# Mixed Model Line Balancing With Smoothed Station Assignments Definition

^{1}Department of Industrial Engineering, Yildiz Technical University, 34349 Istanbul, Turkey^{2}Department of International Trade and Logistic Management, Maltepe University, Maltepe, 34857 Istanbul, Turkey

Copyright © 2013 Şükran Şeker et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Mixed-model assembly line (MMAL) is a type of assembly line where several distinct models of a product are assembled. MMAL is applied in many industrial environments today because of its greater variety in demand. This paper considers the objective of minimizing the work overload (i.e., the line balancing problem) and station-to-station product flows. Generally, transportation time between stations are ignored in the literature. In this paper, Multiobjective Mixed-Integer Programming (MOMIP) model is presented to optimize these two criteria simultaneously. Also, this MOMIP model incorporates a practical constraint that allows to add parallel stations to assembly line to decrease higher station time. In the last section, MOMIP is applied to optimize the cycle time and transportation time simultaneously in mixed-model assembly line of a real consumer electronics firm in Turkey, and computational results are presented.

#### 1. Introduction

Mixed-model assembly lines are one of the important parts of mass production systems and generally useful in small product variety and high-volume industries such as automotive, electronics, and machinery. An assembly line comprises several successive workstations where a set of parts for one or more product types are assembled [1]. The assembly line balancing problem (ALBP) has had significant industrial importance since Henry Ford’s introduction of the assembly line. ALBP is the assignment of product tasks to different stations with considering precedence relations between tasks. In spite of the high cost of settings and operating an assembly line, manufacturers often simultaneously produce one model with different features or several models on a single line [2]. Assembly lines can be classified as “single model,” “multimodel,” and “mixed model” with respect to the number of different products assembled on an assembly line. We can see difference between single-model, mixed-model, and multimodel assembly lines in Figure 1.

**Figure 1: **Difference between single-model, mixed-model, and multi-model assembly lines.

In *single-model assembly lines*, only one model product is produced in the same line. The assembly lines where products of one similar model are assembled with batches are called *multimodel assembly lines*. *Mixed-model assembly lines* are the lines on which in the simultaneous production products of more than one model are assembled [3]. In order to meet the customers’ demand of individual and different models of product, mixed-model assembly lines are used. Thus, there can be produced various models but small quantity of products without setup operations on the same line. This is required to respond to the demand of market quickly and adjust to the change of market environment in time. Mixed-model assembly lines have a strong impact to improve the goal of Just in Time (JIT) and balanced production [4].

Mixed-model assembly has had a big importance because of its diversity. Although other goals of mixed model assembly lines such as low costs, high productivity, and standardization are in contrast with diversity, the success of a company is related to its ability to deal with complex products and process designs [5].

There are two types of mixed-model assembly line problems (MMALPs), which are referred as dual problems in the literature.(i)MMALBP-I minimises the number of workstations for a given cycle time.(ii)MMALBP-II minimises the cycle time for a given number of workstations.

In type I problems, the cycle time (the time elapsed between two consecutive products at the end of the assembly line) and the production rate have to be prespecified. Thus, it is more frequently used in the design of a new assembly line for which the demand can be easily forecasted. Type II problems deal with the maximisation of the production rate of an existing assembly line. For instance, the MMALBP-II is applied when changes in the assembly process or in the product range require the line to be redesigned [6].

Material movement is an important factor in the production line. Although it is an important factor in nonvalue-added cost function, it increases the cost of production. So, in a well-designed system, work and storage areas should be near to their point of use. In an assembly line material handling system, transportation of materials and storage devices require huge capital investment. However, transportation does not add value to the final product.

Transportation time is usually added to the processing time or negligible in assembly line systems. However, minimization of assembly parts from a machine to another decreases the completion time and cost of products. But, minimization of part unit movements can cause workloads imbalance. This leads to unequal total assembly times assigned to stations and longer intermediate queues and bottlenecks in the system as a result. In order to have the best assembly system capabilities, balancing of the line and transfer times between stations should be taken into account simultaneously. Routings of part units are completely defined by the sequence of machines they have to visit.

Although there is a vast literature on the mixed-model assembly line balancing and sequencing problem, transportation times between stations consist of process routings of products and balancing problem generally is not considered in an integrated fashion. In this paper, we propose a mixed-integer programming model to tackle this problem. Also, we assume that there can be parallel machine in some stations, and we add this as a criterion to mathematical model.

With this point, this paper includes two main objectives.(1)The workload balancing assigns tasks to stations in order to equalize station workloads. (2)The total amount of transfers of components from a station to another is minimized. In other words, we look for balancing routings of part units to minimize transportation times that cause the increase of completion time of the product.

To reach these objectives, some constraints are added to the mathematical model. If it is required, we add parallel machine to minimize cycle times of stations. MOMIP model also includes a finite workspace constraint that is considered with line balance. Finite working space might be subject to technical restrictions and space requirements of assigned station. The limited workspace capacity restricts the number of tasks which are assigned to each station.

In Section 2, there is a review of literature on MMALP. Then in Sections 3 and 4, MOMIP model is proposed with results of experiments and real-world application in consumer electronics in Turkey. In Section 5, conclusions are presented.

#### 2. Review of the Existing Literature in MMAL

The mixed-model assembly line deals with solving two primary problems in a production line. The first problem is the design and balancing of the production line, whereas the second problem is the determination of the production sequence for different models [7]. The line balancing comprises the assignment of tasks to stations and determination of the work content and model type per station. However, the production sequence is the model mix arranged with regard to minimum overloads on the assembly line. Balancing and sequencing problems are known as an NP-hard class of combinatorial optimization problems in mixed model assembly line literature.

