Short-term scheduling in multi-stage batch plants through Lagrangean decomposition.

In this work, a continuous-time Mixed-Integer Linear Programming (MILP) model for the short-term scheduling in multi-stage batch plants is used. The MILP model accounts for ready unit times, release order times, sequence-dependent changeovers, transfer times between adjacent processing stages and different intermediates storage policies. A Lagrangean decomposition technique (Conejo et al., 2002) is applied to the MILP model in order to facilitate the resolution of real-world industrial cases. The proposed decomposition technique is thoroughly examined. An industrial case study of a multi-product multi-stage pharmaceuticals batch plant is addressed in order to demonstrate the performance and the advantages of the proposed decomposition scheme. The pharmaceutical plant under study consists of 17 processing equipments. The numerous (30 to 50) final products require 5 to 6 processing stages. Sequence-dependent changeovers are permitted in most stages. It is noteworthy that changeovers are usually of the same order of magnitude or even larger than the processing times. The main optimization goal is the minimization of the makespan. Results obtained are discussed highlighting the advantages and the special characteristics of the proposed scheduling model.Peer ReviewedPostprint (published version

Heuristic Solutions for Loading in Flexible Manufacturing Systems

Production planning in flexible manufacturing system deals with the efficient organization of the production resources in order to meet a given production schedule. It is a complex problem and typically leads to several hierarchical subproblems that need to be solved sequentially or simultaneously. Loading is one of the planning subproblems that has to addressed. It involves assigning the necessary operations and tools among the various machines in some optimal fashion to achieve the production of all selected part types. In this paper, we first formulate the loading problem as a 0-1 mixed integer program and then propose heuristic procedures based on Lagrangian relaxation and tabu search to solve the problem. Computational results are presented for all the algorithms and finally, conclusions drawn based on the results are discussed

Mixed-Integer Optimization Modeling for the Simultaneous Scheduling of Component Replacement and Repair

Maintenance is a critical aspect of many industries, playing an indispensable role in ensuring the optimal functionality, reliability, and longevity of various assets, equipment, and infrastructure. For a system to remain operational, maintenance of its components is required, and for the industry to optimize its operations, establishment of good maintenance policies and practices is vital.This thesis concerns the simultaneous scheduling of preventive maintenance for a fleet of aircraft and their common components along with the maintenance workshop, to which the components are sent for repair. The problem arises from an industrial project with the Swedish aerospace and defence company Saab. In the four papers underlying this thesis, we develop mathematical models\ua0 based on a mixed-binary linear optimization model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We extend this scheduling model with the flow of components through the repair workshop, including stocks of spare components as well as of damaged components to be repaired. The components are modeled either individually, aggregated, or as jobs in the workshop, whose scheduling is considered to be preemptive or non-preemptive. Along with the scheduling, we address and analyze two contracting forms between the stakeholders---the aircraft operator and the repair workshop; namely, an availability of repaired components contract and a repair turn--around time contract of components sent to the repair workshop, leading to a bi-objective optimization problem for each of the two contracting forms. To handle the computational complexity of the problems at hand, we use Lagrangean relaxation and subgradient optimization to find lower bounding functions---in the objective space---of the set of non-dominated solutions, complemented with math-heuristics to identify good feasible solutions. Our modeling enables capturing important properties of the results from the contracting forms and it can be utilized for obtaining a lower limit on the optimal performance of a contracted collaboration between the stakeholders

Exact and Heuristic Algorithms for the Job Shop Scheduling Problem with Earliness and Tardiness Over a Common Due Date

Scheduling has turned out to be a fundamental activity for both production and service organizations. As competitive markets emerge, Just-In-Time (JIT) production has obtained more importance as a way of rapidly responding to continuously changing market forces. Due to their realistic assumptions, job shop production environments have gained much research effort among scheduling researchers. This research develops exact and heuristic methods and algorithms to solve the job shop scheduling problem when the objective is to minimize both earliness and tardiness costs over a common due date. The objective function of minimizing earliness and tardiness costs captures the essence of the JIT approach in job shops. A dynamic programming procedure is developed to solve smaller instances of the problem, and a Multi-Agent Systems approach is developed and implemented to solve the problem for larger instances since this problem is known to be NP-Hard in a strong sense. A combinational auction-based approach using a Mixed-Integer Linear Programming (MILP) model to construct and evaluate the bids is proposed. The results showed that the proposed combinational auction-based algorithm is able to find optimal solutions for problems that are balanced in processing times across machines. A price discrimination process is successfully implemented to deal with unbalanced problems. The exact and heuristic procedures developed in this research are the first steps to create a structured approach to handle this problem and as a result, a set of benchmark problems will be available to the scheduling research community

