The bounded single-machine parallel-batching scheduling problem with family jobs and release dates to minimize makespan

Author name used in this publication: C. T. NgAuthor name used in this publication: T. C. E. Cheng2007-2008 > Academic research: refereed > Publication in refereed journalAccepted ManuscriptPublishe

Lagrangian approach to minimize makespan of non-identical parallel batch processing machines

Advisors: Purushothaman Damodaran.Committee members: Omar Ghrayeb; Murali Krishnamurthi; Christine Nguyen.Batch Processing Machines (BPMs) are commonly used in electronics manufacturing, semi-conductor manufacturing, and metal-working - to name a few. Scheduling these machines are not an easy task; practical considerations and the exponential number of decision variables involved impede schedulers (or decision makers) from making good decisions. This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. The first decision is to group jobs to form batches such that the machine capacity is not exceeded. The second decision is to sequence the batches formed on the machines such that the makespan is minimized. Both the decisions are intertwined as the processing time of the batch is determined by the composition of the jobs in the batch. The problem under study is shown to be NP-hard. A mathematical model from the literature is adopted to develop a solution approach which would help the decision maker to make meaningful decisions.Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. Using this decomposition approach, the mathematical model is decomposed and a sub-gradient approach was used to update the multipliers. Two sets of constraints were relaxed to consider two Lagrangian Relaxation models. Experiments were conducted with data sets from the literature. The solution quality of the proposed approach was compared with meta-heuristics (i.e. Particle Swarm Optimization (PSO) and Random Key Genetic Algorithm (RKGA)) published in the literature and a commercial solver (i.e. IBM ILOG CPLEX). On smaller instances (i.e. 10 and 20 jobs), the proposed approach outperformed PSO and RKGA. However, the proposed approach and CPLEX report the same results. On larger instances (i.e. 50, 100 and 200 job instances) with two and four-machines, the proposed approach was better than PSO whenever the variability in the processing times were smaller. The proposed approach generally outperformed RKGA and CPLEX on larger problem instances. Out of 200 experiments conducted, the proposed approach helped to find new improved solution on 34 instances and comparable on 105 instances when compared to PSO. The PSO approach was much faster than all other approaches on larger problem instances. The experimental study clearly identifies the problem instances on which the proposed approach can find a better solution. The proposed Lagrangian Relaxation solution approach helps the schedulers to make more informed decisions. Minor modifications can be made to use the proposed solution approach for other practical considerations (e.g. job ready times, tardiness objective, etc.) The main contribution of this research is the proposed solution approach which is effective in solving a class of non-identical batch processing machine problems with better solution quality when compared to existing meta-heuristics.M.S. (Master of Science

Advances and Novel Approaches in Discrete Optimization

Discrete optimization is an important area of Applied Mathematics with a broad spectrum of applications in many fields. This book results from a Special Issue in the journal Mathematics entitled ‘Advances and Novel Approaches in Discrete Optimization’. It contains 17 articles covering a broad spectrum of subjects which have been selected from 43 submitted papers after a thorough refereeing process. Among other topics, it includes seven articles dealing with scheduling problems, e.g., online scheduling, batching, dual and inverse scheduling problems, or uncertain scheduling problems. Other subjects are graphs and applications, evacuation planning, the max-cut problem, capacitated lot-sizing, and packing algorithms

Fully polynomial time approximation schemes for sequential decision problems

Thesis (S.M.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2005.Includes bibliographical references (p. 65-67).This thesis is divided into two parts sharing the common theme of fully polynomial time approximation schemes. In the first part, we introduce a generic approach for devising fully polynomial time approximation schemes for a large class of problems that we call list scheduling problems. Our approach is simple and unifying, and many previous results in the literature follow as direct corollaries of our main theorem. In the second part, we tackle a more difficult problem; the stochastic lot sizing problem, and give the first fully polynomial time approximation scheme for it. Our approach is based on simple techniques that could arguably have wider applications outside of just designing fully polynomial time approximation schemes.by Mohamed Mostagir.S.M

