Polyhedral Approaches to Hypergraph Partitioning and Cell Formation

Ankara : Department of Industrial Engineering and Institute of Engineering and Science, Bilkent University, 1994.Thesis (Ph.D.) -- -Bilkent University, 1994.Includes bibliographical references leaves 152-161Hypergraphs are generalizations of graphs in the sense that each hyperedge can connect more than two vertices. Hypergraphs are used to describe manufacturing environments and electrical circuits. Hypergraph partitioning in manufacturing models cell formation in Cellular Manufacturing systems. Moreover, hypergraph partitioning in VTSI design case is necessary to simplify the layout problem. There are various heuristic techniques for obtaining non-optimal hypergraph partitionings reported in the literature. In this dissertation research, optimal seeking hypergraph partitioning approaches are attacked from polyhedral combinatorics viewpoint. There are two polytopes defined on r-uniform hypergraphs in which every hyperedge has exactly r end points, in order to analyze partitioning related problems. Their dimensions, valid inequality families, facet defining inequalities are investigated, and experimented via random test problems. Cell formation is the first stage in designing Cellular Manufacturing systems. There are two new cell formation techniques based on combinatorial optimization principles. One uses graph approximation, creation of a flow equivalent tree by successively solving maximum flow problems and a search routine. The other uses the polynomially solvable special case of the one of the previously discussed polytopes. These new techniques are compared to six well-known cell formation algorithms in terms of different efficiency measures according to randomly generated problems. The results are analyzed statistically.Kandiller, LeventPh.D

Part family machine group formation problem in cellular manufacturing systems

Ankara : The Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent Univ. , 1989.Thesis (Master's) -- Bilkent University, 1989.Includes bibliographical references leaves 199-203.The first and the most important stage in the design of Cellular Manufacturing (CM) systems is the Part Family Machine Group Formation (PF/MGF) problem. In this thesis, different approaches to the PF/MG-F problem are discussed. Initially, the design process of CM systems is overviewed. Heuristic techniques developed for the PF/MG-F problem are classified in a general framework. The PF/MG-F problem is defined and some efficiency indices designed to evaluate the PF/MG-F techniques are presented. One of the efficiency indices evaluates the inter-cell flows and inner-cell densities while another one measures the within-cell work-load balances. Another index measures the under-utilization levels of machines. A number of the most promising PF/MG-F techniques are selected for detailed analysis. These selected techniques are evaluated and compared in terms of the efficiency measures by employing randomly generated test problems. Finally, further research areas are addressed.Kandiller, LeventM.S

Vehicle Routing with Compartments Under Product Incompatibility Constraints

This study focuses on a distribution problem involving incompatible products which cannot be stored in a compartment of a vehicle. To satisfy different types of customer demand at minimum logistics cost, the products are stored in different compartments of fleet vehicles, which requires the problem to be modeled as a multiple-compartment vehicle routing problem (MCVRP). While there is an extensive literature on the vehicle routing problem (VRP) and its numerous variants, there are fewer research papers on the MCVRP. Firstly, a novel taxonomic framework for the VRP literature is proposed in this study. Secondly, new mathematical models are proposed for the basic MCVRP, together with its multiple-trip and split-delivery extensions, for obtaining exact solutions for small-size instances. Finally, heuristic algorithms are developed for larger instances of the three problem variants. To test the performance of our heuristics against optimum solutions for larger instances, a lower bounding scheme is also proposed. The results of the computational experiments are reported, indicating validity and a promising performance of an approach

Profit-oriented disassembly-line balancing

As product and material recovery has gained importance, disassembly volumes have increased, justifying construction of disassembly lines similar to assembly lines. Recent research on disassembly lines has focused on complete disassembly. Unlike assembly, the current industry practice involves partial disassembly with profit-maximization or cost-minimization objectives. Another difference between assembly and disassembly is that disassembly involves additional precedence relations among tasks due to processing alternatives or physical restrictions. In this study, we define and solve the profit-oriented partial disassembly-line balancing problem. We first characterize different types of precedence relations in disassembly and propose a new representation scheme that encompasses all these types. We then develop the first mixed integer programming formulation for the partial disassembly-line balancing problem, which simultaneously determines (1) the parts whose demand is to be fulfilled to generate revenue, (2) the tasks that will release the selected parts under task and station costs, (3) the number of stations that will be opened, (4) the cycle time, and (5) the balance of the disassembly line, i.e. the feasible assignment of selected tasks to stations such that various types of precedence relations are satisfied. We propose a lower and upper-bounding scheme based on linear programming relaxation of the formulation. Computational results show that our approach provides near optimal solutions for small problems and is capable of solving larger problems with up to 320 disassembly tasks in reasonable time

Anti-Ship Missile Defense for a Naval Task Group

In this study, we present a new formulation for the air defense problem of warships in a naval task group and propose a solution method. We define the missile allocation problem (MAP) as the optimal allocation of a set of surface-to-air missiles (SAMs) of a naval task group to a set of attacking air targets. MAP is a new treatment of an emerging problem fostered by the rapid increase in the capabilities of anti-ship missiles (ASMs), the different levels of air defense capabilities of the warships against the ASM threat, and new technology that enables a fully coordinated and collective defense. In addition to allocating SAMs to ASMs, MAP also schedules launching of SAM rounds according to shoot-look-shoot engagement policy or its variations, considering multiple SAM systems and ASM types. MAP can be used for air defense planning under a given scenario. As thorough scenario analysis would require repetitive use of MAP, we propose efficient heuristic procedures for solving the problem. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 305-322, 201

A Case Study: Component placement sequencing of a turret style SMT machine

A Case Study: Component placement sequencing of a turret style SMT machine Levent Kandiller, Cankaya University, Department of Industrial Engineering, Cankaya University, Ogretmenler ¨ Caddesi No: 14, 06530, Ankara, Turkey, [email protected], Savas Cengel, Z. Pelin Bayindir The study aims to improve component placement sequencing of PCBs produced on a turret style SMT machine in a leading Turkish electronics company. Because of the concurrent (turret,table,feeder) nature of the machine movement, the sequencing problem is hard to solve optimally. We developed two heuristic approaches and two lower bounding schemes. The heuristic solutions are compared with optimal solutions for randomly generated PCBs, and with the lower bounds for real PCBs in the production line. Our method yielded a considerable improvement (27 %) as compared to the company’s method

A Branch and Bound Algorithm for Sector Allocation of a Naval Task Group

A naval task group (TG) is a collection of naval combatants and auxiliaries that are grouped together for the accomplishment of one or more missions. Ships forming a TG are located in predefined sectors. We define determination of ship sector locations to provide a robust air defense formation as the sector allocation problem (SAP). A robust formation is one that is very effective against a variety of attack scenarios but not necessarily the most effective against any scenario. We propose a 0-1 integer linear programming formulation for SAP. The model takes the size and the direction of threat into account as well as the defensive weapons of the naval TG. We develop tight lower and upper bounds by incorporating some valid inequalities and use a branch and bound algorithm to exactly solve SAP. We report computational results that demonstrate the effectiveness of the proposed solution approach. (C) 2011 Wiley Periodicals, Inc. Naval Research Logistics 58: 655-669, 201