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Creation of the selection list for the Experiment Scheduling Program (ESP)

The efforts to develop a procedure to construct selection groups to augment the Experiment Scheduling Program (ESP) are summarized. Included is a User's Guide and a sample scenario to guide in the use of the software system that implements the developed procedures

Unified Concept of Bottleneck

The term `bottleneck` has been extensively used in operations management literature. Management paradigms like the Theory of Constraints focus on the identification and exploitation of bottlenecks. Yet, we show that the term has not been rigorously defined. We provide a classification of bottleneck definitions available in literature and discuss several myths associated with the concept of bottleneck. The apparent diversity of definitions raises the question whether it is possible to have a single bottleneck definition which has as much applicability in high variety job shops as in mass production environments. The key to the formulation of an unified concept of bottleneck lies in relating the concept of bottleneck to the concept of shadow price of resources. We propose an universally applicable bottleneck definition based on the concept of average shadow price. We discuss the procedure for determination of bottleneck values for diverse production environments. The Law of Diminishing Returns is shown to be a sufficient but not necessary condition for the equivalence of the average and the marginal shadow price. The equivalence of these two prices is proved for several environments. Bottleneck identification is the first step in resource acquisition decisions faced by managers. The definition of bottleneck presented in the paper has the potential to not only reduce ambiguity regarding the meaning of the term but also open a new window to the formulation and analysis of a rich set of problems faced by managers.

Mathematical Modelling and Methods for Load Balancing and Coordination of Multi-Robot Stations

The automotive industry is moving from mass production towards an individualized production, individualizing parts aims to improve product quality and to reduce costs and material waste. This thesis concerns aspects of load balancing and coordination of multi-robot stations in the automotive manufacturing industry, considering efficient algorithms required by an individualized production. The goal of the load balancing problem is to improve the equipment utilization. Several approaches for solving the load balancing problem are suggested along with details on mathematical tools and subroutines employed.Our contributions to the solution of the load balancing problem are fourfold. First, to circumvent robot coordination we construct disjoint robot programs, which require no coordination schemes, are flexible, admit competitive cycle times for several industrial instances, and may be preferred in an individualized production. Second, since solving the task assignment problem for generating the disjoint robot programs was found to be unreasonably time-consuming, we model it as a generalized unrelated parallel machine problem with set packing constraints and suggest a tailored Lagrangian-based branch-and-bound algorithm. Third, a continuous collision detection method needs to determine whether the sweeps of multiple moving robots are disjoint. We suggest using the maximum velocity of each robot along with distance computations at certain robot configurations to derive a function that provides lower bounds on the minimum distance between the sweeps. The lower bounding function is iteratively minimized and updated with new distance information; our method is substantially faster than previously developed methods. Fourth, to allow for load balancing of complex multi-robot stations we generalize the disjoint robot programs into sequences of such; for some instances this procedure provides a significant equipment utilization improvement in comparison with previous automated methods

Matheuristics: using mathematics for heuristic design

Matheuristics are heuristic algorithms based on mathematical tools such as the ones provided by mathematical programming, that are structurally general enough to be applied to different problems with little adaptations to their abstract structure. The result can be metaheuristic hybrids having components derived from the mathematical model of the problems of interest, but the mathematical techniques themselves can define general heuristic solution frameworks. In this paper, we focus our attention on mathematical programming and its contributions to developing effective heuristics. We briefly describe the mathematical tools available and then some matheuristic approaches, reporting some representative examples from the literature. We also take the opportunity to provide some ideas for possible future development

Planning and scheduling in pharmaceutical supply chains

Ph.DDOCTOR OF PHILOSOPH