Definition and Evaluation of Assembly Line Solutions

Assembly line balancing is a classic ill-structured problem where total enumeration is infeasible and optimal solutions uncertain for industrial problems. A quantitative approach to classifying problem difficulty and solution quality is therefore important. Two existing measures of difficulty, Order Strength and West Ratio are compared to a new compound expression of difficulty, Project Index. Project Index is based on individual assessment of precedence (Precedence Index) and task time (Task Time Index). The current working definition of Project Index is given. Early criteria for judging assembly lines use Balance Delay and Smoothness Index, both are flawed as criteria. Line and Balance Efficiency are developed as more appropriate. Project Index, Line and Balance Efficiency will be illustrated for a published test-case examined by the ‘A~Line’ balancing package. The potential for a “learning” approach, selecting models to suit problems using the measures of difficulty, will form part of the conclusions within this paper. INTRODUCTION The operational allocation of work elements to assembly line stations has been the subject of interest for nearly fifty years, starting with early problem definitions [Bryton, 1954] and the first published paper [Salveson, 1955]. The simplest form of assembly line problem involves the assignment of a series of work elements to uniform sequential stations. The speed of the assembly line and length of each uniform station dictates time available per operator, known as Cycle Time. Work elements are self-contained logical task collections capable of irreversibly changing the product. The object of line balancing is to assign elements to stations so as to promote the greatest manufacturing efficiency. Industrial variations on line balancing include resource changes, for example enlarged stations, parallel stations, fixed location resources, station zoning and fixed length lines. Product variation can include mixed-model and multi-model schedules. The addition of stochastic operator and production schedule behaviour produces a challenging range of NP-hard problems difficult to solve in an optimal manner. The ill-structured nature of line balancing, with a mixture of logical and numerate data, is examined to define individual project ‘difficulty’. Systematic numerate definition of difficulty brings forward the possibility of linking problem parameters to selection of solution method in a ‘learning’ mode. Linking problem and solution method requires a standardised evaluation model for goal seeking. The definition of problem ‘difficulty’ and standardised evaluation are examined in this paper. PI = Ps + Pb 2 Ps = c -1 n 1