Relax and fix heuristics to solve one-stage one-machine lot-scheduling models for small-scale soft drink plants

The production planning of regional small-scale soft drink plants can be modeled by mixed integer models that integrate lot sizing and scheduling decisions and consider sequence-dependent setup times and costs. These plants produce soft drinks in different flavors and sizes and they have typically only one production line. The production process is carried out basically in two main stages: liquid preparation (stage I) and bottling (stage II). However, since the production bottleneck of these plants is often in stage II, in this study we represent the problem as a one-stage one-machine lot-scheduling model that considers stage II as the bottleneck but also takes into account a capacity constraint of stage I. To solve the problem, we propose relax and fix heuristics exploring the model structure and we evaluate their computational performances solving different problem instances based on real data of a Brazilian small-scale soft drink company. The solutions obtained are compared to the company solutions and the solutions of a general-purpose optimization software.     

An optimization approach for the lot sizing and scheduling problem in the brewery industry

This study considers a production lot sizing and scheduling problem in the brewery industry. The underlying manufacturing process can be basically divided into two main production stages: preparing the liquids including fermentation and maturation inside the fermentation tanks; and bottling the liquids on the filling lines, making products of different liquids and sizes. This problem differs from other problems in beverage industries due to the relatively long lead times required for the fermentation and maturation processes and because the “ready” liquid can remain in the tanks for some time before being bottled. The main planning challenge is to synchronize the two stages (considering the possibility of a “ready” liquid staying in the tank until bottling), as the production bottlenecks may alternate between these stages during the planning horizon. This study presents a novel mixed integer programming model that represents the problem appropriately and integrates both stages. In order to solve real-world problem instances, MIP-based heuristics are developed, which explore the model structure. The results show that the model is able to comprise the problem requirements and the heuristics produce relatively good-quality solutions.     

The integrated lot sizing and cutting stock problem with saw cycle constraints applied to furniture production

The integrated lot sizing and cutting stock problem is studied in the context of furniture production. The goal is to capture the interdependencies between the determination of the lot size and of the cutting process in order to reduce raw material waste and production and inventory costs. An integrated mathematical model is proposed that includes lot sizing decisions with safety stock level constraints and saw capacity constraints taking into account saw cycles. The model solution is compared to a simulation of the common practice of taking the lot size and the cutting stock decisions separately and sequentially. Given the large number of variables in the model, a column-generation solution method is proposed to solve the problem. An extensive computational study is conducted using instances generated based on data collected at a typical small scale Brazilian factory. It includes an analysis of the performance of the integrated approach against sequential approaches, when varying the costs in the objective function. The integrated approach performs well, both in terms of reducing the total cost of raw materials as well as the inventory costs of pieces. They also indicate that the model can support the main decisions taken and can bring improvements to the factory's production planning.     

Evolutionary algorithms for scheduling m-machine flow shop with lot streaming

This paper addresses the problem of making sequencing and scheduling decisions for n jobs–m-machines flow shops under lot sizing environment. Lot streaming (Lot sizing) is the process of creating sub lots to move the completed portion of a production sub lots to down stream machines. There is a scope for efficient algorithms for scheduling problems in m-machine flow shop with lot streaming. In recent years, much attention is given to heuristics and search techniques. Evolutionary algorithms that belong to search heuristics find more applications in recent research. Genetic algorithm (GA) and hybrid genetic algorithm (HEA) also known as hybrid evolutionary algorithm fall under evolutionary heuristics. On this concern this paper proposes two evolutionary algorithms namely, GA and HEA to evolve best sequence for makespan/total flow time criterion for m-machine flow shop involved with lot streaming and set-up time. The following two algorithms are used to evaluate the performance of the proposed GA and HEA: (i) Baker's algorithm (BA), an optimal solution procedure for two-machine flow shop problem with lot streaming and makespan objective criterion and (ii) simulated annealing algorithm (SA) for m-machine flow shop problem with lot streaming and makespan and total flow time criteria.     

文化算法在越库作业调度中的应用

研究只有一个入库门和一个出库门的带有限暂存区的越库中心的作业调度问题。以额外搬运成本、暂存成本和换车成本总和最小化为目标,建立动态规划模型。构建了具有两层进化机制的文化算法对问题进行求解。算法的种群空间采用遗传算法作为进化模式,信度空间接收种群空间的优良个体形成知识并指导遗传算法的选择操作。通过在大、小规模情形下进行数值实验,验证了文化算法的有效性。     

Glass container production scheduling through hybrid multi-population based evolutionary algorithm

Driven by a real-world application in the capital-intensive glass container industry, this paper provides the design of a new hybrid evolutionary algorithm to tackle the short-term production planning and scheduling problem. The challenge consists of sizing and scheduling the lots in the most cost-effective manner on a set of parallel molding machines that are fed by a furnace that melts the glass. The solution procedure combines a multi-population hierarchically structured genetic algorithm (GA) with a simulated annealing (SA), and a tailor-made heuristic named cavity heuristic (CH). The SA is applied to intensify the search for solutions in the neighborhood of the best individuals found by the GA, while the CH determines quickly values for a relevant decision variable of the problem: the processing speed of each machine. The results indicate the superior performance of the proposed approach against a state-of-the-art commercial solver, and compared to a non-hybridized multi-population GA.     

