Supporting offshoring and nearshoring decisions for mass customization manufacturing processes

European Journal of Operational Research 184 (2008) 490–508 www.elsevier.com/locate/ejor

Production, Manufacturing and Logistics

Supporting offshoring and nearshoring decisions for mass customization manufacturing processes Stefan Bock

*

Business Computing and Operations Research, University of Wuppertal, Gaußstraße 20, D-42097 Wuppertal, Germany Received 14 February 2006; accepted 20 November 2006 Available online 16 January 2007

Abstract Offshore countries attract companies for a possible relocation of production processes through extremely low worker wages. Particularly, mass production processes seem to be highly appropriate for a relocation. However, while the impact of wage reductions can be directly estimated, an appropriate determination of additional cost consequences proves to be a complex task. For instance, on account of lower education standards and higher fluctuation rates, the average worker skills in offshore countries are often significantly lower than in high-wage countries like the United States. In order to appropriately analyze and evaluate the resulting tradeoff between wages and worker skills for mass customization manufacturing systems, this paper introduces a new approach that comprises a detailed mixed-model assembly line balancing. This approach provides a direct comparison of the estimated variable manufacturing costs by generating a country-dependent line layout for all competing locations. In order to validate the efficiency of the balancing approach and, in particular, derive general implications for management, several test series with various country configurations were executed. First, by attaining improvement rates of up to 40%, the capability of a generated Tabu Search procedure for finding appropriate line layouts was proven. Second, as the main result, the complexity of the variant program was identified as a crucial factor for offshoring decisions since it substantially affects variable manufacturing costs. This was particularly proven for countries with low worker skills, which attract offshoring/nearshoring through exceptionally low labor costs. Hence, companies that consider outsourcing production systems to those countries are strongly hold to examine these decisive effects thoroughly. Regarding this, offshoring becomes very promising for manufacturing processes characterized by a moderate variant complexity level.  2006 Published by Elsevier B.V. Keywords: Offshoring; Production; Mass customization; Mixed-model assembly line balancing; Tabu Search

1. Introduction Owing to keen global competition in many markets today, companies are continuously forced to reduce their manufacturing costs. Thus, attracted through substantially lower wages, relocating production processes

*

Tel.: +49 2024392442; fax: +49 2024393434. E-mail address: [email protected]

0377-2217/$ - see front matter  2006 Published by Elsevier B.V. doi:10.1016/j.ejor.2006.11.019

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to foreign countries becomes a promising alternative to producing at home (Nachum and Zaheer, 2005; Trampel, 2004). Offshoring specifically denotes the outsourcing of production processes or services to another, mostly a remote country (Pfannenstein and Tsai, 2004; Liebermann, 2004). Initiated in order to avoid additional costs caused by the adaptation to different languages and cultures, nearshoring characterizes a relocation to closer located countries (Trampel, 2004). Among others, India, Ireland, the Philippines, and China are frequently cited as profitable offshoring destinations for US companies (Hogan, 2004; Trampel, 2004). Contrary, Western European competitors frequently tend to nearshore to Eastern European countries (Farell, 2004; Trampel, 2004). In the following, the term offshoring should stand for both of the above-mentioned definitions. Owing to their simple arrangement and their strong need for efficiency, particularly mass production processes seem to be suitable for a relocation. However, the development towards mass customization has caused considerable increases in complexity within assembly line production processes (Bock, 2005; Fogliatto et al., 2003; Da Silveira et al., 2001). In order to deal with those increases, the personnel employed at the line has to handle the oscillating capacity demand caused by enormous variant mixes. Obviously, mass customization production processes require substantially higher worker skills compared to homogeneous mass production processes. Note that it is not unusual that the theoretical production program of a modern mass customization manufacturing process comprises more than a billion different variants (Blecker et al., 2004; Piller et al., 2003). Hence, ensuring an efficient execution of mass customization production processes becomes a challenging task, even in modern industrial societies where the average education level is high. Deployed workers and floaters are frequently overwhelmed with the fast variant changes occurring throughout these production processes. Note that owing to the extremely high number of variants, it frequently happens that a specific variant is produced at the line for the first time. Consequently, it is not unlikely that, owing to an incorrectly executed or uncompleted task, a non-negligible proportion of product units is not correctly manufactured. In order to resume the production of these items, different measures are thinkable. One possibility is placing these items on the conveyor belt for a second time and thus elongate the manufacturing time of the considered production program by at least one takt time unit. Alternatively, the defective items can be fixed in a specific offline area. But, however it is implemented, those repair measures are extremely costly compared to an accurate production. Thus, the number of those disruptions has to be kept strictly low for an efficient use of assembly lines. This challenging task is even more complicated if a considered offshore country provides only low average worker skills (Swenson, 2005). Note that there may be dramatic differences in the average skill levels of workers due to the development in offshore countries (Swenson, 2005). It can be stated that offshoring decision problems are characterized by an interesting tradeoff in these cases. On the one hand, significant reductions of worker and floater wages can be attained by the considered relocation of the respective manufacturing process. For instance, according to a publication of the US Bureau of Labor Statistics in 2003, the hourly compensation cost for production workers in manufacturing amounts to 21.33$ in the United States, 5.83$ in Hong Kong, 7.27$ in Singapore, and 5.41$ in Taiwan (Hogan, 2004). On the other hand, the lower worker skills more likely result in an increased number of inefficient repair constellations. While it is quite simple to appropriately estimate the aspired wage cuts, the calculation of the additional manufacturing costs incurred through decreased worker skills is a complex problem. It requires a consideration and evaluation of the resulting line layouts. For this purpose, this present paper proposes a new approach which comprises a detailed assembly line balancing planning. In order to assess the potential cost consequences of a considered relocation of a mass manufacturing process, an alternative structure of the respective mixed-model assembly line system is generated for the competing locations. Here, the individual wage level and the different kinds of worker and floater skills are country-dependent impact factors. These parameters are the inputs of the balancing model. The balancing model is introduced in Section 3. Subsequently, a description of a specifically designed solution procedure is provided in Section 4. On account of the high computational complexity of the defined model, this procedure is designed as a Tabu Search heuristic. In order to evaluate the efficiency of the balancing approach and particularly derive strategic implications of offshoring decisions, a detailed analysis of computational tests is conducted in Section 5. The paper concludes with a brief summary of findings and a consideration of future research directions in Section 6.

