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A branch-and-price algorithm for 2-period vehicle routing problems Crama, Yves ; Rezaei Sadrabadi, Mahmood ; E-print/Working paper (2015) We consider a Vehicle Routing Problem (VRP) with deterministic orders in two periods from a set of stores. Orders in period 1 (2) can be postponed (advanced) to the other period but any diversion from the ... [more ▼] We consider a Vehicle Routing Problem (VRP) with deterministic orders in two periods from a set of stores. Orders in period 1 (2) can be postponed (advanced) to the other period but any diversion from the initial orders incurs a penalty. From the perspective of a Logistics Service Provider (LSP), such diversions could be beneficial if savings in the routing costs outweigh the penalties. So could they be from a store's view, as the store can set a high enough penalty to compensate the diversion from its own optimal orders. In this paper, we introduce a new model where we seek a better solution for the LSP, compared to solving two independent VRPs with fixed orders, by allowing orders to be fully postponed or advanced. We apply a branch-and-price algorithm to solve this model to optimality. Many cutting-edge techniques are implemented to have an efficient branch-and-price algorithm, and two ideas to possibly improve the upper bound are tested. We draw algorithmic and managerial insights based on our test instances. [less ▲] Detailed reference viewed: 112 (7 ULg)Branch-and-price: principles and its application to a 2-period vehicle routing problem Rezaei Sadrabadi, Mahmood Scientific conference (2013, April 05) We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch ... [more ▼] We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch-and-price. Implementation of branch-and-price to solve the most basic version of the well-known vehicle routing problem (VRP) is investigated, and some common tricks are introduced. Then, a new extension of VRP is introduced and exploitation of branch-and-price to solve it is discussed. We consider a 2-period vehicle routing problem where each vertex of the network has a positive demand for period 1, 2, or both. Each demand on period 1 can be postponed to period 2 in order to decrease sum of the routing costs on two periods, but it is penalized in the objective function. Similarly, each demand on period 2 can be advanced to period 1, and yet penalized, with the hope of reducing routing costs. We have used many of the classic tricks to implement branch-and-price for solving our 2-period VRP. We have also used new tricks to (1) possibly improve the upper bound during the course of column generation in each node and (2) decrease the computations time to solve pricing problem in column generation. [less ▲] Detailed reference viewed: 38 (1 ULg)Branch-and-price: principles and its application to a 2-period vehicle routing problem Rezaei Sadrabadi, Mahmood Scientific conference (2013, April 05) We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch ... [more ▼] We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch-and-price. Implementation of branch-and-price to solve the most basic version of the well-known vehicle routing problem (VRP) is investigated, and some common tricks are introduced. Then, a new extension of VRP is introduced and exploitation of branch-and-price to solve it is discussed. We consider a 2-period vehicle routing problem where each vertex of the network has a positive demand for period 1, 2, or both. Each demand on period 1 can be postponed to period 2 in order to decrease sum of the routing costs on two periods, but it is penalized in the objective function. Similarly, each demand on period 2 can be advanced to period 1, and yet penalized, with the hope of reducing routing costs. We have used many of the classic tricks to implement branch-and-price for solving our 2-period VRP. We have also used new tricks to (1) possibly improve the upper bound during the course of column generation in each node and (2) decrease the computations time to solve pricing problem in column generation. [less ▲] Detailed reference viewed: 14 (1 ULg)Branch-and-price: principles and its application to a 2-period vehicle routing problem Rezaei Sadrabadi, Mahmood Scientific conference (2013, March 07) We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch ... [more ▼] We review branch-and-price as an efficient algorithm to solve integer programming problems with huge number of variables. In particular, we discuss column generation algorithm as the main engine in branch-and-price. Implementation of branch-and-price to solve the most basic version of the well-known vehicle routing problem (VRP) is investigated, and some common tricks are introduced. Then, a new extension of VRP is introduced and exploitation of branch-and-price to solve it is discussed. We consider a 2-period vehicle routing problem where each vertex of the network has a positive demand for period 1, 2, or both. Each demand on period 1 can be postponed to period 2 in order to decrease sum of the routing costs on two periods, but it