Two-machine flowshop scheduling with flexible operations and controllable processing times

Ankara : The Department of Industrial Engineering and the Graduate School of Engineering and Science of Bilkent University, 2011.Thesis (Master's) -- Bilkent University, 2011.Includes bibliographical references leaves 77-84.In this study, we consider a two-machine flowshop scheduling problem with identical jobs. Each of these jobs has three operations, where the first operation must be performed on the first machine, the second operation must be performed on the second machine, and the third operation (named as flexible operation) can be performed on either machine but cannot be preempted. Highly flexible CNC machines are capable of performing different operations as long as the required cutting tools are loaded on these machines. The processing times on these machines can be changed easily in albeit of higher manufacturing cost by adjusting the machining parameters like the speed of the machine, feed rate, and/or the depth of cut. The overall problem is to determine the assignment of the flexible operations to the machines and processing times for each job simultaneously, with the bicriteria objective of minimizing the manufacturing cost and minimizing makespan. For such a bicriteria problem, there is no unique optimum but a set of nondominated solutions. Using ǫ constraint approach, the problem could be transformed to be minimizing total manufacturing cost objective for a given upper limit on the makespan objective. The resulting single criteria problem is a nonlinear mixed integer formulation. For the cases where the exact algorithm may not be efficient in terms of computation time, we propose an efficient approximation algorithm.Uruk, ZeynepM.S

Quality and production control with opportunities and exogenous random shocks

Cataloged from PDF version of article.In a production process, opportunities arise due to exogenous or indigenous factors, for cost reduction. In this dissertation, we consider such opportunities in quality control chart design and production planning for the lot sizing problem. In the first part of the dissertation, we study the economic design of X control charts for a single machine facing exogenous random shocks, which create opportunities for inspection and repair at reduced cost. We develop the expected cycle cost and expected operating time functions, and invoking the renewal reward theorem, we derive the objective function to obtain the optimum values for the control chart design parameters. In the second part, we consider the quality control chart design for the multiple machine environment operating under jidoka (autonomation) policy, in which the opportunities are due to individual machine stoppages. We provide the exact model derivation and an approximate model employing the single machine model developed in the first part. For both models, we conduct extensive numerical studies and observe that modeling the inspection and repair opportunities provide considerable cost savings. We also show that partitioning of the machines as opportunity takers and opportunity non-takers yields further cost savings. In the third part, we consider the dynamic lot sizing problem with finite capacity and where there are opportunities to keep the process warm at a unit variable cost for the next period if more than a threshold value has been produced. For this warm/cold process, we develop a dynamic programming formulation of the problem and establish theoretical results on the optimal policy structure. For a special case, we show that forward solution algorithms are available, and provide rules for identifying planning horizons. Our numerical study indicates that utilizing the undertime option results in significant cost savings, and it has managerial implications for capacity planning and selection.Toy, Ayhan ÖzgürPh.D

Supply Chain

Traditionally supply chain management has meant factories, assembly lines, warehouses, transportation vehicles, and time sheets. Modern supply chain management is a highly complex, multidimensional problem set with virtually endless number of variables for optimization. An Internet enabled supply chain may have just-in-time delivery, precise inventory visibility, and up-to-the-minute distribution-tracking capabilities. Technology advances have enabled supply chains to become strategic weapons that can help avoid disasters, lower costs, and make money. From internal enterprise processes to external business transactions with suppliers, transporters, channels and end-users marks the wide range of challenges researchers have to handle. The aim of this book is at revealing and illustrating this diversity in terms of scientific and theoretical fundamentals, prevailing concepts as well as current practical applications

NASA Tech Briefs, January 1992

Topics include: New Product Ideas; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery/Automation; Fabrication; Mathematics and Information Sciences; Life Sciences