Elsa Silva

2DCPackGen: A problem generator for two-dimensional rectangular cutting and packing problems

Cutting and packing problems have been extensively studied in the literature in recent decades, mainly due to their numerous real-world applications while at the same time exhibiting intrinsic computational complexity. However, a major limitation has been the lack of problem generators that can be widely and commonly used by all researchers in their computational experiments. In this paper, a problem generator for every type of two-dimensional rectangular cutting and packing problems is proposed. The problems are defined according to the recent typology for cutting and packing problems proposed by Wascher, Hausner, and Schumann (2007) and the relevant problem parameters are identified. The proposed problem generator can significantly contribute to the quality of the computational experiments run with cutting and packing problems and therefore will help improve the quality of the papers published in this field.

The pallet loading problem: a review of solution methods and computational experiments

The manufacturers pallet loading problem (MPLP) has been widely studied during the past 50 years. It consists of placing a maximum number of identical rectangular boxes onto a single rectangular pallet. In this paper, we have reviewed the methods that have been proposed for the solution of this problem. Furthermore, the various problem instances and data sets are analyzed that have been used in computational experiments for the evaluation of these methods. The most challenging and yet unsolved methods are identified. By doing so, areas of future research concerning the MPLP can be highlighted.

A SURVEY ON HEURISTICS FOR THE TWO-DIMENSIONAL RECTANGULAR STRIP PACKING PROBLEM

Two-dimensional rectangular strip packing problems belong to the broader class of Cutting and Packing (C&P) problems, in which small items are required to be cut from or packed on a larger object, so that the waste (unused regions of the large object) is minimized. C&P problems differ from other combinatorial optimization problems by the intrinsic geometric constraints: items may not overlap and have to be fully contained in the large object. This survey approaches the specific C&P problem in which all items are rectangles, therefore fully characterized by a width and a height, and the large object is a strip, i.e. a rectangle with a fixed width but an infinite height, being the problems goal to place all rectangles on the strip so that the height is minimized. These problems have been intensively and extensively tackled in the literature and this paper will focus on heuristic resolution methods. Both the seminal and the most recent approaches (from the last decade) will be reviewed, in a rather tutorial flavor, and classified according to their type: constructive heuristics, improvement heuristics with search over sequences and improvement heuristics with search over layouts. Building on this review, research gaps are identified and the most interesting research directions pointed out.

Using Analytics to Enhance a Food Retailer’s Shelf-Space Management

This paper describes the results of our collaboration with the leading Portuguese food retailer to address the shelf-space planning problem of allocating products to shop-floor shelves. Our challenge was to introduce analytical methods into the shelf-space planning process to improve the return on space and automate a process heavily dependent on the experience of the retailer’s space managers. This led to the creation of GAP, a decision support system that the company’s space-management team uses daily. We developed a modular operations research approach that systematically applies mathematical programming models and heuristics to determine the best layout of products on the shelves. GAP combines its analytical strength with an ability to incorporate different types of merchandising rules to balance the tradeoff between optimization and customization.

The Cutting Stock Problem: A Case Study in a Manufacturer of Pet Vivaria

This paper addresses the problem of determining the cutting patterns of metal sheets, which arises in a manufacturer of metal cages, in order to minimize the waste, the number of cuts performed, the number of metal sheets used or a weighted combination of the three. A two stage approach, to solve a 2D guillotine cutting stock problem with single and multiple stock sizes, is presented and compared with the company approach and state-of-the-art algorithms. The results show great improvement compared to the company approach and a very good performance compared to state-of-the-art algorithms.

Integrated Cutting and Production Planning: A Case Study in a Home Textile Manufacturing Company

In this paper we consider the problem of minimizing the waste of textile material in a Portuguese home textile manufacturing company. The company has a vertical structure covering the different production stages of the home textile, from weaving until the finished products. Production planning comprises different decisions: the definition of the widths and lengths of the fabric rolls to be produced, the number of fabric rolls to be used from stock or purchased and the definition of the cutting patterns to be applied to each width of the fabric roll, so that the waste is minimized. We propose a MIP model, solved by a column generation method, to tackle the problem.

