Integrated storage space allocation and ship scheduling problem in bulk cargo terminals

This study is motivated by the practices of large iron and steel companies that have steady and heavy demands for bulk raw materials, such as iron ore, coal, limestone, etc. These materials are usually transported to a bulk cargo terminal by ships (or to a station by trains). Once unloaded, they are moved to and stored in a bulk material stockyard, waiting for retrieval for use in production. Efficient storage space allocation and ship scheduling are critical to achieving high space utilization, low material loss, and low transportation costs. In this article, we study the integrated storage space allocation and ship scheduling problem in the bulk cargo terminal. Our problem is different from other associated problems due to the special way that the materials are transported and stored. A novel mixed-integer programming model is developed and then solved using a Benders decomposition algorithm, which is enhanced by the use of various valid inequalities, combinatorial Benders cuts, variable reduction tests, and an iterative heuristic procedure. Computational results indicate that the proposed solution method is much more efficient than the standard solution software CPLEX

A Heuristic Approach to the Consecutive Ones Submatrix Problem

أعطيت مصفوفة (0،1)، تم اقتراح مسألة المصفوفة الجزئية ذات الواحدات المتعاقبة والتي تهدف إلى إيجاد تبديل للأعمدة التي تزيد من عدد الأعمدة التي تحتوي معًا على قالب واحد فقط من الواحدات المتعاقبة في كل صف. سيتم اقتراح اسلوب الاستدلال لحل المسألة. كما سيتم دراسة مسألة تقليل القوالب المتتالية ذات الصلة بمسألة المصفوفة الجزئية ذات الواحدات المتعاقبة. تم اقتراح اجراء جديد لتحسين طريقة إدراج العمود. يتم بعد ذلك تقييم مصفوفات العالم الحقيقي ومصفوفات متولدة عشوائيًا من مسألة غطاء المجموعة و تعرض النتائج الحسابية.Given a matrix, the Consecutive Ones Submatrix (C1S) problem which aims to find the permutation of columns that maximizes the number of columns having together only one block of consecutive ones in each row is considered here. A heuristic approach will be suggested to solve the problem. Also, the Consecutive Blocks Minimization (CBM) problem which is related to the consecutive ones submatrix will be considered. The new procedure is proposed to improve the column insertion approach. Then real world and random matrices from the set covering problem will be evaluated and computational results will be highlighted

Mathematical models and decomposition methods for the multiple knapsack problem

We consider the multiple knapsack problem, that calls for the optimal assignment of a set of items, each having a profit and a weight, to a set of knapsacks, each having a maximum capacity. The problem has relevant managerial implications and is known to be very difficult to solve in practice for instances of realistic size. We review the main results from the literature, including a classical mathematical model and a number of improvement techniques. We then present two new pseudo-polynomial formulations, together with specifically tailored decomposition algorithms to tackle the practical difficulty of the problem. Extensive computational experiments show the effectiveness of the proposed approaches

Reformulation and decomposition of integer programs

In this survey we examine ways to reformulate integer and mixed integer programs. Typically, but not exclusively, one reformulates so as to obtain stronger linear programming relaxations, and hence better bounds for use in a branch-and-bound based algorithm. First we cover in detail reformulations based on decomposition, such as Lagrangean relaxation, Dantzig-Wolfe column generation and the resulting branch-and-price algorithms. This is followed by an examination of Benders’ type algorithms based on projection. Finally we discuss in detail extended formulations involving additional variables that are based on problem structure. These can often be used to provide strengthened a priori formulations. Reformulations obtained by adding cutting planes in the original variables are not treated here.Integer program, Lagrangean relaxation, column generation, branch-and-price, extended formulation, Benders' algorithm

Models and Solutions of Resource Allocation Problems based on Integer Linear and Nonlinear Programming

