Srimathy Mohan

A Tabu-Search Heuristic for the Capacitated Lot-Sizing Problem with Set-up Carryover

This paper presents a tabu-search heuristic for the capacitated lot-sizing problem (CLSP) with set-up carryover. This production-planning problems allows multiple items to be produced within a time period, and setups for items to be carried over from one period to the next. Two interrelated decisions, sequencing and lot sizing, are present in this problem. Our tabu-search heuristic consists of five basic move types--three for the sequencing decisions and two for the lot-sizing decisions. We allow infeasible solutions to be generated at a penalty during the course of the search. We use several search strategies, such as dynamic tabu list, adaptive memory, and self-adjusting penalties, to strengthen our heuristic. We also propose a lower-bounding procedure to estimate the quality of our heuristic solution. We have also modified our heuristic to produce good solutions for the CLSP without set-up carryover. The computational study, conducted on a set of 540 test problems, indicates that on average our heuristic solutions are within 12% of a bound on optimality. In addition, for the set of test problems our results indicate an 8% reduction in total cost through set-up carryover.

Scheduling part-time personnel with availability restrictions and preferences to maximize employee satisfaction

With the economy continually moving towards retail and services, the size of the part-time workforce is increasing constantly. In this paper, we consider the problem of scheduling a workforce consisting entirely of part-time workers. The part-time workers have availabilities, preferences for the shifts, and also a seniority level. We propose an integer programming model to maximize employee satisfaction and to meet the demand requirements for each shift. The model is tested on randomly generated instances. The results demonstrate the effectiveness of branch-and-cut methods in reducing computation time.

The Stochastic Eulerian Tour Problem

This paper defines the stochastic Eulerian tour problem (SETP) and investigates several characteristics of this problem. Given an undirected Eulerian graph G = (V, E), a subset R (|R| = n) of the edges in E that require service, and a probability distribution for the number of edges in R that have to be visited in any given instance of the graph, the SETP seeks an a priori Eulerian tour of minimum expected length. We derive a closed-form expression for the expected length of a given Eulerian tour when the number of required edges that have to be visited follows a binomial distribution. We also show that the SETP is NP-hard, even though the deterministic counterpart is solvable in polynomial time. We derive further properties and a worst-case ratio of the deviation of the expected length of a random Eulerian tour from the expected length of the optimal tour. Finally, we present some of the desirable properties in a good a priori tour using illustrative examples.

A note on modelling the capacitated lot-sizing problem with set-up carryover and set-up splitting

The capacitated lot-sizing problem with set-up carryover and set-up splitting (CLSP-SCSS) is formulated as a mixed integer linear program. We define set-up carryover as the production of a product that is continued over from one period to another without incurring an extra set-up. Set-up splitting occurs when the set-up for a product is started at the end of a period and completed at the beginning of the next period. We allow product dependent set-ups. Initial experimentation highlights the importance of including set-up splitting in the CLSP model. In 12 out of the 18 problem instances tested, our model yielded better solutions or removed infeasibility when compared with a CLSP model without set-up splitting.

Heuristics for the Stochastic Eulerian Tour Problem

The Stochastic Eulerian Tour Problem (SETP) seeks the Eulerian tour of minimum expected length on an undirected Eulerian graph, when demand on the arcs that have to be serviced is probabilistic. The SETP is NP-hard and in this paper, we develop three constructive heuristics for this problem. The first two are greedy tour construction heuristics while the third is a sub-tour concatenation heuristic. Our experimental results show that for grid networks, the sub-tour concatenation heuristic performs well when the probability of service of each edge is greater than 0.1. For Euclidean networks, as the number of edges increases, the second heuristic performs the best among the three. Also, the expected length of our overall best solution is lower than the expected length of a random tour by up to 10% on average for grid networks and up to 2% for Euclidean networks.

Capacity Planning and Allocation for Web‐Based Applications

Motivated by the technology division of a financial services firm, we study the problem of capacity planning and allocation for Web-based applications. The steady growth in Web traffic has affected the quality of service (QoS) as measured by response time (RT), for numerous e-businesses. In addition, the lack of understanding of system interactions and availability of proper planning tools has impeded effective capacity management. Managers typically make decisions to add server capacity on an ad hoc basis when systems reach critical response levels. Very often this turns out to be too late and results in extremely long response times and the system crashes. We present an analytical model to understand system interactions with the goal of making better server capacity decisions based on the results. The model studies the relationships and important interactions between the various components of a Web-based application using a continuous time Markov chain embedded in a queuing network as the basic framework. We use several structured aggregation schemes to appropriately represent a complex system, and demonstrate how the model can be used to quickly predict system performance, which facilitates effective capacity allocation decision making. Using simulation as a benchmark, we show that our model produces results within 5% accuracy at a fraction of the time of simulation, even at high traffic intensities. This knowledge helps managers quickly analyze the performance of the system and better plan server capacity to maintain desirable levels of QoS. We also demonstrate how to utilize a combination of dedicated and shared resources to achieve QoS using fewer servers.

A discrete event simulation tool for performance management of web-based application systems

Web-based computer applications connect the end-user with information via the internet. These applications typically operate in distributed computing environments, collecting and collating information from multiple computers that host databases or traditional computer applications. The increase in internet traffic is a clear reflection of the increase in demand for various web-based applications. Managers often find it essential to have the capability to predict performance of these systems in order to maintain service levels, as measured by response time. We present a generic discrete event simulation tool for modelling web-based application systems. Modelling information flow for decision making in such systems requires constructs not typically available in simulation software. We have developed several constructs that can be used in constructing models for various kinds of web-based applications. An example system is modelled using the tool, the impact of different variables (eg transaction volume) on the system performance is analysed and some preliminary insights are presented.

Impact of resource locking on performance of web-based applications

This paper develops a model and an algorithm to evaluate the effects of resource locking on the performance of internet applications. Resource locking is the phenomenon in which, after a request is sent, a front-end server is kept busy until the requests processing is completed at a secondary external server. This is related to, but different from, blocking in queueing networks and has significant capacity implications. The algorithm developed enables evaluation of a simplified Markov model for the system. The model is evaluated by benchmarking against simulation. The results can be used to aid performance evaluation, capacity planning and management.