Asynchronous teams for joint lot-sizing and scheduling problem in flow shops

The integrated production scheduling and lot-sizing problem in a flow shop environment consists of establishing production lot sizes and allocating machines to process them within a planning horizon in a production line with machines arranged in series. The problem considers that demands must be met without backlogging, the capacity of the machines must be respected, and machine setups are sequence-dependent and preserved between periods of the planning horizon. The objective is to determine a production schedule to minimise the setup, production and inventory costs. A mathematical model from the literature is presented, as well as procedures for obtaining feasible solutions. However, some of the procedures have difficulty in obtaining feasible solutions for large-sized problem instances. In addition, we address the problem using different versions of the Asynchronous Team (A-Team) approach. The procedures were compared with literature heuristics based on Mixed Integer Programming. The proposed A-Team procedures outperformed the literature heuristics, especially for large instances. The developed methodologies and the results obtained are presented.

Computing primal solutions with exact arithmetics in SCIP.

The research for exact solutions of mixed integer problems is an active topic in the scientific community. State-of-the-art MIP solvers exploit a floating- point numerical representation, therefore introducing small approximations. Although such MIP solvers yield reliable results for the majority of problems, there are cases in which a higher accuracy is required. Indeed, it is known that for some applications floating-point solvers provide falsely feasible solutions, i.e. solutions marked as feasible because of approximations that would not pass a check with exact arithmetic and cannot be practically implemented. The framework of the current dissertation is SCIP, a mixed integer programs solver mainly developed at Zuse Institute Berlin. In the same site we considered a new approach for exactly solving MIPs. Specifically, we developed a constraint handler to plug into SCIP, with the aim to analyze the accuracy of provided floating-point solutions and compute exact primal solutions starting from floating-point ones. We conducted a few computational experiments to test the exact primal constraint handler through the adoption of two main settings. Analysis mode allowed to collect statistics about current SCIP solutions' reliability. Our results confirm that floating-point solutions are accurate enough with respect to many instances. However, our analysis highlighted the presence of numerical errors of variable entity. By using the enforce mode, our constraint handler is able to suggest exact solutions starting from the integer part of a floating-point solution. With the latter setting, results show a general improvement of the quality of provided final solutions, without a significant loss of performances.

Optimización de la programación(scheduling) en Talleres de Mecanizado

Los problemas de programación de tareas son muy importantes en el mundo actual. Se puede decir que se presentan en todos los fundamentos de la industria moderna, de ahí la importancia de que estos sean óptimos, de forma que se puedan ahorrar recursos que estén asociados al problema. La programación adecuada de trabajos en procesos de manufactura, constituye un importante problema que se plantea dentro de la producción en muchas empresas. El orden en que estos son procesados, no resulta indiferente, sino que determinará algún parámetro de interés, cuyos valores convendrá optimizar en la medida de lo posible. Así podrá verse afectado el coste total de ejecución de los trabajos, el tiempo necesario para concluirlos o el stock de productos en curso que será generado. Esto conduce de forma directa al problema de determinar cuál será el orden más adecuado para llevar a cabo los trabajos con vista a optimizar algunos de los anteriores parámetros u otros similares. Debido a las limitaciones de las técnicas de optimización convencionales, en la presente tesis se presenta una metaheurística basada en un Algoritmo Genético Simple (Simple Genetic Algorithm, SGA), para resolver problemas de programación de tipo flujo general (Job Shop Scheduling, JSS) y flujo regular (Flow Shop Scheduling, FSS), que están presentes en un taller con tecnología de mecanizado con el objetivo de optimizar varias medidas de desempeño en un plan de trabajo. La aportación principal de esta tesis, es un modelo matemático para medir el consumo de energía, como criterio para la optimización, de las máquinas que intervienen en la ejecución de un plan de trabajo. Se propone además, un método para mejorar el rendimiento en la búsqueda de las soluciones encontradas, por parte del Algoritmo Genético Simple, basado en el aprovechamiento del tiempo ocioso. ABSTRACT The scheduling problems are very important in today's world. It can be said to be present in all the basics of modern industry, hence the importance that these are optimal, so that they can save resources that are associated with the problem. The appropriate programming jobs in manufacturing processes is an important problem that arises in production in many companies. The order in which they are processed, it is immaterial, but shall determine a parameter of interest, whose values agree optimize the possible. This may be affected the total cost of execution of work, the time needed to complete them or the stock of work in progress that will be generated. This leads directly to the problem of determining what the most appropriate order to carry out the work in order to maximize some of the above parameters or other similar. Due to the limitations of conventional optimization techniques, in this work present a metaheuristic based on a Simple Genetic Algorithm (Simple Genetic Algorithm, SGA) to solve programming problems overall flow rate (Job Shop Scheduling, JSS) and regular flow (Flow Shop Scheduling, FSS), which are present in a workshop with machining technology in order to optimize various performance measures in a plan. The main contribution of this thesis is a mathematical model to measure the energy consumption as a criterion for the optimization of the machines involved in the implementation of a work plan. It also proposes a method to improve performance in finding the solutions, by the simple genetic algorithm, based on the use of idle time.