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2. Literature review This paper introduces a new approach that supports offshoring decisions. It is mainly based on the determination and application of a specifically defined mixed-model assembly line balancing procedure. For a better understanding of the model, this present subsection provides a brief overview of existing mixed-model balancing approaches. First, it can be stated that the simple Mixed-Model Assembly Line Balancing Problem Family (MALBP) (for details, see Scholl, 1999; Becker and Scholl, 2006), which can be interpreted as the direct counterpart to the Simple Assembly Line Balancing Problem Family (SALBP), is too restrictive to be used within the proposed approach. For instance, by combining all variants into an aggregated product, the problem of handling an oscillating capacity demand is completely neglected. In contrast to this, an appropriate balancing approach has to incorporate a consideration and evaluation of all possible variant configurations for all stations. For this purpose, Thomopoulos (1970) once proposed the well-known smoothing criterion. It pursues task allocations that guarantee that the operating times of all variants in all stations are close to the average station time of the respective variant. Since costly bottlenecks derive only from work overload, Scholl (1999) proposes replacing the smoothing criterion by a minimization of takt time violations of all variants in all stations. Merengo et al. (1999) propose two balancing criteria: The first pursues the avoidance of variants with a dominating processing time in some station. The second seeks the finding of balanced constellations where the differences of the execution times to an average variant are minimized for all variants at each station. In contrast to this, Vilarinho and Simaria (2002) suggest an extension of MALBP-1 by the introduction of two secondary balancing goals pursuing workload smoothing between as well as in stations. More specific performance issues of mixed-model assembly line balancing have been examined by Macaskill (1972) (minimization of occurring idle times within the production process), by Fremery (1991) (station coefficient of variation measure), and by Bukchin (1998) (model variability and bottleneck measure). For a maximization of operational throughput, Bukchin shows empirically that the bottleneck measure outperforms the measures introduced in the past (Bukchin, 1998; Bukchin et al., 2002). Additionally, Bukchin et al. (2002) propose a three-stage approach. In the first phase, tasks that have to be assigned to an identical station for all variants are allocated. In the second phase, the task assignment is completed and balanced for each variant by complying with the existing allocation constraints. Finally, in order to improve the layout found, a neighborhood search is conducted in the third phase. While the approaches examined so far set the focus of the layout planning process on a pure task allocation problem, recent contributions intend to provide a more comprehensive understanding of the problem. Therefore, additional aspects that are relevant to an efficient practical use of mixed-model assembly lines have been integrated. For example, Askin and Zhou (1997) introduce parallel stations and selections of equipment while the solution quality is measured by the total resulting costs for installation. Kim et al. (2000) generate specific genetic algorithms for minimizing the utility work, i.e., the amount of work that is not completed within the given length of the workstation. For this purpose, a combined scheduling and balancing problem is examined. Karabati and Sayin (2003) incorporate operating aspects into the balancing problem. Specifically, they propose minimizing the total takt time of the line by integrating its sequencing information. The specific attributes of U-shaped mixed-model assembly lines are examined, for instance, by Sparling and Miltenburg (1998), Kim et al. (2006), and Miltenburg (2002). In order to be useful in the offshoring decision support approach proposed in the present paper, the incorporated mixed-model assembly line balancing has to fulfill specific prerequisites. First, it has to be capable of handling extremely complex variant programs. Note that it is not unusual that the theoretical production program of a modern mass customization manufacturing process comprises more than a billion different variants. Additionally, the balancing approach has to include a sophisticated personnel planning instrument in order to examine offshoring decisions appropriately. Specifically, the number of workers and floaters employed at the line has to be estimated as precisely as possible. Besides, the balancing approach has to integrate an appropriate consideration of available worker skills and their consequences for a detailed exploration of offshoring effects. Despite the itemized extensions towards a more realistic mapping of mixed-model assembly lines, none of the approaches proposed in literature so far fulfills one of these prerequisites. First, each variant is still defined as a complete product in these models. Consequently, for instance by determining variant-depending contributions

