Variants of the Two Machine Flow Shop Problem connected with factorization of matrix functions

In this paper we consider a number of variants of the Two Machine Flow Shop Problem. In these variants the makespan is given and the problem is to find a schedule that meets this makespan, thereby minimizing the infeasibilities of the jobs in a prescribed sense: In the max-variant the maximum infeasibility of the jobs is to be minimized, whereas in the sum-variant the objective is to minimize the sum of the infeasibilities of the jobs. For both variants observations about the structure of the optimal schedules are presented. In particular, it is proved that every instance of these problems has an optimal permutation schedule. It is also shown that the max-variant can be solved by Johnson's Rule. For the sum-variant this is not the case: For solving this problem to optimality something quite different is necessary. Both variants are connected with factorization problems for certain rational matrix functions. The factorizations involved are optimal in some sense and generalize the notion of complete factorization. In this way a connection is established between job scheduling theory on one hand, and mathematical systems theory on the other

Machine Loading in Flexible Manufacturing system using Artificial Immune algorithm

In this project thesis the FMS loading problem is discussed with the objective to minimize the system unbalance and throughput by the use of Artificial Immune system. Manufacturing technology focuses primarily on flexibility and productivity. With the product variety and product life being the characterizing standards it is important that the flexibility of the job shop is maintained as its efficiency is increases. The complexity of a basic Machine loading problem in FMS is very high due to the different flexibility criteria as Part selection, Operation allocation and the various constraints involved. This dissertation proposes a soft computing technique with constraints on tool capacity and workload of the machine. The aim of using this algorithm is to reach an optimal solution and to ease the tedious computations in large problems involving loading which are NP hard problems. Immune algorithm is a very suitable method due to its self learning and memory acquisition abilities. First some sample machine loading problems are collected from the literature and the optimal system unbalance of the machine is calculated using LINGO optimization software. This project improves some issues inherent in existing techniques and proposes an effective Immune algorithm with reduced memory requirements and reduced computational complexity. The proposed Algorithm is tested on 3 problems adopted from literatures and the results reveal substantial improvement in solution quality over the existing basic mathematical approaches

Dynamic resource constrained multi-project scheduling problem with weighted earliness/tardiness costs

In this study, a conceptual framework is given for the dynamic multi-project scheduling problem with weighted earliness/tardiness costs (DRCMPSPWET) and a mathematical programming formulation of the problem is provided. In DRCMPSPWET, a project arrives on top of an existing project portfolio and a due date has to be quoted for the new project while minimizing the costs of schedule changes. The objective function consists of the weighted earliness tardiness costs of the activities of the existing projects in the current baseline schedule plus a term that increases linearly with the anticipated completion time of the new project. An iterated local search based approach is developed for large instances of this problem. In order to analyze the performance and behavior of the proposed method, a new multi-project data set is created by controlling the total number of activities, the due date tightness, the due date range, the number of resource types, and the completion time factor in an instance. A series of computational experiments are carried out to test the performance of the local search approach. Exact solutions are provided for the small instances. The results indicate that the local search heuristic performs well in terms of both solution quality and solution time

From ERP to advanced resource planning: Improving the operational performance by getting the inputs right.

In this paper, we show that the planning and decision support capabilities of the MPC (Manufacturing Planning and Control) system, which forms the core of any ERP package, may be greatly enhanced by including an Advanced Resource Planning (ARP) module as an add-on at the midterm planning level. This ARP module enables to estimate the impact of variability, complexity and dynamic system behavior on key planning parameters. As such, it yields realistic information both for short-term planning purposes and for reliable lead time quotations. We show how dynamic behavior impacts the operational performance of a manufacturing system, and discuss the framework for incorporating the ARP module into the ERP system.Planning; Operational performance; Performance; International; Science;

Advanced resource planning as decision support module to ERP.

In this paper, we show that the planning and decision-support capabilities of the MPC (Manufacturing Planning and Control) system, which forms the core of any ERP (Enterprise Resource Planning) package, may be substantively enhanced by including a Decision Support Module (DSM) as an add-on at the midterm planning level. This DSM, called Advanced Resource Planning (ARP), serves as parameter setting process as well as tool for improving the structure of the ERP system itself. The ultimate goal of the DSM is to yield realistic information both for scheduling, sales and marketing, strategic and operational decision making and suppliers and customers.

Hierarchical production planning

Includes bibliographical references.Partially supported by the Leaders for Manufacturing Program.Gabriel R. Bitran, Devanath Tirupati

A Digital Twin Framework for Production Planning Optimization: Applications for Make-To-Order Manufacturers

In this dissertation, we develop a Digital Twin framework for manufacturing systems and apply it to various production planning and scheduling problems faced by Make-To-Order (MTO) firms. While this framework can be used to digitally represent a particular manufacturing environment with high fidelity, our focus is in using it to generate realistic settings to test production planning and scheduling algorithms in practice. These algorithms have traditionally been tested by either translating a practical situation into the necessary modeling constructs, without discussion of the assumptions and inaccuracies underlying this translation, or by generating random instances of the modeling constructs, without assessing the limitations in accurately representing production environments. The consequence has been a serious gap between theory advancement and industry practice. The major goal of this dissertation is to develop a framework that allows for practical testing, evaluation, and implementation of new approaches for seamless industry adoption. We develop this framework as a modular software package and emphasize the practicality and configurability of the framework, such that minimal modelling effort is required to apply the framework to a multitude of optimization problems and manufacturing systems. Throughout this dissertation, we emphasize the importance of the underlying scheduling problems which provide the basis for additional operational decision making. We focus on the computational evaluation and comparisons of various modeling choices within the developed frameworks, with the objective of identifying models which are both effective and computationally efficient. In Part 1 of this dissertation, we consider a class of Production Planning and Execution problems faced by job shop manufacturing systems. In Part 2 of this dissertation, we consider a class of scheduling problems faced by manufacturers whose production system is dominated by a single operation

Models for robust resource allocation in project scheduling.

The vast majority of resource-constrained project scheduling efforts assumes complete information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule will be executed. In reality, however, project activities are subject to considerable uncertainty which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects the makespan of a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed robust resource allocation problem in exact and approximate formulations. The procedure relies on constraint propagation during its search. We report on computational results obtained on a set of benchmark problems.Model; Resource allocation; Scheduling;

Stability and resource allocation in project planning.

The majority of resource-constrained project scheduling efforts assumes perfect information about the scheduling problem to be solved and a static deterministic environment within which the pre-computed baseline schedule is executed. In reality, project activities are subject to considerable uncertainty, which generally leads to numerous schedule disruptions. In this paper, we present a resource allocation model that protects a given baseline schedule against activity duration variability. A branch-and-bound algorithm is developed that solves the proposed resource allocation problem. We report on computational results obtained on a set of benchmark problems.Constraint satisfaction; Information; Model; Planning; Problems; Project management; Project planning; Project scheduling; Resource allocati; Scheduling; Stability; Uncertainty; Variability;