Browsing by Subject "Mathematical programming"
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Item Open Access Assortment planning considering split orders(Bilkent University, 2021-08) Söylemez, DuyguWhen multi-item orders cannot be satisfied through a single shipment stemming from not having all the items in an order in the same warehouse, the cost of packaging and transportation increases and the delivery of the orders can be delayed. In this regard, split order problem is one of the most significant challenges that the online retailers face. As the capacities of the warehouses are limited, it is not possible to stock every item in every warehouse. To minimize the number of orders that cannot be satisfied in a single shipment, it is important to determine how the limited capacities of the warehouses should be allocated to items or it is necessary to decrease the transportation costs through consolidating the split orders. Since this problem is NP-hard, the previous studies in the literature are based on heuristic algorithms. In this study, exact and heuristic methods have been examined to solve large scale problems. Some of the heuristic algorithms offered uses the LP relaxation of the model provided by Jehl et al.(2018). In this sense, the analytical characterization of the optimal solution of the LP relaxation has also been revealed. It is proved that the allocation variables can only take three different values at most one being fractional. It is shown that this solution can be found without actually solving the LP relaxation by benefiting from an algorithm offered in literature to solve 0-1 fractional programming problems. Moreover, it is proved that a similar characterization is preserved for multiple warehouses or when a central depot with unlimited capacity and a forward distribution center are considered together. Additionally, the working principle of the greedy ranking algorithm offered in the literature is theoretically justified and a dynamic version of this algorithm is developed. To evaluate the performance of the heuristic algorithms offered and the run time of the integer programming problem, an extensive numerical study has been conducted. The change in the difficulty level of the problem based on the plant capacity, the number of orders, and the number of stock keeping units (SKU) is scrutinized. Furthermore, the assortment allocation problem is modeled together with the consolidation problem. The performance of the model is evaluated through comparing its solution to the solution obtained through solving two problems consecutively.Item Open Access Automated robotic assembly line design with unavailability periods and tool changes(Inderscience Publishers, 2016) Gultekin, H.; Tula, A.; Akturk, M. S.We focus on an assembly line design problem of a fully automated robotic spot-welding line. Different from existing studies, we take the prescheduled unavailability periods, such as lunch and tea breaks, into account in order to reflect a more realistic production environment. This problem includes allocating operations to the stations and satisfying the demand and cycle time within a desired interval for each model to be produced. We also ensure that assignability, precedence, and tool life constraints are met. Furthermore, the existing studies in the literature overlook the limited lives of the tools that are used for production. Tool replacement decisions not only affect the tooling cost, but also the production rate. Therefore, we determine the number of stations and allocate the operations into the stations in such a way that tool change periods coincide with the unavailability periods to eliminate tool change related line stoppages in a mixed model robotic assembly line. We provide a mathematical formulation, propose a two-stage local search algorithm and test the performances of these methods using different problem instances with varying parameters. [Received: 12 November 2012; Revised: 8 February 2016; Accepted: 18 February 2016]Item Open Access Bounds on the opportunity cost of neglecting reoptimization in mathematical programming(INFORMS, 2000) Oğuz, O.Postoptimality or sensitivity analysis are well-developed subjects in almost all branches of mathematical programming. In this note, we propose a simple formula which can be used to get preliminary bounds on the value of this type of analysis for a specific class of mathematical programming problems. We also show that our bounds are tight.Item Open Access A characterization of the optimal set of linear programs based on the augmented lagrangian(Taylor & Francis, 1999) Pınar, M. Ç.It is proved that in a certain neighborhood of the optimal set of multipliers, the set of minimizers of the augmented lagrangian nmction generates a new characterization of the optimal solution set of the linear program.Item Open Access A comparative study of computational procedures for the resource constrained project scheduling problem(Elsevier, 1994) Oğuz, O.; Bala, H.Performance of two new integer programming based heuristics together with some special purpose algorithms for project scheduling are tested from a computational point of view. The objective of the study is to compare the quality of solutions obtained by using these algorithms and reach conclusions about their relative merits on this specific problem. © 1994.Item Open Access Coordinated