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to the objective function, these approaches cannot be applied to constellations that are characterized by billions of theoretical variants. Moreover, no approach provides a detailed personnel planning instrument. Hence, the following section introduces a considerably extended problem formulation which addresses the above-mentioned shortcomings of the existing models. 3. Mathematical definition of the balancing model In this section, a new mixed-model assembly line balancing model that is specifically designed for a more comprehensive examination of offshoring decisions is introduced. One significant characteristic of the model is the incorporation of a detailed personnel planning instrument that is based on predetermined wages and skills of the available workers. Thus, the model enables a direct comparison of line layouts that are respectively adapted to the specific constellations provided by the competing locations. Two different groups of human resources are employed at the line. First, there are ordinary workers who are firmly assigned to a station. Since they constantly perform the same tasks, they are specifically trained. In order to deal with work overload scenarios caused by the oscillating capacity demand at the line, floaters are additionally employed. These floaters are temporarily assigned to stations where the currently employed personnel cannot guarantee a timely completion of a manufactured item. In order to guarantee a more economical deployment of floaters, they are additionally assigned to areas aside the line. Note that this offline work is assumed to be lower paid and non-time critical. Thus, it can be interrupted if a temporary assignment of the floater is required at the line. Owing to their higher flexibility, floaters receive a significantly higher income than ordinary workers. This means that if a floater is not employed at the line, the line itself has to compensate for the gap between the wage aside the line and the wage for the work at the line. This can be interpreted as the price for the availability of additional flexible resources (Bock et al., 2006). In order to appropriately estimate the personnel costs that are incurred, it is necessary to determine the size and the composition of the employee pool. It is required that enough personnel is available to complete the occurring work in each station within the predetermined takt time. More precisely, the total number of workers and floaters has to guarantee a timely production of all variants for all configurations at all stations. Note that this also covers a worst case constellation when the most complex variant is simultaneously produced in all stations of the line. Besides the personnel planning, further assumptions are made for an appropriate integration of offline costs. It is assumed that all defectively produced items are remanufactured. For this purpose, they are placed on the conveyor belt for a second time. Note that this procedure is independent of the kind of the defect. Consequently, each defective item stretches the total processing time by an additional takt time. Thus, the model charges the respective wages for this scenario. Therefore, offline costs are transformed into personnel costs. The model is based on a modular variant definition (Duray et al., 2000). By defining variants as bundles of specific options that can be selected by customers, even mass customization programs that comprise more than a billion different variants can be handled efficiently. In contrast to this, traditional balancing approaches, which are based on an integral variant definition, cannot be efficiently applied to those scenarios (a detailed depiction of these approaches can be found in Scholl (1999) or Becker and Scholl (2006)). In order to reduce the redundancy in the mapping of the varying execution times of tasks caused by the variant mix, one single option that affects its execution is predetermined for each task. Therefore, only differences of the chosen values of this so-called relevant option may have an impact on the execution of the task. Within the subsequent model definitions, the following shortcuts, which denote specific base units, are used: [], i.e., without any base unit; [MU], i.e., monetary units; [PU], i.e., product units; [TU], i.e., time units. 3.1. Parameters N – Total number of tasks to be executed for all variants [–] O – Number of product options that affect some task executions at the line [–] P – Estimated number of product items to be produced throughout the planning period in question [PU] C – Takt time of the assembly line, i.e., every C time units, a new item is produced. This parameter predetermines a lower bound for the rate of production that has to be achieved by the assembly line [TU/PU]

