A relax-and-fix with fix-and-optimize heuristic applied to multi-level lot-sizing problems

In this paper, we propose a simple but efficient heuristic that combines construction and improvement heuristic ideas to solve multi-level lot-sizing problems. A relax-and-fix heuristic is firstly used to build an initial solution, and this is further improved by applying a fix-and-optimize heuristic. We also introduce a novel way to define the mixed-integer subproblems solved by both heuristics. The efficiency of the approach is evaluated solving two different classes of multi-level lot-sizing problems: the multi-level capacitated lot-sizing problem with backlogging and the two-stage glass container production scheduling problem (TGCPSP). We present extensive computational results including four test sets of the Multi-item Lot-Sizing with Backlogging library, and real-world test problems defined for the TGCPSP, where we benchmark against state-of-the-art methods from the recent literature. The computational results show that our combined heuristic approach is very efficient and competitive, outperforming benchmark methods for most of the test problems

Integrated Production Planning and Scheduling Optimization

Este trabalho propõe um método de solução iterativa para abordar a integração do planeamento táctico (dimensionamento de lotes) e operacional (sequenciamento) numa produção industrial com setups dependentes da sequencia. Este método quebra o problema da integração em dois. No primeiro sub-problema do planeamento táctico, o plano de produção é optimizado sem ter em conta setups necessários. O sequenciamento dos produtos é depois definido usando estratégias de pesquisa local que irão conceber regras para complementarem o primeiro sub-problema. De seguida, o planeamento táctico é repetido, considerando as novas regras definidas anteriormente. O algoritmo continua iterativamente até que as funções objectivo dos dois níveis convirjam. De modo a analisar resultados obtidos, dois experimentos computacionais são propostos. O primeiro para comparar o método iterativo com outros métodos de solução encontrados na literatura para problemas similares, nomeadamente meta-heuristicas e modelos MIP. Por fim, a investigação foi focada num caso de uma indústria de nutrição animal, onde o setup de produção é dependente da sequência e normalmente não-triangular, podendo produtos evitarem limpeza se produzidos entre outros dois que de outro modo necessitariam de setup. O propósito do segundo experimento é avaliar os eventuais ganhos a uma abordagem hierárquica usualmente usada nesta indústria.This work proposes an iterative solution method to address the integration of the tactical (lot-sizing) and operational (scheduling) levels in production planning with sequence dependent setups. This method breaks the integrated lot-sizing and scheduling problem into two. In the first sub-problem, at the tactical level, the production plan is optimized with production setups disregarded. The production scheduling solution is then defined using local search strategies that will also construct rules for the tactical level. After that, the tactical level is optimized again, considering the rules defined from the operational level. The algorithm continues iteratively until objective functions from both levels converge. In order to analyse results, two computational experiments are proposed. The first is performed to compare the solution method proposed with mixed-integer programming models and meta-heuristics from the literature. Then the research will focus on an animal-feed industry case, in which production setup is sequence dependent and usually presents non-triangular setups, so products can avoid cleaning setups if produced between two products that otherwise would require a setup. The purpose of the second experiment is to evaluate the potential gains to a hierarchical approach usually used in this industry

An Expandable Machine Learning-Optimization Framework to Sequential Decision-Making

We present an integrated prediction-optimization (PredOpt) framework to efficiently solve sequential decision-making problems by predicting the values of binary decision variables in an optimal solution. We address the key issues of sequential dependence, infeasibility, and generalization in machine learning (ML) to make predictions for optimal solutions to combinatorial problems. The sequential nature of the combinatorial optimization problems considered is captured with recurrent neural networks and a sliding-attention window. We integrate an attention-based encoder-decoder neural network architecture with an infeasibility-elimination and generalization framework to learn high-quality feasible solutions to time-dependent optimization problems. In this framework, the required level of predictions is optimized to eliminate the infeasibility of the ML predictions. These predictions are then fixed in mixed-integer programming (MIP) problems to solve them quickly with the aid of a commercial solver. We demonstrate our approach to tackling the two well-known dynamic NP-Hard optimization problems: multi-item capacitated lot-sizing (MCLSP) and multi-dimensional knapsack (MSMK). Our results show that models trained on shorter and smaller-dimensional instances can be successfully used to predict longer and larger-dimensional problems. The solution time can be reduced by three orders of magnitude with an average optimality gap below 0.1%. We compare PredOpt with various specially designed heuristics and show that our framework outperforms them. PredOpt can be advantageous for solving dynamic MIP problems that need to be solved instantly and repetitively

Comparison of different approaches to multistage lot sizing with uncertain demand

We study a new variant of the classical lot sizing problem with uncertain demand where neither the planning horizon nor demands are known exactly. This situation arises in practice when customer demands arriving over time are confirmed rather lately during the transportation process. In terms of planning, this setting necessitates a rolling horizon procedure where the overall multistage problem is dissolved into a series of coupled snapshot problems under uncertainty. Depending on the available data and risk disposition, different approaches from online optimization, stochastic programming, and robust optimization are viable to model and solve the snapshot problems. We evaluate the impact of the selected methodology on the overall solution quality using a methodology-agnostic framework for multistage decision-making under uncertainty. We provide computational results on lot sizing within a rolling horizon regarding different types of uncertainty, solution approaches, and the value of available information about upcoming demands

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

A dynamic ordering policy for a stochastic inventory problem with cash constraints

This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product from suppliers and sells it to a market while facing non-stationary demands. In each period, the retailer's available cash restricts the maximum quantity that can be ordered. There exists a fixed ordering cost for the retailer when purchasing. We partially characterize the optimal ordering policy by showing it has an $\bf s-C$ structure: for each period, when initial inventory is above the $\bf$s threshold, no product should be ordered no matter how much initial cash it has; when initial inventory is not large enough to be a $\bf s$ threshold, it is also better to not order when initial cash is below the threshold $C$. The values of $C$ may be state-dependent and related to each period's initial inventory. A heuristic policy $(s, C(x), S)$ is proposed: when initial inventory $x$ is less than $s$ and initial cash is greater than $C(x)$, order a quantity that brings inventory as close to $S$ as possible; otherwise, do not order. We first determine the values of the controlling parameters $s$, $C(x)$ and $S$ based on the results of stochastic dynamic programming and test their performance via an extensive computational study. The results show that the $(s, C(x), S)$ policy performs well with a maximum optimality gap of less than 1\% and an average gap of approximately 0.01\%. We then develop a simple and time-efficient heuristic method for computing policy $(s, C(x), S)$ by solving a mixed-integer linear programming problem and approximate newsvendor models: the average gap for this heuristic is approximately 2\% on our test bed