Currently practiced formulations for the assembly line balance problem

Abstract

EXECUTIVE SUMMARYNew formulations for the assembly line balance problem are proposed based on interviews and surveys of practicing engineers. These formulations are the basis for a model in goal programming form. A branch-and-bound algorithm is developed which can solve the model for an optimum solution. Computational studies show that computer run time is very modest for moderate size problems.Interviews and a survey of practicing engineers were used to develop a list of goals or constraints germane to the assembly line balance problem. These included minimizing working areas or employees, making sure tasks assigned to a station do not exceed the cycle time, and adhering to sequence constraints. These constraints are included in most traditional models. However, additional goals were mentioned. These included avoiding changes in workload assigned to a work area, adhering to layout requirements of the plant, making combinations of tasks interesting, avoiding the combination of physiologically demanding tasks, etc.The additional goals above are incorporated in a new formulation for the assembly line balance problem. This formulation is in goal programming form. The goal programming model attempts to minimize deviations from goals. If deviations are necessary, lowest rankedgoals are violatedJrst. The objective function of the model is based on an ordinal ranking of goals only. The survey mentioned above showed that engineers did not find it d@cult to rank the importance of goals.The proposed goal programming model is a mixed integer linear program. Previous studies have shown that cutting plane and implicit enumeration techniques are inferior to branch-and-bound algo-*

Simultaneous balancing and buffer allocation decisions for the design of mixed-model assembly lines with parallel workstations and stochastic task times

“…After a number G of iterations the algorithm stops and the individual with the best fitness is considered the final solution. The proposed approach has been tested on 5 problems (Bartholdi, 1993;Gunther et al, 1983;Rosenberg and Ziegler, 1992;Scholl, 1993;Wee and Magazine, 1981) of different size, varying the number of tasks between a minimum of 25 and a maximum of 297. With the aim of exploring a larger number of cases, each of the 5 problems has been solved for 4 different cycle times (see Table 4).…”

The effect of strengthened linear formulations on improving the lower bounds for the part families with precedence constraints problem

“…Even so, the average gap from BF2cut is the best among the gaps given by all the formulations. Moreover, in Table 7.2 one may see that the optima given by the linear relaxations of the strengthened formulations (columns (6) and (9)) significantly improve the initial null values which do not appear in the table. Additionally, one finds that BF2cut produced lower bounds that are appreciably better than those obtained from BF1cut, and this difference between the two lower bounds is slightly more marked and frequent in the case of instances with equal capacity for the families (for example I 6 ).…”

“…Precedence constraints were mentioned in [4] by Finke and Kusiak and in [14] by Moon et al Viswanathan [23] refers to the capacity constraints imposed by the number of parts to attribute to a machine or cell of machines, noting that this parameter is indicated by the production design analyst. The PFP was also motivated by the problem proposed by Gunther et al [6], in which the objective is to assign operations that use common tools to the same work station. However, the PFP is a more general issue insofar it considers all these features simultaneously.…”

Preventing ergonomic risks with integrated planning on assembly line balancing and parts feeding

“…Gunther, Johnson, and Peterson 1983;Carnahan, Norman, and Redfern 2001;Akyol and Baykasoğlu 2016;BatallaGarcía 2016a, 2016b). Case studies and computational experiments show that alternative solutions, which are optimal with respect to productivity criteria, may differ a lot in terms of ergonomic risks they impose on assembly operators (see Colombini and Occhipinti 2006;Otto and Scholl 2011;Battini et al 2016b).…”