In this thesis we deal with two problems of resource allocation solved through a Mixed-Integer Linear Programming approach and a Mixed-Integer Nonlinear Chance Constraint Programming approach. In the first part we propose a framework to model general guillotine restrictions in two dimensional cutting problems formulated as Mixed-Integer Linear Programs (MILP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a state of-the-art MIP solver, can tackle instances of challenging size. Our objective is to propose a way of modeling general guillotine cuts via Mixed Integer Linear Programs (MILP), i.e., we do not limit the number of stages (restriction (ii)), nor impose the cuts to be restricted (restriction (iii)). We only ask the cuts to be guillotine ones (restriction (i)). We mainly concentrate our analysis on the Guillotine Two Dimensional Knapsack Problem (G2KP), for which a model, and an exact procedure able to significantly improve the computational performance, are given. In the second part we present a Branch-and-Cut algorithm for a class of Nonlinear Chance Constrained Mathematical Optimization Problems with a finite number of scenarios. This class corresponds to the problems that can be reformulated as Deterministic Convex Mixed-Integer Nonlinear Programming problems, but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows. We apply the Branch-and-Cut algorithm to the Mid-Term Hydro Scheduling Problem, for which we propose a chance-constrained formulation. A computational study using data from ten hydro plants in Greece shows that the proposed methodology solves instances orders of magnitude faster than applying a general-purpose solver for Convex Mixed-Integer Nonlinear Problems to the deterministic reformulation, and scales much better with the number of scenarios

Systems Analysis by Multilevel Methods: With Applications to Economics and Management

This book presents a survey of usable multilevel methods for modeling and solving decision problems in economics and management. The methods are largely extensions of linear programming and fall within the realm of column generation and decomposition. About one third of the book is concerned with methods and the rest describes case studies where these methods have actually been used. They are taken from areas such as national and regional economic planning, production planning, and transportation planning

Solving crew scheduling problem in offshore supply vessels, heuristics and decomposition methods

For the efficient utilisation of resources in various transportation settings, scheduling is a significant area of research. Having crew as the main resource for operation maintenance, scheduling crew have been a powerful decision making tool for optimisation studies. This research provides a detailed real case study analysis regarding the difficulties in planning crew in maritime industry. As a special case study, this thesis researches crew scheduling in offshore supply vessels which are used for specific operations of a global scaled company in oil and gas industry deeply with modified formulations, heuristics and decomposition methods.An extended version of computational study for a simple formulation approach (Task Based Model) is applied as deeper analysis to Leggate (2016). Afterwards, more realistic approach to the same problem is revised. Following the revision, a customized and thorough computational study on the heuristic method with various settings is designed and implemented in C++. After elaborated analysis completed on the suggested models firstly, a modification on Time Windows model is presented to increase the efficacy. This modification provides a sharp decrease in upper bounds within a short time compared to the previously suggested models. Through this suggestion, more economic schedules within a short period of time are generated.Achieving high performances from the modified model, an application of a decomposition algorithm is provided. We implemented a hybrid solution of Benders Decomposition with a customized heuristic for the modified model. Although this hybrid solution does not provide high quality solutions, it evaluates the performance of possible decomposed models with potential improvements for future research. An introduction to robust crew scheduling in maritime context is also given with a description of resources of uncertainty in this concept and initial robust formulations are suggested.For the efficient utilisation of resources in various transportation settings, scheduling is a significant area of research. Having crew as the main resource for operation maintenance, scheduling crew have been a powerful decision making tool for optimisation studies. This research provides a detailed real case study analysis regarding the difficulties in planning crew in maritime industry. As a special case study, this thesis researches crew scheduling in offshore supply vessels which are used for specific operations of a global scaled company in oil and gas industry deeply with modified formulations, heuristics and decomposition methods.An extended version of computational study for a simple formulation approach (Task Based Model) is applied as deeper analysis to Leggate (2016). Afterwards, more realistic approach to the same problem is revised. Following the revision, a customized and thorough computational study on the heuristic method with various settings is designed and implemented in C++. After elaborated analysis completed on the suggested models firstly, a modification on Time Windows model is presented to increase the efficacy. This modification provides a sharp decrease in upper bounds within a short time compared to the previously suggested models. Through this suggestion, more economic schedules within a short period of time are generated.Achieving high performances from the modified model, an application of a decomposition algorithm is provided. We implemented a hybrid solution of Benders Decomposition with a customized heuristic for the modified model. Although this hybrid solution does not provide high quality solutions, it evaluates the performance of possible decomposed models with potential improvements for future research. An introduction to robust crew scheduling in maritime context is also given with a description of resources of uncertainty in this concept and initial robust formulations are suggested