In this paper we study the Resource Allocation (RA) in Orthogonal Frequency Division Multiplexing (OFDM)-based Cognitive Radio (CR) networks, under the consideration of many practical limitations such as imperfect spe...
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In this paper we study the Resource Allocation (RA) in Orthogonal Frequency Division Multiplexing (OFDM)-based Cognitive Radio (CR) networks, under the consideration of many practical limitations such as imperfect spectrum sensing, limited transmission power, different traffic demands of secondary users, etc. The general RA optimization framework leads to a complex mixed integer programming task which is computationally intractable. We propose to address this hard task in two steps. For the first step, we perform subchannel allocation to satisfy heterogeneous users' rate requirements roughly and remove the intractable integer constraints of the optimization problem. For the second step, we perform power distribution among the OFDM subchannels. By exploiting the problem structure to speedup the Newton step, we propose a barrier-based method which is able to achieve the optimal power distribution with an almost linear complexity, significantly better than the complexity of standard techniques. Moreover, we propose a method which is able to approximate the optimal solution with a constant complexity. Numerical results validate that our proposal exploits the overall capacity of CR systems well subjected to different traffic demands of users and interference constraints with given power budget.
This paper studies the problem of constructing the workforce schedules of an aircraft maintenance company. The problem involves both a staffing and a scheduling decision. We propose an enumerative algorithm with bound...
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This paper studies the problem of constructing the workforce schedules of an aircraft maintenance company. The problem involves both a staffing and a scheduling decision. We propose an enumerative algorithm with bounding in which each node of the enumeration tree represents a mixedinteger linear problem (MILP). We reformulate the MILP such that it becomes tractable for commercial MILP solvers. Extensive computational tests on 40 instances that are derived from a real-life setting indicate that the algorithm is capable of finding close-to-optimal solutions. (C) 2012 Elsevier Ltd. All rights reserved.
This paper deals with the optimal selection and protection of part suppliers and order quantity allocation in a supply chain with disruption risks. The protection decisions include the selection of suppliers to be pro...
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This paper deals with the optimal selection and protection of part suppliers and order quantity allocation in a supply chain with disruption risks. The protection decisions include the selection of suppliers to be protected against disruptions and the allocation of emergency inventory of parts to be pre-positioned at the protected suppliers. The decision maker needs to decide which supplier to select for parts delivery and how to allocate orders quantity among the selected suppliers, and which of the selected suppliers to protect against disruptions and how to allocate emergency inventory among the protected suppliers. The problem objective is to achieve a minimum cost of suppliers protection, emergency inventory pre-positioning, parts ordering, purchasing, transportation and shortage and to mitigate the impact of disruption risks by minimizing the potential worst-case cost. As a result a resilient supply portfolio is identified with protected suppliers capable of supplying parts in the face of disruption events. A mixed integer programming approach is proposed to determine risk-neutral, risk-averse or mean-risk supply portfolios, with conditional value-at-risk applied to control the risk of worst-case cost. Numerical examples are presented and some computational results are reported. (C) 2012 Elsevier Ltd. All rights reserved.
This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and sh...
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This research considers a stochastic lot-sizing problem with multi-supplier and quantity discounts. The objectives are to minimise total costs, where the costs include ordering cost, holding cost, purchase cost and shortage cost, and to maximise service level of the system. In this paper, we first formulate the stochastic lot-sizing problem as a multi-objective programming (MOP) model. We then transform the model into a mixed integer programming (MIP) model. Finally, an efficient heuristic dynamic programming (HDP) model is constructed for solving large-scale stochastic lot-sizing problems. An illustrative example with two cases for a touch panel manufacturer is used to illustrate the practicality of these models, and a sensitivity analysis is applied to understand the impact of the changes in parameters to the outcomes. The results demonstrate that the proposed two models are effective and accurate tools for determining the replenishment of touch panels from multiple suppliers for multi-periods.
Adequate response performance is required for the planning of a cooperative logistic network covering multiple enterprises, because this process needs a human expert's evaluation from many aspects. To satisfy this...
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Adequate response performance is required for the planning of a cooperative logistic network covering multiple enterprises, because this process needs a human expert's evaluation from many aspects. To satisfy this requirement, we propose an accurate model based on mixed integer programming for optimizing cooperative logistics networks where "round transportation" exists together with "depot transportation" including lower limit constraints of loading ratio for round transportation vehicles. Furthermore, to achieve interactive response performance, a dummy load is introduced into the model instead of integer variables. The experimental result shows the proposed method obtains an accurate solution within interactive response time. (c) 2008 Wiley Periodicals, Inc.
We address short-term batch process scheduling problems contaminated with uncertainty in the data. The mixedinteger linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, In...