Managing daily surgery schedules in a teaching hospital: a mixed-integer optimization approach

Background: This study examined the daily surgical scheduling problem in a teaching hospital. This problem relates to the use of multiple operating rooms and different types of surgeons in a typical surgical day with deterministic operation durations (preincision, incision, and postincision times). Teaching hospitals play a key role in the health-care system; however, existing models assume that the duration of surgery is independent of the surgeon's skills. This problem has not been properly addressed in other studies. We analyze the case of a Spanish public hospital, in which continuous pressures and budgeting reductions entail the more efficient use of resources. Methods: To obtain an optimal solution for this problem, we developed a mixed-integer programming model and user-friendly interface that facilitate the scheduling of planned operations for the following surgical day. We also implemented a simulation model to assist the evaluation of different dispatching policies for surgeries and surgeons. The typical aspects we took into account were the type of surgeon, potential overtime, idling time of surgeons, and the use of operating rooms. Results: It is necessary to consider the expertise of a given surgeon when formulating a schedule: such skill can decrease the probability of delays that could affect subsequent surgeries or cause cancellation of the final surgery. We obtained optimal solutions for a set of given instances, which we obtained through surgical information related to acceptable times collected from a Spanish public hospital. Conclusions: We developed a computer-aided framework with a user-friendly interface for use by a surgical manager that presents a 3-D simulation of the problem. Additionally, we obtained an efficient formulation for this complex problem. However, the spread of this kind of operation research in Spanish public health hospitals will take a long time since there is a lack of knowledge of the beneficial techniques and possibilities that operational research can offer for the health-care system.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

Mathematical Optimization for the Train Timetabling Problem

AMS Subj. Classification: 90C57; 90C10;

Train scheduling and rolling stock assignment in high speed trains

The Train Timetabling Problem (TTP) has been widely studied for freight and passenger rail systems. A lesser effort has been devoted to the study of high-speed rail systems. A modeling issue that has to be addressed is to model departure time choice of passengers on railway services. Passengers who use these systems attempt to travel at predetermined hours due to their daily life necessities (e.g., commuter trips). We incorporate all these features into TTP focusing on high-speed railway systems. We propose a Rail Scheduling and Rolling Stock (RSch-RS) model for timetable planning of high-speed railway systems. This model is composed of two essential elements: i) an infrastructure model for representing the railway network: it includes capacity constraints of the rail network and the Rolling-Stock constraints; and ii) a demand model that defines how the passengers choose the departure time. The resulting model is a mixed-integer programming model which objective function attempts to maximize the profit for the rail operator

A robust reactive scheduling model for intensive care units

The ICU is an integral part of any hospital and is under great load from patient arrivals as well as resource limitations. Scheduling of patients in the ICU is complicated by the two general types; elective surgery and emergency arrivals. This complicated situation is handled by creating a tentative initial schedule and then reacting to uncertain arrivals as they occur. For most hospitals there is little or no flexibility in the number of beds that are available for use now or in the future. We propose an integer programming model to handle a parallel machine reacting system for scheduled and unscheduled arrivals.

