Technical note: Finite-time regret analysis of Kiefer-Wolfowitz stochastic approximation algorithm and nonparametric multi-product dynamic pricing with unknown demand

We consider the problem of nonparametric multi-product dynamic pricing with unknown demand and show that the problem may be formulated as an online model-free stochastic program, which can be solved by the classical Kiefer-Wolfowitz stochastic approximation (KWSA) algorithm. We prove that the expected cumulative regret of the KWSA algorithm is bounded above by where κ₁, κ₂ are positive constants and T is the number of periods for any T = 1, 2, … . Therefore, the regret of the KWSA algorithm grows in the order of , which achieves the lower bounds known for parametric dynamic pricing problems and shows that the nonparametric problems are not necessarily more difficult to solve than the parametric ones. Numerical experiments further demonstrate the effectiveness and efficiency of our proposed KW pricing policy by comparing with some pricing policies in the literature.     

A case study in bio-inspired engineering design: defense applications of exoskeletal sensors

As part of a bio-inspired design process, the authors examine exoskeletal sensors found in insects and their potential application to armor and hardened buildings. In this way, the outer hardening of a structure or vehicle would not limit the ability of occupants to arrive at an actionable picture of the outer environment. To this end, various sensor modalities employed by insects are compared and contrasted with their current human-engineered equivalents. In several sensing modalities, biosensors perform better, are smaller, and more energy efficient than human-engineered equivalents. They note that biological designs tend to employ non-linear response to signal amplitude and respond with heightened sensitivity over a greater dynamic range of signals than human-engineered sensors. The insect biological sensors have structural and mechanical innovations that preserve the protective capacity of the exoskeleton.     

Efficient computational devices for the capacitated transportation problem

This paper presents the details for applying and specializing the work of Ellis Johnson [10] and [11] to develop a primal code for the well-known capacitated transportation problem. The code was developed directly from the work of Johnson, but is similar to codes developed by Glover, Karney, Klingman, and Napier [6] and Srinivasan and Thompson [14]. The emphasis in the presentation is the use of the graphical representation of the basis to carry out the revised simplex operations. This is a means of exploiting the special structure and sparseness of the constraint matrix to minimize computational effort and storage requirements. We also present the results of solving several large problems with the code developed.     

They protect us,but are they using protection? The potential impact of HIV on the South African Police Service

The drivers of HIV/AIDS in the South African Police Service (SAPS) and impact of the disease on this workforce are neglected areas of research. Existing evidence suggests that while the occupational risk for contracting HIV is low, there are factors associated with the profession that, if left unmanaged, place police officers at risk of contracting HIV. This study's two aims are to identify the potential pathways of HIV infection within policing services and determine the probable impact of HIV/AIDS on SAPS. Through a systematic literature review on HIV/AIDS within police services, and by analysing selected SAPS human resource data, the causal pathways and impact of HIV/AIDS on police services are explored. The study finds that police officers (particularly male officers) are likely to be highly susceptible to HIV infection as a result of risky sexual behaviours born out of occupational characteristics such as high levels of stress, difficult working conditions, living away from home and interactions with sex workers. The problem is exacerbated by the ‘macho’ culture that often prevails among police officers. HIV/AIDS interventions within SAPS must focus on sustained behaviour change. Further, HIV programmes must equip officers with the knowledge and awareness to avoid engaging in high-risk sexual practices that may compromise their health and the effectiveness of the policing service.     

Nonextreme point solution strategies for linear programs

This exposition presents two algorithms for linear programs which allow a value change in more than one nonbasic variable at each iteration. The computational formulae are developed and errors which have appeared in the literature are noted. One algorithm is a multiple basis exchange procedure while the second is a feasible direction method. There remain many computational challenges in the area of linear programming and we hope that this investigation will encourage additional work in the directions indicated in this exposition.     

Fully sequential indifference‐zone selection procedures with variance‐dependent sampling

Fully sequential indifference‐zone selection procedures have been proposed in the simulation literature to select the system with the best mean performance from a group of simulated systems. However, the existing sequential indifference‐zone procedures allocate an equal number of samples to the two systems in comparison even if their variances are drastically different. In this paper we propose new fully sequential indifference‐zone procedures that allocate samples according to the variances. We show that the procedures work better than several existing sequential indifference‐zone procedures when variances of the systems are different. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

Polynomial algorithms for center location on spheres

When locating facilities over the earth or in space, a planar location model is no longer valid and we must use a spherical surface. In this article, we consider the one-and two-center problems on a sphere that contains n demand points. The problem is to locate facilities to minimize the maximum distance from any demand point to the closest facility. We present an O(n) algorithm for the one-center problem when a hemisphere contains all demand points and also give an O(n) algorithm for determining whether or not the hemisphere property holds. We present an O(n³ log n) algorithm for the two-center problem for arbitrarily located demand points. Finally, we show that for general p, the p center on a sphere problem is NP-hard. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 341–352, 1997     

A new storage reduction technique for the solution of the group problem

This paper shows that by making use of an unusual property of the decision table associated with the dynamic programming solution to the goup problem, it is possible to dispense with table storage as such, and instead overlay values for both the objective and history functions. Furthermore, this storage reduction is accomplished with no loss in computational efficiency. An algorithm is presented which makes use of this technique and incorporates various additional efficiencies. The reduction in storage achieved for problems from the literature is shown.     

On gamma estimation via matrix kriging

In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.