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We address short-term batch process scheduling problems contaminated with uncertainty in the data. The mixedinteger linear programming (MILP) scheduling model, based on the formulation of Ierapetritou and Floudas, Ind Eng Chem Res. 1998;37(11):4341-4359, contains parameter dependencies at multiple locations, yielding a general multiparametric (mp) MILP problem. A proactive scheduling policy is obtained by solving the partially robust counterpart formulation. The counterpart model may remain a multiparametric problem, yet it is immunized against uncertainty in the entries of the constraint matrix and against all parameters whose values are not available at the time of decision making. We extend our previous work on the approximate solution of mp-MILP problems by embedding different uncertainty sets (box, ellipsoidal and budget parameter regulated uncertainty), and by incorporating information about the availability of uncertain data in the construction of the partially robust scheduling model. For any parameter realization, the corresponding schedule is then obtained through function evaluation. (c) 2013 American Institute of Chemical Engineers AIChE J, 59: 4184-4211, 2013
Transformer design optimization is determined by minimizing the transformer cost taking into consideration constraints imposed both by international specifications and customer needs. The main purpose of this work is ...
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Transformer design optimization is determined by minimizing the transformer cost taking into consideration constraints imposed both by international specifications and customer needs. The main purpose of this work is the development and validation of an optimization technique based on a parallel mixedinteger nonlinear programming methodology in conjunction with the finite element method, in order to reach a global optimum design of wound core power transformers. The proposed optimization methodology has been implemented into software able to provide a global feasible solution for every given set of initial values for the design variables, rendering it suitable for application in the industrial transformer design environment.
In modern MIP solvers, primal heuristics play a key role in finding high-quality solutions. However, classical performance measures reflect the impact of primal heuristics on the overall solving process badly. In this...
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In modern MIP solvers, primal heuristics play a key role in finding high-quality solutions. However, classical performance measures reflect the impact of primal heuristics on the overall solving process badly. In this article, we introduce a new performance measure, the "primal integral", which depends on the quality of solutions and on the time when they are found. We compare five state-of-the-art MIP solvers w.r.t. the newly proposed measure, and show that heuristics improve their performance by up to 80%. (C) 2013 Elsevier B.V. All rights reserved.
This paper presents a timetable rescheduling algorithm based on mixed integer programming (MIP) formulation when train traffic is disrupted. We minimize further inconvenience to passengers instead of consecutive delay...
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This paper presents a timetable rescheduling algorithm based on mixed integer programming (MIP) formulation when train traffic is disrupted. We minimize further inconvenience to passengers instead of consecutive delays caused by the disruption, since loss of time and satisfaction of the passengers are considered implicitly and insufficiently in the latter optimization. We presume that inconvenience of traveling by train consists of the traveling time on board, the waiting time at platforms and the number of transfers. Hence, the objective function is calculated on the positive difference between the inconvenience which each passenger suffers on his/her route in a rescheduled timetable and that in a planned timetable. The inconvenience-minimized rescheduling is often achieved at the cost of further train delays. Some trains dwell longer at a station to wait for extra passengers to come or to keep a connection, for instance. In the MIP model, train operation, each passenger's behavior and the amount inconvenience are simultaneously expressed by a system of integer linear inequalities. As countermeasures against the disruption, changes of train types and rolling stock operation schedules at termini as well as changes of departing order of trains and assignment of a track to trains in stations are performed. We also consider capacities of a line between adjacent stations as well as those of a track in stations. We have conducted numerical experiments using actual data and have obtained better rescheduled timetables in terms of customer satisfaction within practical time in proper solution space. (C) 2013 The Authors. Published by Elsevier Ltd.
In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to ...
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In automated test assembly (ATA), 0-1 linear programming (0-1 LP) methods are applied to select questions (items) from an item bank to assemble an optimal test. The objective in this 0-1 LP optimization problem is to assemble a test that measures, in as precise a way as possible, the ability of candidates. Item response theory (IRT) is commonly applied to model the relationship between the responses of candidates and their ability level. Parameters that describe the characteristics of each item, such as difficulty level and the extent to which an item differentiates between more and less able test takers (discrimination) are estimated in the application of the IRT model. Unfortunately, since all parameters in IRT models have to be estimated, they do have a level of uncertainty to them. Some of the other parameters in the test assembly model, such as average response times, have been estimated with uncertainty as well. General 0-1 LP methods do not take this uncertainty into account, and overestimate the predicted level of measurement precision. In this paper, alternative robust optimization methods are applied. It is demonstrated how the Bertsimas and Sim method can be applied to take this uncertainty into account in ATA. The impact of applying this method is illustrated in two numerical examples. Implications are discussed, and some directions for future research are presented.
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