Infeasibility handling in genetic algorithm using nested domains for production planning

In this paper we present a genetic algorithm with new components to tackle capacitated lot sizing and scheduling problems with sequence dependent setups that appear in a wide range of industries, from soft drink bottling to food manufacturing.Finding a feasible solution to highly constrained problems is often a very difficult task. Various strategies have been applied to deal with infeasible solutions throughout the search. We propose a new scheme of classifying individuals based on nested domains to determine the solutions according to the level of infeasibility, which in our case represents bands of additional production hours (overtime). Within each band, individuals are just differentiated by their fitness function. As iterations are conducted, the widths of the bands are dynamically adjusted to improve the convergence of the individuals into the feasible domain.The numerical experiments on highly capacitated instances show the effectiveness of this computational tractable approach to guide the search toward the feasible domain. Our approach outperforms other state-of-the-art approaches and commercial solvers.     

A NEW EXPERIMENTAL STUDY OF GENETIC ALGORITHM AND SIMULATED ANNEALING WITH BOUNDED VARIABLES

Genetic algorithms (GA) can work in very large and complex spaces, which gives them the ability to solve many complex real-world problems. The bounded variables linear programming is formulated as genetic algorithms and simulated annealing (SA). This article demonstrates that genetic algorithms and simulated annealing are much easier to implement for solving network problems compared with constructing mathematical programming formulations, because it is a very simple matter to implement a new cost function and solution constraints when using a GA and SA. Finally, the presented results show that the genetic algorithm and simulated annealing provide a good scheduling methodology to bounded variables programming.     

病毒进化遗传算法在机车检修系统工单调度中的应用

为解决机务段检修工单调度中人力资源的分配问题,建立工单调度数学模型,采用病毒进化遗传算法求解型,并验证模型的科学性及病毒进化遗传算法求解问题的优越性.     

A robust genetic algorithm for scheduling realistic hybrid flexible flow line problems

This article addresses the problem of hybrid flexible flow line where some constraints are considered to alleviate the chasm between the real-world industries scheduling and the production scheduling theories. Sequence-dependent setup times, machine release date and time lags are three constraints deemed to project the circumstances commonly found in real-world industries. To tackle the complexity of the problem at hand, we propose an approach base on genetic algorithm (GA). However, the performance of most evolutionary algorithms is significantly impressed by the values determined for the miscellaneous parameters which these algorithms possess. Hence, response surface methodology is applied to set the parameters of GA and to estimate the proper values of GA parameters in continually intervals. Finally, problems of various sizes are utilized to test the performance of the proposed algorithm and to compare it with some existing heuristic in the literature such as SPT, LPT and NEH.     

A review of applications of genetic algorithms in lot sizing

Lot sizing problems are production planning problems with the objective of determining the periods where production should take place and the quantities to be produced in order to satisfy demand while minimizing production, setup and inventory costs. Most lot sizing problems are combinatorial and hard to solve. In recent years, to deal with the complexity and find optimal or near-optimal results in reasonable computational time, a growing number of researchers have employed meta-heuristic approaches to lot sizing problems. One of the most popular meta-heuristics is genetic algorithms which have been applied to different optimization problems with good results. The focus of this paper is on the recent published literature employing genetic algorithms to solve lot sizing problems. The aim of the review is twofold. First it provides an overview of recent advances in the field in order to highlight the many ways GAs can be applied to various lot sizing models. Second, it presents ideas for future research by identifying gaps in the current literature. In reviewing the relevant literature the focus has been on the main features of the lot sizing problems and the specifications of genetic algorithms suggested in solving these problems.     

Development of hybrid evolutionary algorithms for production scheduling of hot strip mill

A hot strip mill (HSM) produces hot rolled products from steel slabs, and is one of the most important production lines in a steel plant. The aim of HSM scheduling is to construct a rolling sequence that optimizes a set of given criteria under constraints. Due to the complexity in modeling the production process and optimizing the rolling sequence, the HSM scheduling is a challenging task for hot rolling production schedulers. This paper first introduces the HSM production process and requirements, and then reviews previous research on the modeling and optimization of the HSM scheduling problem. According to the practical requirements of hot rolling production, a mathematical model is formulated to describe two important scheduling sub-tasks: (1) selecting a subset of manufacturing orders and (2) generating an optimal rolling sequence from the selected manufacturing orders. Further, hybrid evolutionary algorithms with integration of genetic algorithm (GA) and extremal optimization (EO) are proposed to solve the HSM scheduling problem. Computational results on industrial data show that the proposed HSM scheduling solution can be applied in practice to provide satisfactory performance.     

