-server Markovian queue with synchronized abandonment and multiple vacations. Customers receive the system information upon arrival, and decide whether to join or balk, based on a linear reward-cost structure under the acquired information. Waiting customers are served in a first-come-first-serve discipline, and no service is rendered during vacation. Server’s vacation becomes the cause of impatience for the waiting customers, which leads to synchronous abandonment at the end of vacation. That is, customers consider simultaneously but independent of others, whether to renege the system or to remain. We are interested to study the effect of both information and reneging choice on the balking strategies of impatient customers. We examine the customers’ equilibrium and socially optimal balking strategies under four cases of information: fully/almost observable and fully/almost unobservable cases, assuming the linear reward-cost structure. We compare the social benefits under all the information policies.
PubDate: 2020-01-01T00:00:00.000Z
DOI: 10.1017/S1446181120000115
Issue No: Vol. 62, No. 1 (2020)

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