movement of multiple mobile sinks in a wireless sensor network for improved lifetime(SpringerOpen, 2015) Koç, M.; Korpeoglu, I.Sink mobility is one of the most effective solutions for improving lifetime and has been widely investigated for the last decade. Algorithms for single-sink mobility are not directly applied to the multiple-sink case due to the latter’s specific challenges. Most of the approaches proposed in the literature use mathematical programming techniques to solve the multiple-sink mobility problem. However, doing so leads to higher complexities when traffic flow information for any possible sink-site combinations is included in the model. In this paper, we propose two algorithms that do not consider all possible sink-site combinations to determine migration points. We first present a centralized movement algorithm that uses an energy-cost matrix for a user-defined threshold number of combinations to coordinate multiple-sink movement. We also give a distributed algorithm that does not use any prior network information and has a low message exchange overhead. Our simulations show that the centralized algorithm gives better network lifetime performance compared to previously proposed MinDiff-RE, random movement, and static-sink algorithms. Our distributed algorithm has a lower network lifetime than centralized algorithms; sinks travel significantly less than in all the other schemes.Item Open Access Data dependent worst case bound improving techniques in zero-one programming(Elsevier BV, 1991) Oğuz, OsmanA simple perturbation of data is suggested for use in conjunction with approximation algorithms for the purpose of improving the available bounds (upper and lower), and the worst case bounds. The technique does not require the approximation algorithm (heuristic) to provide a worst case bound to be applicable.Item Open Access A data-level parallel linear-quadratic penalty algorithm for multicommodity network flows(Association for Computing Machinery, 1994) Pinar, M. C.; Zenios, S. A.We describe the development of a data-level, massively parallel software system for the solution of multicommodity network flow problems. Using a smooth linear-quadratic penalty (LQP) algorithm we transform the multicommodity network flow problem into a sequence of independent min-cost network flow subproblems. The solution of these problems is coordinated via a simple, dense, nonlinear master program to obtain a solution that is feasible within some user-specified tolerance to the original multicommodity network flow problem. Particular emphasis is placed on the mapping of both the subproblem and master problem data to the processing elements of a massively parallel computer, the Connection Machine CM-2. As a result of this design we can solve large and sparse optimization problems on current SIMD massively parallel architectures. Details of the implementation are reported, together with summary computational results with a set of test problems drawn from a Military Airlift Command application.Item Open Access A goal programming approach to mixed-model assembly line balancing problem(Elsevier, 1997) Gokcen, H.; Erel, E.In this paper, a binary goal programming model for the mixed-model assembly line balancing (ALB) problem is developed. The model is based on the concepts developed by Patterson and Albracht [1] and the model of Deckro and Rangachari [2] developed for the single-model ALB problem. The proposed model provides a considerable amount of flexibility to the decision maker since several conflicting goals can be simultaneously considered.Item Open Access Incorporating just-in-time into a decision support system environment(Elsevier BV, 1991) Oǧuz, Ceyda; Dinçer, CemalIn this paper, a Decision Support System is proposed for a Just-In-Time production system. The Decision Support System includes three components: database, model base, and interface. The database contains the predefined parameters together with the data generated for the considered Just-In-Time production system. In the model base, both deterministic and stochastic aspects of the system are considered. The deterministic system is examined by constructing a linear programming model whereas simulation is used as a tool for the stochastic system. Furthermore, a sensitivity analysis is performed on the Just-In-Time production system with the help of the Decision Support System environment for the unit load size changes under different demand patterns by using the alternative solutions obtained from the model base.Item Open Access An integrated process planning approach for CNC machine tools(Springer-Verlag, 1996) Aktürk, M. S.; Avcı, S.In view of the high investment and tooling cost of a CNC machining centre, the cutting and idle times should be optimised by considering the tool consumption and the non-machining time cost components. In this paper, we propose a detailed mathematical model for the operation of a CNC machine tool which includes the system characterisation, the cutting conditions and tool life relationship, and related constraints. This new module will be a part of an overall computer-aided process planning system to improve the system effectiveness and to provide consistent process plans. A hierarchical approach is presented for finding tool-operation assignments, machining conditions, appropriate tool magazine organisation and an