The economic lot scheduling problem in limited-buffer flexible flow shops: Mathematical models and a discrete fruit fly algorithm

This paper considers the lot scheduling problem in the flexible flow shop with limited intermediate buffers to minimize total cost which includes the inventory holding and setup costs. The single available mathematical model by Akrami et al. (2006) for this problem suffers from not only being non-linear but also high size-complexity. In this paper, two new mixed integer linear programming models are developed for the problem. Moreover, a fruit fly optimization algorithm is developed to effectively solve the large problems. For model’s evaluation, this paper experimentally compares the proposed models with the available model. Moreover, the proposed algorithm is also evaluated by comparing with two well-known algorithms (tabu search and genetic algorithm) in the literature and adaption of three recent algorithms for the flexible flow shop problem. All the results and analyses show the high performance of the proposed mathematical models as well as fruit fly optimization algorithm.     

Mathematical modeling and solving procedure of the planar storage location assignment problem

This paper focuses on the planar storage location assignment problem (PSLAP) that needs to be clearly defined and newly formulated. In addition, the solving procedure should be developed. The PSLAP can be defined as the assignment of the inbound and outbound objects to the storage yard with aim of minimizing the number of obstructive object moves. The storage yard allows only planar moves of objects. The PSLAP usually occurs in the assembly block stockyard operations at a shipyard. This paper formulates the PSLAP using a mathematical programming model, but which belongs to the NP-hard problems category. Thus this paper utilizes an efficient genetic algorithm (GA) to solve the PSLAP for real-sized instances. The performance of the proposed mathematical programming model and developed GA is verified by a number of numerical experiments.     

基于GA-PSO的天基预警系统资源调度方法

为解决天基预警系统中的卫星资源调度问题,从预警任务特点出发,在对预警任务进行分解的基础上,建立了资源调度模型．结合传统遗传算法（GA）和粒子群算法（PSO）的优点,采用一种混合遗传粒子群（GA-PSO）算法来求解资源调度问题．该算法在解决粒子编解码问题的前提下,将遗传算法的遗传算子应用于粒子群算法,改善了粒子群算法的寻优能力．实验结果表明,提出的算法能有效解决多目标探测时天基预警系统的资源调度问题,调度结果优于传统粒子群算法和遗传算法．     

A hybrid genetic algorithm for the single machine scheduling problem with sequence-dependent setup times

This paper presents a hybrid approach based on the integration between a genetic algorithm (GA) and concepts from constraint programming, multi-objective evolutionary algorithms and ant colony optimization for solving a scheduling problem. The main contributions are the integration of these concepts in a GA crossover operator. The proposed methodology is applied to a single machine scheduling problem with sequence-dependent setup times for the objective of minimizing the total tardiness. A sensitivity analysis of the hybrid approach is carried out to compare the performance of the GA and the hybrid genetic algorithm (HGA) approaches on different benchmarks from the literature. The numerical experiments demonstrate the HGA efficiency and effectiveness which generates solutions that approach those of the known reference sets and improves several lower bounds.     

An efficient algorithm for solving a new mathematical model for a quay crane scheduling problem in container ports

This paper presents a novel, mixed-integer programming (MIP) model for the quay crane (QC) scheduling and assignment problem, namely QCSAP, in a container port (terminal). Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper, thus, proposes a genetic algorithm (GA) to solve the above-mentioned QCSAP for the real-world situations. Further, the efficiency of the proposed GA is compared against the LINGO software package in terms of computational times for small-sized problems. Our computational results suggest that the proposed GA is able to solve the QCSAP, especially for large sizes.     

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (1) the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry's own practice.     

Minimizing total earliness and tardiness through unrelated parallel machine scheduling using distributed release time control

Using unrelated parallel machine scheduling to minimize the total earliness and tardiness of jobs with distinct due dates is a nondeterministic polynomial-hard problem. Delayed customer orders may result in penalties and reduce customer satisfaction. On the other hand, early completion creates inventory storage costs, which increase the total cost. Although parallel machines can increase productivity, machine assignments also increase the complexity of production. Therefore, the challenge in parallel machine scheduling is to dynamically adjust the machine assignment to complete the job within the shortest possible time. In this paper, we address an unrelated parallel machine scheduling problem for jobs with distinct due dates and dedicated machines. The objective is to dynamically allocate jobs to unrelated parallel machines in order to minimize the total earliness and tardiness time. We formulate the problem as a mixed integer linear programming (MILP) model and develop a modified genetic algorithm (GA) with a distributed release time control (GARTC) mechanism to obtain the near-optimal solution. A preliminary computational study indicates that the developed GARTC not only provides good quality solutions within a reasonable amount of time, but also outperforms the MILP model, a classic GA and heuristic approaches described in the literature.