A risk-averse two-stage stochastic programming model for a joint multi-item capacitated line balancing and lot-sizing problem

The aim of this work is to propose a solution approach for a capacitated lot sizing and scheduling real problem with parallel machines and shared buffers, arising in a packaging company producing yoghurt. The problem has been formulated as a hybrid Continuous Set-up and Capacitated Lot Sizing Problem (CSLP–CLSP). A new effective two stage optimisation heuristic based on the decomposition of the problem into a lot sizing problem and a scheduling problem has been developed. An assignment of mixture to buffers is made in the first stage, and therefore the corresponding orders are scheduled on the production lines by performing a local search. Computational tests have been performed on the real data provided by the company. The heuristic exhibits near-optimal solutions, all obtained in a very short computational time.

ABSTRACTIn the context of Industry 4.0, a production line must be flexible and adaptable to stochastic or real‐world environments. As a result, the assembly line balancing (ALB) problem involves managing uncertainty or stochasticity. Several methods have been proposed, including stochastic mathematical programming models and simulations. However, programming models can only incorporate a few sources of uncertainty that result in impractical or unfeasible solutions to implement due to overlooked complexities, while simulation is only used to test solutions from deterministic approaches or adjust parameters without maintaining their optimum value. The proposed methodology uses a deterministic mathematical model to minimize the cycle time, followed by the simulation to measure the impact of selected sources of uncertainty on the cycle time. Finally, the optimum value of the stochastic parameters is computed using simulation‐based optimization to maintain the average cycle time close to the deterministic one. A real‐life assembly line balancing problem for a motorcycle manufacturing company is solved to test the proposed methodology. The sources of uncertainty are the tasks' stochastic processing times, inter‐arrival time, the number of workers in each station, and the speed of the material handling system. Results show that the average cycle time is above 2.7% from the deterministic value computed by the programming model when the inter‐arrival time is set to 270 60 s; the processing times are allowed to increase or decrease by 3 s; the material handling system's speed is 1.5 m/s; and the number of workers in cells is between 4 and 6, with a speed of 2 m/s. The reader can download the source code and the simulation model to apply the methodology to other instances.

In this paper, we refer to a real case study of an industrial partner recently committed to its project on the design of a multi-unit and multi-product manufacturing system. Although the considered problem refers to an actual complex manufacturing system, it can be theoretically classified as a union of two key problems that need to be solved during the transfer line design stage: the transfer line balancing problem (TLBP) and the buffer allocation problem (BAP). As two closely related problems, TLBP and BAP usually have similar optimizing directions and share the same purpose: finding a balance between the performance of the transfer line system as well as minimizing investment costs. These problems are usually solved sequentially, but this leads to solutions close to a local optimum in the solution space and not to the global optimum of the overall problem. This paper presents a multi-objective optimization for concurrently solving transfer line balancing and buffer allocation problems. The new approach is based on a combination of evolutionary and heuristic-based algorithms and takes into account the uncertainty of market demand. To validate the proposed approach, an industrial case study in a multi-unit manufacturing system producing multiple products (four engine blocks) is discussed.

A goal programming mixed-model line balancing for processing time and physical workload

Gökçen et al. (2006) have proposed several procedures and a mathematical model on single-model (product) assembly line balancing (ALB) problem with parallel lines. In parallel ALB problem, the goal is to balance more than one assembly line together. In this paper, a network model for parallel ALB problem has been proposed and illustrated on a numerical example. This model is a new approach for parallel ALB and it provides a different point of view for interested researchers.

Purpose The purpose of this paper is to find the most efficient assembly line balancing solution across many heuristic line balancing methods, in assistance with a developed computer program. Design/methodology/approach In this paper, assembly line balancing problem was analyzed using t-shirt and knitted pants data. A computer program using MATLAB software for the solution of assembly line balancing problems has been developed. In this study, following heuristic assembly line balancing methods were applied: Hoffman method; position weight method; COMSOAL method; and Kilbridge and Wester method. A MATLAB program has been developed by taking into account of theoretical solution of all these methods. Later the program is developed further by analyzing solutions made manually and is made to verify the developed program. Findings Pre-studies which were conducted in order to decide which programming language would be the best choice for line balancing methods’ application came out with the result that MATLAB, from between C, C++, C# and Java, would be the best software choice. The main reason for this choice is that MATLAB is a powerful matrix operation software with a powerful user interface designing tool and has the tools to make development program to be used universally in every computer. Originality/value When the researches were investigated, it is clearly seen that, this study is the first research on using computer program for solving assembly line balancing problem.

Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms

Different from a large number of existing studies in the literature, this paper addresses two important issues in managing production lines, the problems of line balancing and model sequencing, concurrently. A novel hybrid agent-based ant colony optimization–genetic algorithm approach is developed for the solution of mixed model parallel two-sided assembly line balancing and sequencing problem. The existing agent-based ant colony optimization algorithm is enhanced with the integration of a new genetic algorithm-based model sequencing mechanism. The algorithm provides ants the opportunity of selecting a random behavior among ten heuristics commonly used in the line balancing domain. A numerical example is given to illustrate the solution building procedure of the algorithm and the evolution of the chromosomes. The performance of the developed algorithm is also assessed through test problems and analysis of their solutions through a statistical test, namely paired sample t test. In accordance with the test results, it is statistically proven that the integrated genetic algorithm-based model sequencing engine helps agent-based ant colony optimization algorithm robustly find significantly better quality solutions.

