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.     

Class scheduling algorithms for Navy training schools

The problem of developing good schedules for Navy C-Schools has been modeled as a combinatorial optimization problem. The only complicating feature of the problem is that classes must be grouped together into sequences known as pipelines. An ideal schedule will have all classes in a pipeline scheduled in consecutive weeks. The objective is to eliminate the nonproductive time spent by sailors at C-Schools who are waiting for the next class in a pipeline. In this investigation an implicit enumeration procedure for this problem was developed. The key component of our algorithm is a specialized greedy algorithm which is used to obtain a good initial incumbent. Often this initial incumbent is either an optimal schedule or a near optimal schedule. In an empirical analysis with the only other competing software system, our greedy heuristic found equivalent or better solutions in substantially less computer time. This greedy heuristic was extended and modified for the A-School scheduling problem and was found to be superior to its only competitor. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 533–551, 1998     

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     

A note on splitting the bump in an elimination factorization

This exposition presents a method for incorporating a technique known as “splitting the bump” within an elimination form reinversion algorithm. This procedure is designed to reduce fill-in during reinversion and should improve the efficiency of linear programming systems which already use the superior elimination form of the inverse.