abstract: This research is motivated by a deterministic scheduling problem that is fairly common in manufacturing environments, where there are certain processes that call for a machine working on multiple jobs at the same time. An example of such an environment is wafer fabrication in the semiconductor industry where some stages can be modeled as batch processes. There has been significant work done in the past in the field of a single stage of parallel machines which process jobs in batches. The primary motivation behind this research is to extend the research done in this area to a two-stage flow-shop where jobs arrive with unequal ready times and belong to incompatible job families with the goal of minimizing total weighted tardiness. As a first step to propose solutions, a mixed integer mathematical model is developed which tackles the problem at hand. The problem is NP-hard and thus the developed mathematical program can only solve problem instances of smaller sizes in a reasonable amount of time. The next step is to build heuristics which can provide feasible solutions in polynomial time for larger problem instances. The basic nature of the heuristics proposed is time window decomposition, where jobs within a moving time frame are considered for batching each time a machine becomes available on either stage. The Apparent Tardiness Cost (ATC) rule is used to build batches, and is modified to calculate ATC indices on a batch as well as a job level. An improvisation to the above heuristic is proposed, where the heuristic is run iteratively, each time assigning start times of jobs on the second stage as due dates for the jobs on the first stage. The underlying logic behind the iterative approach is to improve the way due dates are estimated for the first stage based on assigned due dates for jobs in the second stage. An important study carried out as part of this research is to analyze the bottleneck stage in terms of its location and how it affects the performance measure. Extensive experimentation is carried out to test how the quality of the solution varies when input parameters are varied between high and low values. / Dissertation/Thesis / M.S. Industrial Engineering 2012

The purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs.