Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints

Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing

Integrated capacitated lot sizing and scheduling problems in a flexible flow line

The lot sizing and scheduling problem in a Flexible Flow Line (FFL) has extensive real-world applications in many industries. An FFL consists of several production stages in series with parallel machines at each stage. The decisions to be taken are the determination of production quantities (lots), machine assignments and production sequences (schedules) on each machine at each stage in an FFL. Lot sizing and scheduling problems are closely interrelated. Solving them separately and then coordinating their interdependencies is often ineffective. However due to their complexity, there is a lack of mathematical modelling and solution procedures in the literature to combine and jointly solve them.Up to now most research has been focused on combining lotsizing and scheduling for the single machine configuration, and research on other configurations like FFL is sparse. This thesis presents several mathematical models with practical assumptions and appropriate algorithms, along with experimental test problems, for simultaneously lotsizing and scheduling in FFL. This problem, called the ‘General Lot sizing and Scheduling Problem in a Flexible Flow Line’ (GLSP-FFL). The objective is to satisfy varying demand over a finite planning horizon with minimal inventory, backorder and production setup costs. The problem is complex as any product can be processed on any machine, but these have different processing rates and sequence-dependent setup times & costs. As a result, even finding a feasible solution of large problems in reasonable time is impossible. Therefore the heuristic solution procedure named Adaptive Simulated Annealing (ASA), with four well-designed initial solutions, is designed to solve GLSP-FFL.A further original contribution of this study is to design linear mixed-integer programming (MILP) formulations for this problem, incorporating all necessary features of setup carryovers, setup overlapping, non-triangular setup while allowing multiple lot production per periods, lot splitting and sequencing through ATSP-adaption based on a variety of subtour elimination

A novel flexible model for lot sizing and scheduling with non-triangular, period overlapping and carryover setups in different machine configurations

© 2017, Springer Science+Business Media New York. This paper develops and tests an efficient mixed integer programming model for capacitated lot sizing and scheduling with non-triangular and sequence-dependent setup times and costs incorporating all necessary features of setup carryover and overlapping on different machine configurations. The model’s formulation is based on the asymmetric travelling salesman problem and allows multiple lots of a product within a period. The model conserves the setup state when no product is being processed over successive periods, allows starting a setup in a period and ending it in the next period, permits ending a setup in a period and starting production in the next period(s), and enforces a minimum lot size over multiple periods. This new comprehensive model thus relaxes all limitations of physical separation between the periods. The model is first developed for a single machine and then extended to other machine configurations, including parallel machines and flexible flow lines. Computational tests demonstrate the flexibility and comprehensiveness of the proposed models

Production planning in different stages of a manufacturing supply chain under multiple uncertainties

This thesis focuses on designing stochastic programming models for production planning at different stages in a manufacturing supply chain under multiple sources of uncertainties. Various decision makers along the manufacturing supply chain often have to make planning decisions with embedded risks and uncertainties. In an effort to reduce risks and to ensure that the customer demand is met in the most efficient and cost effective way, the production plans at each stage need to be strategically planned. To assist production planning decisions, a two-stage stochastic programming model is developed with the objective of minimizing the total cost including production, inventory, and backorder costs. The proposed framework is validated with case studies in an automobile part manufacturer with real data based on literature. The results demonstrate the robustness of the stochastic model compared with various deterministic models. Sensitivity analysis is performed for the production capacity parameter to derive managerial insights regarding lot-sizing and scheduling decisions under different scenarios

A review of discrete-time optimization models for tactical production planning

This is an Accepted Manuscript of an article published in International Journal of Production Research on 27 Mar 2014, available online: http://doi.org/10.1080/00207543.2014.899721[EN] This study presents a review of optimization models for tactical production planning. The objective of this research is to identify streams and future research directions in this field based on the different classification criteria proposed. The major findings indicate that: (1) the most popular production-planning area is master production scheduling with a big-bucket time-type period; (2) most of the considered limited resources correspond to productive resources and, to a lesser extent, to inventory capacities; (3) the consideration of backlogs, set-up times, parallel machines, overtime capacities and network-type multisite configuration stand out in terms of extensions; (4) the most widely used modelling approach is linear/integer/mixed integer linear programming solved with exact algorithms, such as branch-and-bound, in commercial MIP solvers; (5) CPLEX, C and its variants and Lindo/Lingo are the most popular development tools among solvers, programming languages and modelling languages, respectively; (6) most works perform numerical experiments with random created instances, while a small number of works were validated by real-world data from industrial firms, of which the most popular are sawmills, wood and furniture, automobile and semiconductors and electronic devices.This study has been funded by the Universitat Politècnica de València projects: ‘Material Requirement Planning Fourth Generation (MRPIV)’ (Ref. PAID-05-12) and ‘Quantitative Models for the Design of Socially Responsible Supply Chains under Uncertainty Conditions. Application of Solution Strategies based on Hybrid Metaheuristics’ (PAID-06-12).Díaz-Madroñero Boluda, FM.; Mula, J.; Peidro Payá, D. (2014). A review of discrete-time optimization models for tactical production planning. International Journal of Production Research. 52(17):5171-5205. doi:10.1080/00207543.2014.899721S51715205521

Stochastic make-to-stock inventory deployment problem: an endosymbiotic psychoclonal algorithm based approach

Integrated steel manufacturers (ISMs) have no specific product, they just produce finished product from the ore. This enhances the uncertainty prevailing in the ISM regarding the nature of the finished product and significant demand by customers. At present low cost mini-mills are giving firm competition to ISMs in terms of cost, and this has compelled the ISM industry to target customers who want exotic products and faster reliable deliveries. To meet this objective, ISMs are exploring the option of satisfying part of their demand by converting strategically placed products, this helps in increasing the variability of product produced by the ISM in a short lead time. In this paper the authors have proposed a new hybrid evolutionary algorithm named endosymbiotic-psychoclonal (ESPC) to decide what and how much to stock as a semi-product in inventory. In the proposed theory, the ability of previously proposed psychoclonal algorithms to exploit the search space has been increased by making antibodies and antigen more co-operative interacting species. The efficacy of the proposed algorithm has been tested on randomly generated datasets and the results compared with other evolutionary algorithms such as genetic algorithms (GA) and simulated annealing (SA). The comparison of ESPC with GA and SA proves the superiority of the proposed algorithm both in terms of quality of the solution obtained and convergence time required to reach the optimal/near optimal value of the solution

Just-In-Time in high variety / low volume manufacturing environments.

Available from British Library Document Supply Centre-DSC:DXN049763 / BLDSC - British Library Document Supply CentreSIGLEGBUnited Kingdo

Integrated Production and Distribution planning of perishable goods

Tese de doutoramento. Programa Doutoral em Engenharia Industrial e Gestão. Faculdade de Engenharia. Universidade do Porto. 201