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#### A special class of fuzzy integer programming model with all different constraints [electronic resource]

, Article Scientia Iranica ; Vol. 16, No. 1, pp. 1-10, 2009 ; Nematian, Javad ; Sharif University Of Technology
Abstract

In this paper, a fuzzy approach is applied to special classes of integer programming problems with all diierent constraints. In the rst model, a fuzzy integer programming model is developed to represent the all-diierent constraints in mathematical programming. In order to solve the proposed model, a new branching scheme for the Branch and Bound algorithm is also presented. In the second model, a special class of large-scale multi-objective fuzzy integer programming problems with all-diierent constraints is introduced. A solution method for the proposed model is also developed by using the decomposition technique, weighting method and Branch and Bound algorithm. An illustrative numerical...

####
Discrete Network Design Using Parallel Branch-and-Bound Algorithms

,
M.Sc. Thesis
Sharif University of Technology
;
hafahi, Yusof
(Supervisor)
Abstract

Discrete Network Design (DND) is a classical combinatorial problem in transportation planning. According to its exponential nature, the problem has a costly exact solution. In recent decades, however, the advent of parallel computing facilities motivated researchers to apply exact solutions on many combinatorial problems. As a result, parallel Branch-and-Bound (B&B) algorithms emerged as robust methods to address combinatorial problems. This dissertation will investigate the parallel behavior of B&B algorithms in DND through some case studies. Parallelization results suggest that parallel B&B algorithms can achieve linear speed-ups in DND for a large number of processors

#### Branch and bound algorithms for resource constrained project scheduling problem subject to nonrenewable resources with prescheduled procurement

, Article Mathematical Problems in Engineering ; Vol. 2014, issue , 2014 ; ISSN: 1024123X ; Shadrokh, S ; Fathi, Y ; Sharif University of Technology
Abstract

A lot of projects in real life are subject to some kinds of nonrenewable resources that are not exactly similar to the type defined in the project scheduling literature. The difference stems from the fact that, in those projects, contrary to the common assumption in the project scheduling literature, nonrenewable resources are not available in full amount at the beginning of the project, but they are procured along the project horizon. In this paper, we study this different type of nonrenewable resources. To that end, we extend the resource constrained project scheduling problem (RCPSP) by this resource type (RCPSP-NR) and customize four basic branch and bound algorithms of RCPSP for it,...

#### A branch and bound algorithm for the dynamic quantity discount lot sizing

, Article 38th International Conference on Computers and Industrial Engineering 2008 ; Volume 3 , 2008 , Pages 2996-3005 ; 9781627486828 (ISBN) ; Shadrokh, S ; Sharif University of Technology
2008

Abstract

This paper presents an optimal algorithm based on Branch and Bound approach for determining lot sizes for purchased component in Material Requirement Planning (MRP) environments with deterministic dynamic demand pattern and constant ordering cost with zero lead time, where all units discounts are available from vendors and shortage is not allowed. Based on the properties of an optimal order policy proven in the literature, a tree search procedure is designed to construct sequences of orders in the optimal policy. Some useful fathom rules have been proven to make the algorithm very efficient. Copyright©(2008) by Computers & Industrial Engineering

#### An algorithm for the weighted earliness-tardiness unconstrained project scheduling problem

, Article Journal of Applied Sciences ; Volume 8, Issue 9 , 2008 , Pages 1651-1659 ; 18125654 (ISSN) ; Shadrokh, S ; Sharif University of Technology
2008

Abstract

This research considers a project scheduling problem with the object of minimizing weighted earliness-tardiness penalty costs, taking into account a deadline for the project and precedence relations among the activities. An exact recursive method has been proposed for solving the basic form of this problem. We present a new depth-first branch and bound algorithm for extended form of the problem, which time value of money is taken into account by discounting the cash flows. The algorithm is extended with two bounding rules in order to reduce the size of the branch and bound tree. Finally, some test problems are solved and computational results are reported. © 2008 Asian Network for Scientific...

#### Optimal placement of PMUs for power system observability using topology based formulated algorithms

, Article Journal of Applied Sciences ; Volume 9, Issue 13 , 2009 , Pages 2463-2468 ; 18125654 (ISSN) ; Sharif University of Technology
2009

Abstract

This study presents optimal placement of Phasor Measurement Units (PMUs) for the purpose of power system observability using topology based formulated algorithms. The optimal PMU placement problem is formulated to minimize the number of PMUs installation subject to full network observability. The Branch and Bound (B and B) and genetic algorithm optimization methods are selected to solve the problem, which are suitable for problems with integer and Boolean variables. Topology-based algorithm used for observability analysis and a hybrid method of topology transformation and nonlinear constraint is used to form constraints. The IEEE 14, 30, 57 and 118-bus and the New England 39-bus test systems...

