A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders

Pitombeira‐Neto, Anselmo Ramalho; Prata, Bruno de Athayde

doi:10.1007/s11750-019-00531-3

Cited by 22 publications

(14 citation statements)

References 27 publications

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“…Since the demand may often not be supplied in a single time period, cutting operations have to be scheduled so as to optimize makespan, tardiness or other performance measure. In this case, it has been referred to in the literature as a combined cutting stock and scheduling problem (Trkman & Gradisar, 2007;Reinertsen & Vossen, 2010;Arbib & Marinelli, 2014;Prata et al, 2015;Pitombeira-Neto & Prata, 2019). Other papers address the CSP in a dynamic deterministic make-to-stock setting, in which point forecasts of future demands are available for a finite horizon and decisions on how manye objects to cut are taken in advance.…”

Section: Related Workmentioning

confidence: 99%

A Reinforcement Learning Approach to the Stochastic Cutting Stock Problem

Pitombeira-Neto,

Murta

2021

Preprint

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We propose a formulation of the stochastic cutting stock problem as a discounted infinite-horizon Markov decision process. At each decision epoch, given current inventory of items, an agent chooses in which patterns to cut objects in stock in anticipation of the unknown demand. An optimal solution corresponds to a policy that associates each state with a decision and minimizes the expected total cost. Since exact algorithms scale exponentially with the state-space dimension, we develop a heuristic solution approach based on reinforcement learning. We propose an approximate policy iteration algorithm in which we apply a linear model to approximate the action-value function of a policy. Policy evaluation is performed by solving the projected Bellman equation from a sample of state transitions, decisions and costs obtained by simulation. Due to the large decision space, policy improvement is performed via the cross-entropy method. Computational experiments are carried out with the use of realistic data to illustrate the application of the algorithm. Heuristic policies obtained with polynomial and Fourier basis functions are compared with myopic and random policies. Results indicate the possibility of obtaining policies capable of adequately controlling inventories with an average cost up to 80% lower than the cost obtained by a myopic policy.

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Section: Related Workmentioning

confidence: 99%

A Reinforcement Learning Approach to the Stochastic Cutting Stock Problem

Pitombeira-Neto,

Murta

2021

Preprint

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“…A. R. Pitombeira-Neto et al [17] presented an integer linear programming model for the scheduling and one-dimensional cutting stock problem with heterogeneous orders. A novel metaheuristic algorithm was proposed based on a fix-and-optimize strategy hybridized with a random local search.…”

Section: Literature Reviewmentioning

confidence: 99%

“…The gross area of the selected master and stocked reels can be estimated using Equations (15) and (16), respectively. Finally, Equations (17) and (18) evaluate the net area of selected master reels and stocked reels, respectively.…”

Section: Mathematical Modelmentioning

confidence: 99%

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

et al. 2020

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One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment.

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“…Test results showed that the hybrid-generated solutions were superior to the solutions received from the BFD algorithm alone. Anselmo [35] proposed a novel matheuristic algorithm based on a fix-and-optimize strategy hybridized with a random local search; this performed better than the CPLEX solver in larger instances, with an average relative percentage deviation (RPD) for objective values as high as 72%.…”

Section: Introductionmentioning

confidence: 99%

Solution to Solid Wood Board Cutting Stock Problem

et al. 2021

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In the production process for wooden furniture, the raw material costs account for more than 50% of furniture costs, and the utilization rate of raw materials depends mainly on the layout scheme. Therefore, a reasonable layout is an important measure to reduce furniture costs. This paper investigates the solid wood board cutting stock problem (CSP) and establishes an optimization model, with the goal of the highest possible utilization rate for original boards. An ant colony-immune genetic algorithm (ACIGA) is designed to solve this model. The solutions of the ant colony algorithm are used as the initial population of the immune genetic algorithm, and the optimal solution is obtained using the immune genetic algorithm after multiple iterations are transformed into the accumulation of global pheromones, which improves the search ability and ensures the solution quality. The layout process of the solid wood board is abstracted into the construction process of the solution. At the same time, in order to prevent premature convergence, several improved methods, such as a global pheromone hybrid update and adaptive crossover probability, are proposed. Comparative experiments are designed to verify the feasibility and effectiveness of the ACIGA, and the experimental results show that the ACIGA has better solution precision and global search ability compared with the ant colony algorithm (ACA), genetic algorithm (GA), grey wolf optimizer (GWO), and polar bear optimization (PBO). The utilization rate increased by more than 2.308%, which provides effective theoretical and methodological support for furniture enterprises to improve economic benefits.

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A matheuristic algorithm for the one-dimensional cutting stock and scheduling problem with heterogeneous orders

Cited by 22 publications

References 27 publications

A Reinforcement Learning Approach to the Stochastic Cutting Stock Problem

A Reinforcement Learning Approach to the Stochastic Cutting Stock Problem

A Mathematical Model for Reduction of Trim Loss in Cutting Reels at a Make-to-Order Paper Mill

Solution to Solid Wood Board Cutting Stock Problem

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