operations sequence which results in the minimum production cost. © 1996 Springer-Verlag London Limited.Item Open Access Keyframe reduction techniques for motion capture data(IEEE, 2008-05) Önder, Onur; Güdükbay, Uğur; Özgüç, Bülent; Erdem, T.; Erdem, Ç.; Özkan, M.Two methods for keyframe reduction of motion capture data are presented. Keyframe reduction of motion capture data enables animators to easily edit motion data with smaller number of keyframes. One of the approaches achieves keyframe reduction and noise removal simultaneously by fitting a curve to the motion information using dynamic programming. The other approach uses curve simplification algorithms on the motion capture data until a predefined threshold of number of keyframes is reached. Although the error rate varies with different motions, the results show that curve fitting with dynamic programming performs as good as curve simplification methods. ©2008 IEEE.Item Open Access Modeling of bus transit driver availability for effective emergency evacuation in disaster relief(2013) Morgul, E.; Cavus, O.; Ozbay, K.; Iyigun, C.Potential evacuees without access to personal automobiles are expected to use transit, especially buses, to reach safer regions. For a transit agency, operation problems to be considered include establishing bus launch areas, positioning the minimum number of required buses, and coordinating transit operators, especially determining whether the number of drivers will be sufficient to cover the number of vehicles (i.e., buses) to be used during the evacuation. It is also highly probable that during an emergency, absenteeism rates for bus drivers might increase. In this study, the authors developed two stochastic models to determine the need for extra drivers during an emergency evacuation and to provide optimal solutions using well-established concepts in mathematical programming. First, the authors reviewed the literature to develop an effective methodology for the development of optimal extraboard management strategies. The authors found that although several recent reports clearly mentioned the problem of not having enough bus drivers during emergency evacuation operations, no analytical study incorporated the optimal extraboard size problem into emergency evacuation operations. Second, two mathematical models are presented in this paper. The aim of the developed models is to fill the gap in the literature for determining optimal extraboard size for transit operations during emergency evacuations. The models are specifically designed to capture risk-averse behavior of decision makers. Finally, these models were tested with hypothetical examples from real-world data from New Jersey. Results show that both models give reasonable extraboard size estimates, and under different conditions, these models are responsive to the changes in cost and quality of service preferences. The results are encouraging in terms of the models' usefulness for real-world applications.Item Open Access A multi product loading problem: a model and a solution method(Elsevier, 1997) Yuceer, U.An important operational problem arises during the transportation and delivery of several products, which cannot be mixed, in the same vehicle at regular intervals. The vehicle has compartments to keep the products separately. Therefore, a scheme of allocation of compartments which we call vehicle loading problem to maximize the efficiency of the system while the demands for the products at the destination(s) are satisfied. A mixed binary model is developed for this multi-product loading problem. The solution method is based on simultaneously exploring the primal and dual structures derived from the Lagrangian relaxation. Subset sum problems are obtained as subproblems to the partial Lagrangian. An algorithm is developed and its convergence is proved. The efficiency of the method is demonstrated by running randomly chosen test problems. An initial solution finding method is also developed.Item Open Access New heuristic for the dynamic layout problem(Palgrave Macmillan, 2003) Erel, E.; Ghosh, J. B.; Simon, J. T.The dynamic layout problem addresses the situation where the traffic among the various units within a facility changes over time. Its objective is to determine a layout for each period in a planning horizon such that the total of the flow and the relocation costs is minimized. The problem is computationally very hard and has begun to receive attention only recently. In this paper, we present a new heuristic scheme, based on the idea of viable layouts, which is easy to operationalize. A limited computational study shows that, depending upon how it is implemented, this scheme can be reasonably fast and can yield results that are competitive with those from other available solution methods.Item Open Access Optimization framework for simultaneous transmit and receive operations in wireless local area network(Bilkent University, 2022-05) Bilaloğlu, EgeFull duplex communication technology draws substantial interest among wireless network operators due to its ability to increase the network capacity through concurrent transmissions. Despite this advantage, interference issue caused by close distances between stations makes it challenging to integrate simultaneous transmit and receive mode into wireless networks. Motivated by the objective of minimal overhead in full duplex