is penalized in the objective function. Similarly, each demand on period 2 can be advanced to period 1, and yet penalized, with the hope of reducing routing costs. We have used many of the classic tricks to implement branch-and-price for solving our 2-period VRP. We have also used new tricks to (1) possibly improve the upper bound during the course of column generation in each node and (2) decrease the computations time to solve pricing problem in column generation. [less ▲] Detailed reference viewed: 17 (1 ULg)A heuristic method to schedule training programs for Small and Medium Enterprises Rezaei Sadrabadi, Mahmood ; ; et al in European Journal of Operational Research (2012), 217 During the life period of Small and Medium Enterprises (SMEs) in incubators they need some training programs to acquire the required knowledge in order to survive and succeed in the business environment ... [more ▼] During the life period of Small and Medium Enterprises (SMEs) in incubators they need some training programs to acquire the required knowledge in order to survive and succeed in the business environment. This paper presents a heuristic method based on an optimization model to schedule these programs at the most suitable times. Based on the proposed heuristic, each training program is implemented in a suitable time by considering the SMEs’ requirements and some other logical constraints. The proposed heuristic is described in detail, and its implementation is demonstrated via a real-life numerical example. The numerical results of the heuristic are compared with other methods. [less ▲] Detailed reference viewed: 74 (9 ULg)Identification of the linear parts of nonlinear systems for fuzzy modeling Rezaei Sadrabadi, Mahmood in Applied Soft Computing (2011), 11 In direct approach to fuzzy modeling, structure identification is one of the most critical tasks. In modeling the nonlinear system, this fact is more crucial. In this paper, a new hybrid method is ... [more ▼] In direct approach to fuzzy modeling, structure identification is one of the most critical tasks. In modeling the nonlinear system, this fact is more crucial. In this paper, a new hybrid method is proposed to cluster the data located in the linear parts on the nonlinear systems. The proposed method can partition the input–output data in two groups: data located in the linear parts and data in the extrema. It is shown that the first group of data is suitable to be clustered by Fuzzy C-Regression Model (FCRM) clustering algorithm and the second group by Fuzzy C-Means (FCM). Then, based on the above findings, a new hybrid clustering algorithm is proposed. Finally, the proposed approach is tested and validated by several numerical examples of nonlinear functions. [less ▲] Detailed reference viewed: 57 (30 ULg)Facility location via fuzzy modeling and simulation Rezaei Sadrabadi, Mahmood ; in Applied Soft Computing (2011), 11(8), 5330-5340 This paper presents a continuous facility location model with fuzzy methodology. The developments concern mainly to some drawbacks in the initial model which takes it far from being used in practice. A ... [more ▼] This paper presents a continuous facility location model with fuzzy methodology. The developments concern mainly to some drawbacks in the initial model which takes it far from being used in practice. A fuzzy modeling method is proposed to estimate the required functions in the initial model. Structure identification in the proposed fuzzy modeling method is carried out using subtractive clustering, and parameter identification is conducted via some heuristics as well as an optimization problem. Furthermore, a simulation method along with some heuristic relations is used for implementation and evaluation of the modified model. Efficiency of the proposed method to fuzzy modeling as well as the proposed simulation method is presented by a numerical example. [less ▲] Detailed reference viewed: 184 (21 ULg)A new method to fuzzy modeling and its application in performance evaluation of tenants in incubators Rezaei Sadrabadi, Mahmood in International Journal of Advanced Manufacturing Technology (2008), 37 As we know fuzzy modeling is one of the most powerful techniques to extract experts’ knowledge in the form of fuzzy if-then rules. In this research work, a new method to fuzzy modeling is proposed in ... [more ▼] As we know fuzzy modeling is one of the most powerful techniques to extract experts’ knowledge in the form of fuzzy if-then rules. In this research work, a new method to fuzzy modeling is proposed in which the main goal is to construct a fuzzy rule-base of the type of Mamdani. In the proposed method, fuzzy c-means (FCM) clustering is used for structure identification and two optimization problems are used for parameter identification. The proposed method is used to simulate experts’ knowledge for performance evaluation of tenants in incubators. The authors have implemented their proposed method in a real numerical example successfully. [less ▲] Detailed reference viewed: 31 (4 ULg) |
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