#### Special classes of fuzzy integer programming models with all-different constraints

, Article Scientia Iranica ; Volume 16, Issue 1 E , 2009 , Pages 1-10 ; 10263098 (ISSN) ; Nematian, J ; Sharif University of Technology
2009

Abstract

In this paper, a fuzzy approach is applied to special classes of integer programming problems with all different constraints. In the first model, a fuzzy integer programming model is developed to represent the all-different constraints in mathematical programming. In order to solve the proposed model, a new branching scheme for the Branch and Bound algorithm is also presented. In the second model, a special class of large-scale multi-objective fuzzy integer programming problems with all-different constraints is introduced. A solution method for the proposed model is also developed by using the decomposition technique, weighting method and Branch and Bound algorithm. An illustrative numerical...

#### A branch-and-bound algorithm for the single machine sequence-dependent group scheduling problem with earliness and tardiness penalties

, Article Applied Mathematical Modelling ; 2015 ; 0307904X (ISSN) ; Savelsbergh, M ; Salmasi, N ; Sharif University of Technology
2015

Abstract

The NP-hard single machine sequence-dependent group scheduling problem with minimization of total weighted earliness and tardiness is investigated. An arc-time-indexed formulation is presented and a Lagrangian-based branch-and-bound algorithm is proposed. The Lagrangian relaxation of the arc-time-indexed formulation is solved as a shortest path problem. The results of an extensive computational study demonstrate the efficacy of the proposed algorithm and establish characteristics of some hard to solve instances

#### A branch-and-bound algorithm for the single machine sequence-dependent group scheduling problem with earliness and tardiness penalties

, Article Applied Mathematical Modelling ; Volume 39, Issue 20 , October , 2015 , Pages 6410–6424 ; 0307904X (ISSN) ; Savelsbergh, M ; Salmasi, N ; Sharif University of Technology
Abstract

The NP-hard single machine sequence-dependent group scheduling problem with minimization of total weighted earliness and tardiness is investigated. An arc-time-indexed formulation is presented and a Lagrangian-based branch-and-bound algorithm is proposed. The Lagrangian relaxation of the arc-time-indexed formulation is solved as a shortest path problem. The results of an extensive computational study demonstrate the efficacy of the proposed algorithm and establish characteristics of some hard to solve instances

#### A branch and bound algorithm for the dynamic quantity discount lot size problem with resale

, Article 38th International Conference on Computers and Industrial Engineering 2008, Beijing, 31 October 2008 through 2 November 2008 ; Volume 1 , 2008 , Pages 3-11 ; 9781627486828 (ISBN) ; Shadrokh, S ; Sharif University of Technology
2008

Abstract

This paper presents an optimal algorithm based on Branch and Bound approach for determining lot sizes for purchased component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and constant ordering cost with zero lead time. Backlog is not permitted and the unit purchasing price depends on the quantity of an order and resale of the excess is possible at the ordering time. We assume an all-units discount system with single price break point. Based on proven properties of an optimal order policy, a tree search procedure is designed to construct the sequences of orders and resales amount in optimal order policy. Some useful fathom rules have been proven to...

#### An optimal procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem

, Article Computers and Industrial Engineering ; Volume 62, Issue 1 , 2012 , Pages 264-270 ; 03608352 (ISSN) ; Khalilzadeh, M ; Kianfar, F ; Etminani, K ; Sharif University of Technology
Abstract

We present an optimal solution procedure for minimizing total weighted resource tardiness penalty costs in the resource-constrained project scheduling problem. In this problem, we assume the constrained renewable resources are limited to very expensive equipments and machines that are used in other projects and are not available in all periods of time of a project. In other words, for each resource, there is a dictated ready date as well as a due date such that no resource can be available before its ready date but the resources are permitted to be used after their due dates by paying penalty cost depending on the resource type. We also assume that only one unit of each resource type is...

