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#### Application of Branch-and-bound Method, Scatter Search Algorithm, and Particle Swarm Optimization Method in Solving Some Resource-Constrained Project Scheduling Problems

, Ph.D. Dissertation Sharif University of Technology ; Kianfar, Fereydoon (Supervisor) ; Rowghangar Ranjbar, Mohammad (Supervisor)
Abstract

The main goal of this thesis is to reduce the gap between the theoretical and actual project scheduling problems by introducing three problems and then proposing three different exact and meta-heuristic algorithms to solve them. These problems are as follows: the Resource-Constrained Project Scheduling Problem with Minimization of Total Weighted Resource Tardiness Penalty Costs (RCPSP-TWRTPC), the Resource-Constrained Project Scheduling Problem with Discounted Cash Flows of Weighted Earliness-Tardiness Costs (RCPSP-DCWET), and the Multi-Mode Resource-Constrained Project Scheduling Problem with Minimization of Total Weighted Resource Tardiness Penalty Costs (MRCPSP-TWRTPC). Also, we develop a...

#### 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...

#### , M.Sc. Thesis Sharif University of Technology ; Eshghi, Koorosh (Supervisor)

Abstract

The focus of this research is to present a model to verify the acceptance of projects with time and cost dependency on the usage of equipments. Decision on these projects is based on a dynamic programming in which at each stage, the profit of available projects in this stage, equipment value and the best choice of future stage are decision keys. In other words, after the completion of a project, it should be decided between doing a project or selling the equipment and leaving the remaining projects. For each projects, there is a product network that includes projects jobs and operations. After accepting projects, equipments of the projects will not be renewed and the usage of the equipments...

#### Robust Scheduling to Hedge Against Processing Time Uncertainty in Flow Shop

, M.Sc. Thesis Sharif University of Technology ; Salmasi, Naser (Supervisor)
Abstract

This study focuses on two-machine flow shop problem where processing times are uncertain and the objective function is makespan. All information available about the processing time is an upper and lower bound and also expected value. The min-max and min-max regret version of the problem are adopted. In this study, in order to control the degree of conservatism of the solution, we suppose in each scenario the number of processing times on each machine that can deviate from its expected value is controllable. By considering the duality theorem, we present a mixed-integer programming model for the min-max problem. For each of two problems, we present an algorithm for finding objective value. We...

#### Material Ordering in a Deterministic Time-Phased Demand Environment with All-Units Discount in Purchasing

, Ph.D. Dissertation Sharif University of Technology ; Shadrokh, Shahram (Supervisor)
Abstract

More than 60% of sales account for materials, and so the roles and responsibilities of the material managers have been recognized as more important within a firm or in a large scale project than before. However, in many purchasing situations, different considerations conflict with one another. In these situations material planning plays an essential role in the total cost minimization process. Here, the optimal material ordering policy for an item in a deterministic time-phased demand environment with all-units discount in purchasing is considered. Based on proven properties of the optimal order policy, a tree search procedure is designed to construct sequences of orders in the optimal...

#### 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

#### Branch and bound algorithms for resource constrained project scheduling problem subject to cumulative resources

, Article Proceedings - 2011 4th International Conference on Information Management, Innovation Management and Industrial Engineering, ICIII 2011, 26 November 2011 through 27 November 2011, Shenzhen ; Volume 1 , 2011 , Pages 147-152 ; 9780769545233 (ISBN) ; Shadrokh, S ; Sharif University of Technology
Abstract

Renewable and nonrenewable resources are the most studied resource types in the field of resource-constrained project scheduling problems, however cumulative resources are another type of resources, widespread in practical cases that have been theoretically studied much less than the two aforementioned types. So in the current paper we study resource-constrained project scheduling problem subject to cumulative resources (RCPSP-Cu), focusing on development of exact algorithms for the problem. We customize three resource-constrained project scheduling problem (RCPSP) branch and bound algorithms of extension alternatives, minimal delaying alternatives and minimal forbidden sets for RCPSP-Cu. We...