Rostering ambulance services

This paper developed a model for rostering ambulance crew in order to maximise the coverage throughout a planning horizon and minimise the number of ambulance crew. Rostering Ambulance Services is a complex task, which considers a large number of conflicting rules related to various aspects such as limits on the number of consecutive work hours, the number of shifts worked by each ambulance staff and restrictions on the type of shifts assigned. The two-stage models are developed using nonlinear integer programming technique to determine the following sub-problems: the shift start times; the number of staff required to work for each shift; and a balanced schedule of ambulance staff. At the first stage, the first two sub-problems have been solved. At the second stage, the third sub-problem has been solved using the first stage outputs. Computational experiments with real data are conducted and the results of the models are presented.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia.

On the optimal capacity expansion of electric power systems

The analysis of investment in the electric power has been the subject of intensive research for many years. The efficient generation and distribution of electrical energy is a difficult task involving the operation of a complex network of facilities, often located over very large geographical regions. Electric power utilities have made use of an enormous range of mathematical models. Some models address time spans which last for a fraction of a second, such as those that deal with lightning strikes on transmission lines while at the other end of the scale there are models which address time horizons consisting of ten or twenty years; these usually involve long range planning issues. This thesis addresses the optimal long term capacity expansion of an interconnected power system. The aim of this study has been to derive a new, long term planning model which recognises the regional differences which exist for energy demand and which are present in the construction and operation of power plant and transmission line equipment. Perhaps the most innovative feature of the new model is the direct inclusion of regional energy demand curves in the nonlinear form. This results in a nonlinear capacity expansion model. After review of the relevant literature, the thesis first develops a model for the optimal operation of a power grid. This model directly incorporates regional demand curves. The model is a nonlinear programming problem containing both integer and continuous variables. A solution algorithm is developed which is based upon a resource decomposition scheme that separates the integer variables from the continuous ones. The decompostion of the operating problem leads to an interactive scheme which employs a mixed integer programming problem, known as the master, to generate trial operating configurations. The optimum operating conditions of each trial configuration is found using a smooth nonlinear programming model. The dual vector recovered from this model is subsequently used by the master to generate the next trial configuration. The solution algorithm progresses until lower and upper bounds converge. A range of numerical experiments are conducted and these experiments are included in the discussion. Using the operating model as a basis, a regional capacity expansion model is then developed. It determines the type, location and capacity of additional power plants and transmission lines, which are required to meet predicted electicity demands. A generalised resource decompostion scheme, similar to that used to solve the operating problem, is employed. The solution algorithm is used to solve a range of test problems and the results of these numerical experiments are reported. Finally, the expansion problem is applied to the Queensland electricity grid in Australia

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Metaheuristics for minimizing the makespan of the dynamic shop scheduling problem

For the shop scheduling problems such as flow-shop, job-shop, open-shop, mixed-shop, and group-shop, most research focuses on optimizing the makespan under static conditions and does not take into consideration dynamic disturbances such as machine breakdown and new job arrivals. We regard the shop scheduling problem under static conditions as the static shop scheduling problem, while the shop scheduling problem with dynamic disturbances as the dynamic shop scheduling problem. In this paper, we analyze the characteristics of the dynamic shop scheduling problem when machine breakdown and new job arrivals occur, and present a framework to model the dynamic shop scheduling problem as a static group-shop-type scheduling problem. Using the proposed framework, we apply a metaheuristic proposed for solving the static shop scheduling problem to a number of dynamic shop scheduling benchmark problems. The results show that the metaheuristic methodology which has been successfully applied to the static shop scheduling problems can also be applied to solve the dynamic shop scheduling problem efficiently.

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.