When defining the layout for a production line, it is necessary to assign tasks to workstations, so that the work is performed in a feasible sequence and approximately equal amounts of time are needed at each workstation, a process called line balancing. Therefore, the need for balancing production lines involves the distribution of sequential activities for jobs in order to allow high labour and equipment utilisation and minimise the idle time. Line balancing problems are complex to treat, being used distinct methodologies to perform it. This paper describes an application for line balancing using two genetic algorithms (the first obtains solutions to the problem and the second optimises those solutions), associated with a graphical interface for the problem data input and visualisation of results. Results demonstrate advantages over heuristic methods as it is possible to obtain more than one solution and it is more practical to use the developed application.

This study suggests a mathematical modelling approach to sub-assembly detection and assembly line balancing problems. The sub-assembly detection problem involves two issues as follows: 1 determine which components of products are assembled in sub-assembly area; 2 determine which components of the products are assembled directly in the line. In assembly line balancing problem tasks are assigned to the workstations. The main motivation of this study is to determine the best compromised assembly line structure by solving the sub-assembly detection and the line balancing problems jointly. A multi-objective mathematical model is developed to formulate the above mentioned problems in which two conflicting costs of sub-assembly generation and assembly line labour cost are involved. Since the applications in real life are imprecise, fuzzy goal programming is adapted to the developed model to determining the vague goal. Then the model is implemented in a real life automotive manufacturers assembly line balancing.

Implementation of mixed-model U-shaped assembly lines (MMUL) is emerging and thriving in modern manufacturing systems owing to adaptation to changes in market demand and application of just-in-time production principles. In this study, the line balancing and model sequencing (MS) problems in MMUL are considered simultaneously, which results in the NP-hard mixed-model U-line balancing and sequencing (MMUL/BS) problem. A colonial competitive algorithm (CCA) is developed and modified to solve the MMUL/BS problem. The modified CCA (MCCA) improves performance of original CCA by introducing a third type of country, independent country, to the population of countries maintained by CCA. Implementation details of the proposed CCA and MCCA are elaborated using an illustrative example. Performance of the proposed algorithms is tested on a set of test-bed problems and compared with that of existing algorithms such as co-evolutionary algorithm, endosymbiotic evolutionary algorithm, simulated annealing, and genetic algorithm. Computational results and comparisons show that the proposed algorithms can improve the results obtained by existing algorithms developed for MMUL/BS.

SUMMARYIn this paper, an integrated mathematical model for the balancing and sequencing problems of a mixed-model assembly line (MMAL) is developed. The proposed model minimizes the total overload and idleness times. For the sake of reality, the impact of operator’s learning and fatigue issues on the optimization of the assembly line balancing and sequencing problems is considered. Furthermore, it is assumed that the Japanese mechanism is used in this assembly line to deal with the overload issue. With respect to the complexity level of the proposed model, a genetic algorithm is developed to solve the model. In order to set the parameters of the developed genetic algorithm, the well-known Taguchi method is used and the efficiency of this solution method is compared with the GAMS software using several test problems with different sizes. Finally, the sensitivity of the balancing and sequencing problems to the parameters such as station length, learning rate, and fatigue rate are analyzed and the impact of changing these parameters on the model is studied.

Capacitated lot sizing problem (CLSP) finds its applications in manufacturing, production as-well-as process industries. Typical size of the real life problems is much larger compared to the sizes that can be handled by commercial solvers, as CLSP is an NP-hard problem. Researchers have attempted different variants of CLSP in last few decades and provided many classical, exact, heuristic and metaheuristic solution approaches. In this paper, we attempt to solve the multi item capacitated dynamic lot sizing problem with backorders and setup times (CLSPBS). We apply Lagrangian relaxation on the material balance constraint, to reduce the problem into several single constraint continuous knapsack problems with upper bound on the real variables. Bounded variable linear program determines the values of real variables. For the negative or positive value of coefficients in the Lagrangian function, we fix the setup variables at zero or one respectively. Thus, the reduced problem is solved in polynomial time, as the main effort required is only sorting of numbers. We use the set up variable that are at one, to develop yet another good upper bound. Branch-and-bound procedure benefits immensely by using these bounds to make a warm start.

Firstly, aimed at the existing problem of reconfigurable assembly line (RAL) balancing, the characteristics of RAL are analyzed and the special requirements of balancing are studied. Secondly, the mathematical model is proposed based on two factors, which are integrated including the cycle time and the assembly line efficiency. Then a new hybrid genetic algorithm is developed for finding optimal solution of the problems. Finally, example verification is carried out, and which indicates the validity of the proposed algorithm.

This paper addresses the problem of profit-oriented disassembly line design and balancing considering partial disassembly, presence of hazardous parts and uncertainty of task processing times. Few papers have studied the stochastic disassembly line balancing problem and existing approaches have focused on heuristic and metaheuristic methods. Most existing work has concentrated on complete disassembly where task times are assumed to be normal random variables and where AND/OR graphs are not considered. The objective of this paper is the design of a serial line that obtains the maximum revenue and then balances the workload under uncertainty. The processing time of a disassembly task is assumed to be a random variable with any known probability distribution. An AND/OR graph is used to model the precedence relationships among tasks. Stochastic programming models and exact-based solution approaches combining the L-shaped algorithm and Monte Carlo sampling techniques are proposed. The relevance and applicability of the proposed models and solution methods are shown by solving efficiently a set of disassembly problem instances from the literature.