Interval scheduling: A survey

In interval scheduling, not only the processing times of the jobs but also their starting times are given. This article surveys the area of interval scheduling and presents proofs of results that have been known within the community for some time. We first review the complexity and approximability of different variants of interval scheduling problems. Next, we motivate the relevance of interval scheduling problems by providing an overview of applications that have appeared in literature. Finally, we focus on algorithmic results for two important variants of interval scheduling problems. In one variant we deal with nonidentical machines: instead of each machine being continuously available, there is a given interval for each machine in which it is available. In another variant, the machines are continuously available but they are ordered, and each job has a given “maximal” machine on which it can be processed. We investigate the complexity of these problems and describe algorithms for their solution. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Multidirectional scheduling scheme in resource‐constrained project schedulingproblem

In 2000, Klein showed that bidirectional scheduling schemes (bidss) outperform single‐directional scheduling schemes (e.g., forward or backward schemes). In 2010, Yoosefzadeh, et al. [J Math Model Algor 9 (2010), 357–373] showed that depending on the nature of the problems and also the type of priority rules used, schedules produced by a so‐called tridirectional scheduling scheme (trdss) yields shorter makespans when compared to forward, backward, and even bidss. Since the justification technique is applied in many of the state‐of‐the‐art algorithms nowadays, we show that the tuned version of the trdss outperforms the double justification technique. Moreover, we investigate the circumstances under which the trdss is more probable to generate schedules with shorter makespans. To this end, we introduce a new measure of resource requirements and their distributions, namely total amount of overflows. Our analytical as well as empirical investigations show that when the new measure is increased, it is more probable to obtain schedules with shorter makespans using the trdss. © 2013 Wiley Periodicals, Inc. Naval Research Logistics 61: 44–55, 2014     

A robust policy for serial agile production systems

One of the major problems in modeling production systems is how to treat the job arrival process. Restrictive assumptions such as Markovian arrivals do not represent real world systems, especially if the arrival process is generated by job departures from upstream workstations. Under these circumstances, cost‐effective policies that are robust with respect to the nature of the arrival process become of interest. In this paper, we focus on minimizing the expected total holding and setup costs in a two‐stage produce‐to‐order production system operated by a cross‐trained worker. We will show that if setup times are insignificant in comparison with processing times, then near‐optimal policies can be generated with very robust performances with respect to the arrival process. We also present conditions under which these near‐optimal policies can be obtained by using only the arrival and service rates. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2005.     

Recent advances in catalytic combustion of AP-based composite solid propellants

Composite solid propellants (CSPs) have widely been used as main energy source for propelling the rockets in both space and military applications. Internal ballistic parameters of rockets like characteristic exhaust velocity, specific impulse, thrust, burning rate etc., are measured to assess and control the performance of rocket motors. The burn rate of solid propellants has been considered as most vital parameter for design of solid rocket motors to meet specific mission requirements. The burning rate of solid propellants can be tailored by using different constituents, extent of oxidizer loading and its particle size and more commonly by incorporating suitable combustion catalysts. Various metal oxides (MOs), complexes, metal powders and metal alloys have shown positive catalytic behaviour during the com-bustion of CSPs. These are usually solid-state catalysts that play multiple roles in combustion of CSPs such as reduction in activation energy, enhancement of rate of reaction, modification of sequences in reaction-phase, influence on condensed-phase combustion and participation in combustion process in gas-phase reactions. The application of nanoscale catalysts in CSPs has increased considerably in recent past due to their superior catalytic properties as compared to their bulk-sized counterparts. A large surface-to-volume ratio and quantum size effect of nanocatalysts are considered to be plausible reasons for improving the combustion characteristics of propellants. Several efforts have been made to produce nanoscale combustion catalysts for advanced propellant formulations to improve their energetics. The work done so far is largely scattered. In this review, an effort has been made to introduce various combustion catalysts having at least a metallic entity. Recent developments of nanoscale combustion catalysts with their specific merits are discussed. The combustion chemistry of a typical CSP is briefly discussed for providing a better understanding on role of combustion catalysts in burning rate enhancement. Available information on different types of combustion nanocatalysts is also presented with critical comments.     

Influence of porosity distribution on nonlinear free vibration and transient responses of porous functionally graded skew plates

This article deals with the investigation of the effects of porosity distributions on nonlinear free vibration and transient analysis of porous functionally graded skew (PFGS) plates. The effective material properties of the PFGS plates are obtained from the modified power-law equations in which gradation varies through the thickness of the PFGS plate. A nonlinear finite element (FE) formulation for the overall PFGS plate is derived by adopting first-order shear deformation theory (FSDT) in conjunction with von Karman’s nonlinear strain displacement relations. The governing equations of the PFGS plate are derived using the principle of virtual work. The direct iterative method and Newmark’s integration technique are espoused to solve nonlinear mathematical relations. The influences of the porosity distributions and porosity parameter indices on the nonlinear frequency responses of the PFGS plate for different skew angles are studied in various parameters. The effects of volume fraction grading index and skew angle on the plate’s nonlinear dynamic responses for various porosity distributions are illustrated in detail.