span of control in long assembly lines – segmenting

22nd International Conference on Production Research

SPAN OF CONTROL IN LONG ASSEMBLY LINES – SEGMENTING THE LINE Abstract ID: PSMG10031

Abstract This paper explores the effect of span-of-control on long assembly line managerial segmentation into sections, and provides a framework for deciding the line's managerial structure. Span of control in assembly lines is analyzed, and is shown to be a major motive for segmenting the line. A foreman's supervisory attention is spread across the stations under his/her control. Therefore, span of control of the line's foreman is modeled as a service model, where the foreman gives managerial and relief service to all the stations under his/her control. The paper develops quantitative model to represent the related tradeoff related to the span of control and suggests bounds and optimal solution for the segment length (number of stations per segment). The model enables finding effective upper bounds to number of stations per line section, implicitly establishing the practicality of exact methods for designing and balancing each section. Keywords: Span of control, assembly line, segmentation, zones, team size

1

INTRODUCTION

While the management of long assembly lines is typically divided into zones and segments [1, 2, 3] only scant research has been done on this subject. Almost no work exists on the considerations, justifications, and motivations for segmenting the line. This paper develops a quantitative model for span of control to assist in deciding the division of assembly lines into segments, and to assess the impact of line segmentation. The operation of a long assembly line with hundreds of stations must be managed and controlled constantly to ensure smooth production [4]. Such lines characterized automotive and heavy equipment industries. The shear complexity of managing such lines necessitates the division of the line into segments – each with its own foreman or supervisor [5]. While zones are usually large, and derived from the nature of the process, the segmentation to smaller sections is less obvious. An example of partition into zones could be found in the automotive assembly lines [6], assembly lines for complex appliances, and in the aircraft industry. Woodward [7] reports on departments and zones that averaged over 50 stations each. The division into sections of 8 to 12 stations frequently appears in the literature as the allocation of work into teams [3, 8]. This paper explores the considerations related to span of control in assembly lines and shows that it is a major motive for segmenting the line. The management of a line segment is composed mainly of (1) supervisory assistance, (2) flow control, (3) quality control, (4) worker short replacements, absenteeism and turnover. A foreman's supervisory attention to these factors is spread across the stations under his/her control. Therefore, span of control of the line's foreman is modeled as a service model, where the foreman gives managerial and relief service to all the stations under his/her control. The paper develops quantitative model to represent the related tradeoff related to the span of control and suggests bounds and optimal

solution for the segment length (number of stations per segment). The model enables the designers of assembly lines to determine the appropriate division of the line into sections and zones, and the best allocation of stations to sections. In addition, finding effective upper bounds to number of stations in a section of a line, establishes the practicality of exact methods for designing and balancing each section. 2

LITERATURE REVIEW

The division of assembly lines into zones was mentioned even by the pioneers of assembly line balancing research such as [9, 10]. Many papers on line balancing treated zones as given constraints that complicate line balancing [7, 11, 12]. Bukchin and Meller [13] developed a planning methodology for arranging the zones in an optimal layout. Some research papers try to split the assembly process to teams (e.g., [14, 15]. Bukchin and Masin [15] propose a methodology for assigning parts of the bill of materials (BOM) to teams. They specified assembly line teams of eight to twelve workers. Inman and Blumenfeld [3] simulate the team size and its effects on assembly lines. They recommend team size of twelve stations for a 5% absenteeism rate, and eleven stations for a 10% absenteeism rate. Cross-training increases the optimal team size by about 2 in all cases. Span of control is the focus of this paper, but since its literature proliferated, generating profusion of papers; in this review we focus on either on quantitative results, or load estimation in production settings. The scientific roots of this subject go back to Fayol [16] who presented an indepth discussion about the effects of coordination and control on management hierarchy. Some other pioneers investigated the relationship between nature of managerial attention and span of control (e.g., [17, 18, 19, 20]). Several researchers agree that there is no generally applicable optimum span of control but instead the optimal span of control is an outcome of a tradeoff of several

factors influencing the balance between costs of supervision and supervision quality [21, 22, 23]. Keren and Levhari [24, 25, 26] developed a mathematical method for optimizingl span of control. Their method relies heavily on the interaction time between the supervisor and his subordinates, and supervisor planning time. But even its authors admit that this model is very complicated, and far from being complete or practical. Geanakoplos and Milgrom [27] suggest approximations with questionable accuracy [28]. Qian [29] proves that for optimal span of control, the span grows as incentives fall (i.e., the higher the managers’ hierarchical position, the higher his incentive and the smaller his span of control.) Meier and Bohte [30] recommended narrow spans for first-line supervisors when there is high turnover rate and instability, Smeets and Warzynski [31] mention that problems solving was found to be more dominant than communications, for determining span of control.

So, inequality (28) gives an upper bound on the section’s length (NS) for any combination of estimated event rate (events which requires managerial intervention), and the mean and variance of the managerial intervention duration. The following numerical example illustrates this point: Consider a line with takt time (C) of one minute, where each station generates an event every 100 cycles on the average, foreman’s mean intervention duration of 0.5 minutes with large variation of 0.25. Summarizing the parameter values we have: =0.01 per cycle, and C=1, E[t]=0.5 and Var[t]=0.25, in minutes. In this example k=3 is chosen since Chebyshev's inequality ensures that three standard deviations above the mean, covers at least 8/9=88.9% of the required attention; for normally distributed attention it covers 97.7%. Requiring three standard deviations above the mean changes inequality (4) to:

0.01( NS )(0.5)  3 3 A MODEL BASED ON MEAN MANAGEMENT TIME AND STANDARD DEVIATION In this paper, the managerial span of control of the line’s foreman is modeled as a service model, where the foreman gives managerial and relief service to all the stations under his/her control. Span of control is a function of attention allocation. A section foreman or leader can focus his/her attention at most 100% of the time. If the attention is uniformly allocated among the NS stations in each section, the attention allocated to each station is 1/NS of the time. Attention allocation to stations could be spread uniformly, or according to Pareto efficiency consideration, or in another pattern or form, but it will always be a decreasing function of the number of stations in a section (NS). On the other hand, the performance of a line-section depends on the attention spread. Therefore, an increase of attention would increase performance but with a decreasing marginal addition. We assume the events that require management attention are independent. This assumption leads to an exponential distribution of time intervals between these events, and consequently to a Poisson arrival process. Since each station contributes a rate of  events per time unit, the event rate of a line-section is (NS) Since each event requires random amount of managerial attention (t), it is imperative to consider its duration distribution (F(t)). Assuming i.i.d. event durations, the overall demand for managerial attention (Y) in a section is a compound Poisson distribution with the following mean and variance.

E[Y ]   ( NS )( E[t ])



   ( NS )  Var[t ]   E[t ]

2



(2)

E[Y ]  k Var[Y ]  C

(3)

(5)

( NS )  6 50( NS )  200  0 Designating U= NS quadratic expression:

(6)

and inequality (6) turns into

U 2  6 50(U )  200  0

(7)

which results in U