Waiting time analysis of the M/G/1 queue with finite retrial group

We consider an M/G/1 retrial queue with finite capacity of the retrial group. First, we obtain equations governing the dynamic of the waiting time. Then, we focus on the numerical inversion of the density function and the computation of moments. These results are used to approximate the waiting time of the M/G/1 queue with infinite retrial group for which direct analysis seems intractable. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

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.     

Allocating capacity in parallel queues to improve their resilience to deliberate attack

We develop models that lend insight into how to design systems that enjoy economies of scale in their operating costs, when those systems will subsequently face disruptions from accidents, acts of nature, or an intentional attack from a well‐informed attacker. The systems are modeled as parallel M/M/1 queues, and the key question is how to allocate service capacity among the queues to make the system resilient to worst‐case disruptions. We formulate this problem as a three‐level sequential game of perfect information between a defender and a hypothetical attacker. The optimal allocation of service capacity to queues depends on the type of attack one is facing. We distinguish between deterministic incremental attacks, where some, but not all, of the capacity of each attacked queue is knocked out, and zero‐one random‐outcome (ZORO) attacks, where the outcome is random and either all capacity at an attacked queue is knocked out or none is. There are differences in the way one should design systems in the face of incremental or ZORO attacks. For incremental attacks it is best to concentrate capacity. For ZORO attacks the optimal allocation is more complex, typically, but not always, involving spreading the service capacity out somewhat among the servers. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011