Data mining based framework to assess solution quality for the rectangular 2D strip-packing problem

Abstract In this paper, we explore the use of reference values (predictors) for the optimal objective function value of hard combinatorial optimization problems, instead of bounds, obtained by data mining techniques, and that may be used to assess the quality of heuristic solutions for the problem. With this purpose, we resort to the rectangular two-dimensional strip-packing problem (2D-SPP), which can be found in many industrial contexts. Mostly this problem is solved by heuristic methods, which provide good solutions. However, heuristic approaches do not guarantee optimality, and lower bounds are generally used to give information on the solution quality, in particular, the area lower bound. But this bound has a severe accuracy problem. Therefore, we propose a data mining-based framework capable of assessing the quality of heuristic solutions for the 2D-SPP. A regression model was fitted by comparing the strip height solutions obtained with the bottom-left-fill heuristic and 19 predictors provided by problem characteristics. Random forest was selected as the data mining technique with the best level of generalisation for the problem, and 30,000 problem instances were generated to represent different 2D-SPP variations found in real-world applications. Height predictions for new problem instances can be found in the regression model fitted. In the computational experimentation, we demonstrate that the data mining-based framework proposed is consistent, opening the doors for its application to finding predictions for other combinatorial optimisation problems, in particular, other cutting and packing problems. However, how to use a reference value instead of a bound, has still a large room for discussion and innovative ideas. Some directions for the use of reference values as a stopping criterion in search algorithms are also provided.

Neonatal Apex Resection Triggers Cardiomyocyte Proliferation, Neovascularization and Functional Recovery Despite Local Fibrosis

Summary So far, opposing outcomes have been reported following neonatal apex resection in mice, questioning the validity of this injury model to investigate regenerative mechanisms. We performed a systematic evaluation, up to 180 days after surgery, of the pathophysiological events activated upon apex resection. In response to cardiac injury, we observed increased cardiomyocyte proliferation in remote and apex regions, neovascularization, and local fibrosis. In adulthood, resected hearts remain consistently shorter and display permanent fibrotic tissue deposition in the center of the resection plane, indicating limited apex regrowth. However, thickening of the left ventricle wall, explained by an upsurge in cardiomyocyte proliferation during the initial response to injury, compensated cardiomyocyte loss and supported normal systolic function. Thus, apex resection triggers both regenerative and reparative mechanisms, endorsing this injury model for studies aimed at promoting cardiomyocyte proliferation and/or downplaying fibrosis.

An Intercontinental Replenishment Problem: A Hybrid Approach

This work addresses a case study in an intercontinental supply chain. The problem emerges in a company in Angola dedicated to the trade of consumable goods for construction building and industrial maintenance. The company in Angola sends the replenishment needs to a Portuguese company, which takes the decision of which products and in which quantities will be sent by shipping container to the company in Angola. The replenishment needs include the list of products that reached the corresponding reorder point. The decision of which products and in which quantity should take into consideration a set of practical constraints: the maximum weight of the cargo, the maximum volume the cargo and financial constraints related with the minimum value that guarantees the profitability of the business and a maximum value associated with shipping insurance. A 2-stage hybrid method is proposed. In the first stage, an integer linear programming model is used to select the products that maximise the sales potential. In the second stage, a Container Loading Algorithm is used to effectively pack the selected products in the shipping container ensuring the geometrical constraints, and safety constraints such as weight limit and stability. A new set of problem instances was generated with the 2DCPackGen problem generator, using as inputs the data collected in the company. Computational results for the algorithm are presented and discussed. Good results were obtained with the solution approach proposed, with an average occupation ratio of 92% of the container and an average gap of 4% for the solution of the integer linear programming model.

The Two-Dimensional Strip Packing Problem: What Matters?

This paper presents an exploratory approach to study and identify the main characteristics of the two-dimensional strip packing problem (2D-SPP). A large number of variables was defined to represent the main problem characteristics, aggregated in six groups, established through qualitative knowledge about the context of the problem. Coefficient correlation are used as a quantitative measure to validate the assignment of variables to groups. A principal component analysis (PCA) is used to reduce the dimensions of each group, taking advantage of the relations between variables from the same group. Our analysis indicates that the problem can be reduced to 19 characteristics, retaining most part of the total variance. These characteristics can be used to fit regression models to estimate the strip height necessary to position all items inside the strip.