Several researchers have studied MMAL balancing problems. Thomopoulos [8] and Macaskill [9] are the initial researchers in solving this problem. Macaskill [9] and Chakravarty and Shtub [10] have also studied the line balancing for traditional mixed model straight lines (MMSLs). Also, [11] presents a balancing methodology for mixed-model lines with deterministic task times. The objective is minimizing the total cost of stations (essentially the regular time labor cost) and work overload. Erlebacher and Singh [12] proposes a method to allocate a fixed total processing time variance among multiple stations and to minimize the total expected work overload. Zhang and Gen [13] present random key-based representation method with adapting Genetic Algorithm to assign the suitable task to the suitable station and the allocation of the proper worker to the proper station. The objective is to minimizate the variation of workload and the total cost under the constraint of precedence relationships.

The mixed model assembly line sequencing is investigated in [14] for the first time. Various objectives are reported in the literature in determining the optimal sequence for a mixed model assembly line. The common objectives are minimizing the overall line length [15–19], minimizing the risk of stopping a conveyor [20], minimizing the total utility work [21, 22], and keeping a constant rate of part usage [23–27]. Also, Bard et al. [15], Scholl [28], and Yano and Bolat [29] present several procedures for different versions of the mixed-model-sequencing problems [30].

However, Celano et al. [31] investigate the sequencing of MMAL assuming that the parts usage smoothing is the goal of the sequence selection. Mirzapour Al-E-Hashem et al. [7] present a sequencing problem with a bypass subline with the goals of leveling the part usage rates and reducing line stoppages. To solve this problem, a novel hybrid algorithm incorporating genetic algorithm and event-based procedure is developed to solve the problem.

However, there are a couple of papers dealing with simultaneous assembly line balancing and sequencing [32–37]. Hu et al. [38] also analyze the balancing of mixed model assembly lines and design a new algorithm based on the process exchange according to its attributes and characters. The algorithm could be utilized to make further optimization of mixed model assembly lines on the basis of the best production sequence.

Merengo et al. [39] develop a new balancing and production sequencing method for manual mixed-model assembly lines. Minimization of the number of stations is provided by the balancing method, and a uniform part usage is obtained by the sequencing method. Kim et al. [40] present a new method using a coevolutionary algorithm that can simultaneously solve balancing and sequencing problems in mixed-model assembly lines. Karabatı and Sayın [41] propose the MMALBP with the objective of minimizing the total cycle time by combining the cyclic sequencing information. They propose a mathematical model and an alternative heuristic approach to minimize the maximum subcycle time [42]. Fattahi and Salehi [43] consider a mixed-integer programming model with a variable rate launching interval between products on the assembly line, to minimize the idle and utility time cost, with optimization sequencing and launching interval for each sequence.

Although transportation of units is very important in assembly systems, there are few studies that take into account that part units’ movements in assembly lines. Transportation time is usually added to the processing times or negligible in assembly systems. However, minimization of assembly parts movements from a machine to another decreases the completion time of products.

In our study, we propose a mixed-integer programming that can simultaneously deal with both balancing and sequencing problems in MMAL, and identical parallel machines are allowed at each stage of the serial system. With this approach, we obtain the best task sequences for the models by taking into consideration the minimization of transportation of models between stations; we also solve the balancing problem in the line at the same time. The mathematical model intends for balancing of workloads and routing of unit parts.

#### 3. Model Description

This paper introduces a mathematical model for MMAL, and it can be categorized as MOMIP model. This mathematical model is integrated to real-world application. Our mathematical model is based on Sawik’s integer programming models about mixed model assembly line [44, 45]. The problem objectives are the determination of allocation of assembly tasks among the stations, where they have parallel machines and selection of assembly sequences and assembly routes for a set of products simultaneously to balance station workloads and to minimize total transportation time in assembly line.

We give weights to objectives to solve this multiobjective problem. This problem is solved using ILOG OPL optimization software [46]. The proposed model is used for a mixed model assembly line problem from real world in a Turkish consumer electronics firm. Due to the NP-hard nature of the problem, the size of our model would be large to obtain optimal solutions for problems of realistic sizes. Also, the model suggested in this paper presents a significant improvement relative to the models in the literature.

The assumptions of the proposed model are as follows.(1)Each assembly task must be assigned to at least one station (alternative assignments are allowed).(2)There are parallel machines in some stations.(3)Total space required for the tasks assigned to each station must not exceed the station’s finitework space available.(4)Each product must be routed to the stations subject to precedence relations defined by its assembly plan.(5)Revisiting of stations is not allowed.(6)Each station can perform at most one task at any given time.(7)Transfer times between stations are not negligible.

*Notation*

*Indices*: assembly station , : assembly task : parallel machine at station : product, : assembly sequence, .

*Input Parameters*: working space of station for task : working space for station : number of parallel machines in station : process time for task of model : transportation time from station to station : the set of stations capable of performing task : the set of tasks required for product : the set of immediate predecessor-successor pairs of tasks for assembly sequence such that task must be performed immediately before task : the set of assembly sequences available for product : the set of tasks in assembly sequence .

The following decision variables are introduced to model the loading and routing problem:: the weight factor (),: a big number.

*Decision Variables*, if assembly sequence is selected; otherwise 0;, if task is assigned to station ; otherwise ;, if task is assigned to parallel machine in station ; otherwise ;, if product in sequence is transferred from station after the completion of task to station to perform next task; otherwise ; is the maximum station workload (cycle time), represents the weighted sum of total assembly and transportation time.

We can state the problem formally as follows: subject to

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