#### Accelerating the performance of parallel depth-first-search branch-and-bound algorithm in transportation network design problem

, Article ICORES 2015 - 4th International Conference on Operations Research and Enterprise Systems, Proceedings, 10 January 2015 through 12 January 2015 ; January , 2015 , Pages 359-366 ; 9789897580758 (ISBN) ; Shafahi, Y ; Sharif University of Technology
SciTePress
2015

Abstract

Transportation Network Design Problem (TNDP) aims at selection of a subset of proposed urban projects in budget constraint to minimize the network users' total travel time. This is a well-known resource-intensive problem in transportation planning literature. Application of parallel computing, as a result, can be useful to address the exact solution of TNDP. This paper is going to investigate how the performance of a parallel Branch-and-Bound (B&B) algorithm with Depth-First-Search (DFS) strategy can be accelerated. The paper suggests assigning greedy solutions to idle processors at the start of the algorithm. A greedy solution, considered in this paper, is a budget-wise feasible selection...

#### A hybrid polynomial-time algorithm for the dynamic quantity discount lot size model with resale

, Article Computers and Operations Research ; Volume 39, Issue 7 , 2012 , Pages 1771-1778 ; 03050548 (ISSN) ; Eshghi, K ; Sharif University of Technology
Abstract

We propose an efficient optimal algorithm for determining the lot sizes for purchase component in Material Requirement Planning (MRP) environments with deterministic time-phased demand and zero lead time. In this model, backlog is not permitted, the unit purchasing price is based on the all-units discount system with single price break point and resale of the excess units is acceptable at the ordering time. The problem is divided into the sub-plans with specific properties by the dynamic programming (DP) method already presented. By modifying the main structure of the DP method, we present a branch-and-bound algorithm to obtain the optimal ordering policy for each sub-plans. Furthermore, we...

#### Parallelization of the branch-and-bound algorithm in transportation discrete network design problem

, Article Scientia Iranica ; Volume 23, Issue 2 , 2016 , Pages 407-419 ; 10263098 (ISSN) ; Shafahi, Y ; Sharif University of Technology
Sharif University of Technology

Abstract

Transportation Discrete Network Design Problem (TDNDP) aims at choosing a subset of proposed projects to minimize the users' total travel time with respect to a budget constraint. Because TDNDP is a hard combinatorial problem, recent research has widely addressed heuristic approaches and ignored the exact solution. This paper explores how application of parallel computation can affect the performance of an exact algorithm in TDNDP. First, we show that the Branch-and-Bound (B&B) algorithm, proposed by LeBlanc, is well adapted to a parallel design with synchronized Master-Slave (MS) paradigm. Then, we develop a parallel B&B algorithm and implement it with two search strategies of...

#### A branch and bound algorithm for the weighted earliness-tardiness project scheduling problem with generalized precedence relations

, Article Scientia Iranica ; Volume 16, Issue 1 E , 2009 , Pages 55-64 ; 10263098 (ISSN) ; Shadrokh, S ; Sharif University of Technology
2009

Abstract

In this paper, an exact solution procedure is presented for the Weighted Earliness-Tardiness Project Scheduling Problem (WETPSP) with Generalized Precedence Relations (WETPSP-GPR), taking into account the time value of money (WETPSPDC-GPR) and a fixed deadline for the project. The WETPSP-GPR extends the WETPSP to arbitrary minimal and maximal time-lags between the starting and completion times of activities. We present a new depth-first Branch and Bound (B&B) algorithm for an extended form of the problem, in which the time value of money is taken into account by discounting cash flows, and minimum, as well as maximum, time-lags between different activities may be given. The algorithm is...

#### Optimal PMU placement for power system observability considering secondary voltage control

, Article IEEE Canadian Conference on Electrical and Computer Engineering, CCECE 2008, Niagara Falls, ON, 4 May 2008 through 7 May 2008 ; 2008 , Pages 365-368 ; 08407789 (ISSN) ; 9781424416431 (ISBN) ; Hosseini, S. H ; Sharif University of Technology
2008

Abstract

This paper presents an optimal phasor measurement units (PMUs) placement algorithm for the purpose of power system observability and also increasing the performance of secondary voltage control scheme. The optimal placement problem (OPP) is formulated such that to minimize the number of PMU installations subject to full network observability and monitoring pilot buses of the system to improve secondary voltage control performance. The branch and bound optimization method is adopted to solve the OPP problem which is suitable for problems with integer and boolean variables. Topology-based algorithm is used for observability analysis. Constraint functions considering adjacent zero-injection...