transmissions of access points, we provide an optimization framework to minimize the latest completion time of transmissions. In this problem, we aim to find an optimal schedule of transmissions that maximizes concurrent operations in order to reduce the makespan. We formulate the problem for both single and multiple concurrency assumptions separately. For single concurrency, we provide a mixed integer programming (MIP) model using scheduling based formulation along with a greedy heuristic. Modeling the problem as a matching problem between two disjoint sets of supplies and demands, we develop a linear programming (LP) model with a totally unimodular constraint matrix. We utilize Hopcroft-Karp algorithm for solving the resulting maximum cardinality bipartite matching problem. For multiple concurrency; we formulate a flow based integer programming model, demonstrate properties of the extreme points in its LP relaxation, develop valid inequalities and optimality cuts. As an extension, we add due dates for each station to complete their transmissions and formulate an MIP model and develop an algorithm for this variant. Additionally, we provide a proof for NP-completeness of minimum total tardiness problem with single concurrency. To evaluate the performance of the proposed formulations, we perform a range of computational experiments. Finally, we conduct sensitivity analyses to evaluate the effects of the parameters on the objective value and the solution times.Item Open Access Permuting sparse rectangular matrices into block-diagonal form(SIAM, 2004) Aykanat, Cevdet; Pınar, A.; Çatalyürek Ü. V.We investigate the problem of permuting a sparse rectangular matrix into block-diagonal form. Block-diagonal form of a matrix grants an inherent parallelism for solving the deriving problem, as recently investigated in the context of mathematical programming, LU factorization, and QR factorization. To represent the nonzero structure of a matrix, we propose bipartite graph and hypergraph models that reduce the permutation problem to those of graph partitioning by vertex separator and hypergraph partitioning, respectively. Our experiments on a wide range of matrices, using the state-of-the-art graph and hypergraph partitioning tools MeTiS and PaToH, revealed that the proposed methods yield very effective solutions both in terms of solution quality and runtime.Item Open Access Spatial analysis of single allocation hub location problems(Springer, 2016) Peker, M.; Kara, B. Y.; Campbell, J. F.; Alumur, S. A.Hubs are special facilities that serve as switching, transshipment and sorting nodes in many-to-many distribution systems. Flow is consolidated at hubs to exploit economies of scale and to reduce transportation costs between hubs. In this article, we first identify general features of optimal hub locations for single allocation hub location problems based on only the fundamental problem data (demand for travel and spatial locations). We then exploit this knowledge to develop a straightforward heuristic methodology based on spatial proximity of nodes, dispersion and measures of node importance to delineate subsets of nodes likely to contain optimal hubs. We then develop constraints for these subsets for use in mathematical programming formulations to solve hub location problems. Our methodology can also help narrow an organization’s focus to concentrate on more detailed and qualitative analyses of promising potential hub locations. Results document the value of including both demand magnitude and centrality in measuring node importance and the relevant tradeoffs in solution quality and time.Item Open Access A timetabling problem: constraint and mathematical programming approaches(Bilkent University, 2000-06) Botsalı, Ahmet RehaConstraint programming is a relatively new approach far solving combinatorial optimization problems. This approach is especially effective far large scale scheduling problems with side conditions. University course scheduling problem is one of the hard problems in combinatorial optimization. Furthermore, the specific requirements of each institution make it very difficult to suggest a generalized model and a solution algorithm far this problem. The purpose of this study is to design a system far scheduling courses at Bilkent University. This system utilizes both constraint programming and mathematical programming techniques. The problem is solved in three stages. The first two stages, in tandem, generate a course schedule using constraint programming techniques, and in the last stage classrooms are assigned to courses by means of a mixed integer programming model. The proposed system is validated by experimental runs using Bilkent University course offerings and classroom data from past semesters.Item Open Access Towards finding global representations of the efficient set in multiple objective mathematical programming(John Wiley & Sons, 1997) Benson, H. P.; Sayin, S.We propose and justify the proposition that finding truly global representations of the efficient sets of multiple objective mathematical programs is a worthy goal. We summarize the essential elements of a general global shooting procedure that seeks such representations. This procedure illustrates the potential benefits to be gained from procedures for globally representing efficient sets in multiple objective mathematical programming.