#### 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

#### An exact algorithm for the minimum dilation triangulation problem

, Article Journal of Global Optimization ; Volume 69, Issue 2 , 2017 , Pages 343-367 ; 09255001 (ISSN) ; Izadi, M ; Sharif University of Technology
Abstract

Given a triangulation of a point set on the plane, dilation of any pair of the points is the ratio of their shortest path length to their Euclidean distance. The maximum dilation over all pairs of points is called the dilation of this triangulation. Minimum dilation triangulation problem seeks a triangulation with the least possible dilation of an input point set. For this problem no polynomial time algorithm is known. We present an exact algorithm based on a branch and bound method for finding minimum dilation triangulations. This deterministic algorithm after generating an initial solution, iteratively computes a lower bound for the answer and then applies a branch and bound method to find...

#### 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...

#### Project Scheduling Subject to Nonrenewable Resource with Proscheduled Procurement

, Ph.D. Dissertation Sharif University of Technology ; Shadrokh, Shahram (Supervisor)
Abstract

Among various types of resources defined in the project scheduling literature, the most studies have been conducted on the renewable and nonrenewable resource types. Definition of different resources in the project scheduling literature is based on the specification of the resources in the real projects. Yet there are some sort of nonrenewable resources in the real projects that are not exactly similar to the type defined in the project scheduling literature. The difference stems from this fact that in the project scheduling literature, it is supposed that the nonrenewable resources required for the execution of the project activities are available in full amount at the beginning of the...

#### 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...

#### Financially embedded facility location decisions on designing a supply chain structure: A case study

, Article Systems Engineering ; Volume 21, Issue 6 , 2018 , Pages 520-533 ; 10981241 (ISSN) ; Jalali, S ; Akhavan Niaki, S. T ; Sharif University of Technology
John Wiley and Sons Inc
2018

Abstract

The facility location problem and its related financial issues have a significant impact on the configuration of a supply chain structure (SCS). Although affording the setup cost of facilities requires a huge financial investment, a meticulous planning to recoup it has been neglected by an overwhelming majority of previous studies. To fill this gap, an economical investment plan of facilities is determined by striking a trade-off between the contribution of the stockholders’ capital and the loan arrangement. In the context of a multiperiod three-echelon SCS, the model also determines the optimum location of plants and the best supply and distribution patterns. The model maximizes the fill...

#### Two-machine flow shop scheduling to minimize the sum of maximum earliness and tardiness

, Article International Journal of Production Economics ; Volume 122, Issue 2 , 2009 , Pages 763-773 ; 09255273 (ISSN) ; Mirzaee, M ; Vasei, M ; Modarres, M ; Azaron, A ; Sharif University of Technology
2009

Abstract

This paper presents optimal scheduling in a two-machine flow shop, in which the objective function is to minimize the sum of maximum earliness and tardiness (n/2/P/ETmax). Since this problem tries to minimize earliness and tardiness, the results can be useful for different production systems such as just in time (JIT). This objective function has already been considered for n jobs and m machines, but the proposed algorithms are not efficient to solve large scale problems. In this paper, neighborhood conditions are developed and the dominant set for any optimal solution is determined. The branch-and-bound (B&B) method is used to solve the problem and the proper upper and lower bounds are also...

#### 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...

#### Exhaustive search for long low autocorrelation binary codes using length-increment algorithm

, Article RADAR 2007 - The Institution of Engineering and Technology International Conference on Radar Systems, Edinburgh, 15 October 2007 through 18 October 2007 ; Issue 530 CP , 2007 ; 9780863418488 (ISBN) ; Bastani, M. H ; Sharif University of Technology
2007

Abstract

Finding binary sequences with low autocorrelation is very important in many applications and their construction is a hard computational problem. Here a new exhaustive search algorithm is developed to find all optimal aperiodic binary sequences which are faster than simple one and it achieves its efficiency through a combination of the following four devices: (1) A branch-and-bound search strategy; (2) Search logic that avoids codes redundant relative to two PSL-preserving operations; (3) A fast recursive method for computing autocorrelation functions of binary sequences; (4) A simple scheme for partitioning and parallelizing, made possible by the fixed upper bound on psl