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M – Maximum number of stations installable at the line. Note that this parameter is introduced for technical reasons, i.e., it is not restrictive [–] MW – Maximum number of workers assignable to a station at the line [–] OVo (1 6 o 6 O) – Number of possible values for the oth (product) option [–] Fo,v (1 6 o 6 O; 1 6 v 6 OVo) – Assumed frequency of choosing the vth value of the oth option in the period in question. If no utilizable information is available for the in question, an equipartition can be P option o assumed instead. For all options, it holds: 8o 2 f1; . . . ; Og : OV F ¼ P [PU] o;v v¼1 ROi (1 6 i 6 N) – Option relevant to task i. Note that only alternating values for this option affect the execution of the ith task and therefore the respective processing times as well [–] ti;v;w ð1 6 i 6 N ; 1 6 v 6 OV ROi ; 1 6 w 6 MW Þ – Estimated processing time for the execution of the ith task by employing w workers to produce the vth value for the ROith option. Note that these parameters are based on a predetermined maximum performance level independent of the country in question. Consequently, in order to attain country-dependent results, these parameters have to be transformed by taking the respective factors into consideration. These country-dependent performance factors are introduced below [TU/PU] Ci  {1, . . . , N} (1 6 i 6 N) – Set of successors of task i in the precedence graph. Consequently, in a feasible execution of the manufacturing process, all tasks belonging to the set Ci can only be executed after the implementation of task i [–] WW – Wage per period for an ordinary worker employed at the line [MU] WF – Wage per time unit received by a floater [MU/TU] WOF – Wage per time unit paid in the offline area. In the following, it holds WOF < WF. In addition, it is assumed that independent of the frequency of his employment at the line during the production process, a floater always receives the entire wage WF [MU/TU] 3.2. Variables An assembly line layout is entirely defined by the determination of the following groups of variables si,m (1 6 i 6 N;1 6 m 6 M) – Allocation of the tasks to stations, i.e., si,m = 1 () task i is assigned to station m [–] wm (1 6 m 6 M) – Number of workers directly assigned to the mth station of the line [–] fm (1 6 m 6 M)P– Number of floaters reserved for an employment at station m in a worst case scenario. In addition, F ¼ M m¼1 fm is introduced [–] In order to simplify the subsequent model formulation, the following abbreviations are introduced: GT ðx; yÞ ðx; y 2 ZÞ – Binary function indicating ‘‘Greater than’’ (GT) for two whole numbers  1 when x > y; maxfx; yg  y 8x; y 2 Z : GT ðx; yÞ ¼ ¼ maxf1; x  yg 0 otherwise: Eqðx; yÞ ðx; y 2 ZÞ – Binary function indicating ‘‘Equality’’ (Eq) for two whole numbers  1 when x ¼ y; 8x; y 2 Z : Eqðx; yÞ ¼ ð1  GT ðx; yÞÞ  ð1  GT ðy; xÞÞ ¼ 0 otherwise:

ð1Þ

ð2Þ

S Tm ð1 6 m 6 MÞ – Set of tasks allocated to station m 8m 2 f1; . . . ; Mg : S Tm ¼ fij1 6 i 6 N ^ si;m ¼ 1g: S RO m

ð3Þ

ð1 6 m 6 MÞ – Set of options being relevant to the execution of the tasks allocated to the mth station 8 9 0 1 < = X 8m 2 f1; . . . ; Mg : S RO oj1 6 o 6 O ^ GT @ EqðROi ; oÞ; 0A ¼ 1 : ð4Þ m ¼ : ; T i2S m

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Note that only options belonging to this set can influence the execution  RO  of the work at station m. In order to S g is introduced. pm(o) unambiguously simplify the following notations, a permutation pm : S RO ! f1; . . . ; m m RO RO defines the position of o 2 S m in the set S m . S Cm ð1 6 m 6 MÞ – Set of all possible value constellations of the options that are relevant to the tasks allocated to station m n o RO 8m 2 f1; . . . ; Mg : S Cm ¼ ðv1 ; . . . ; vjS RO Þj8o 2 f1; . . . ; jS jg : 1 6 v 6 OV ð5Þ 1 o pm ðoÞ : m m j

3.3. Complexity measures The following abbreviations characterize the complexity of the production program to be manufactured in the considered planning horizon. Specifically, a tuple of two different parameters (r, q) is introduced in order to measure the complexity. • r – Total (theoretical) number of variants belonging to the offered production program. Hence, it holds: r¼

O Y

ð6Þ

OV o :

o¼1

• q – Variety of work content in the production program. Specifically, it measures the average deviation from the average execution time per task in percent for the employment of a single worker. ! POV ROi N POV ROi X 1 ti;v;1 v¼1 jt i;v;1  t i;1 j q¼  : ð7Þ ; with 8i 2 f1; . . . ; N g : ti;1 ¼ v¼1 N ti;1  OV ROi OV ROi i¼1

3.4. Personnel skills In order to integrate the estimated skill levels of the staff employable at the location in question, specific abbreviations are introduced. • x – Average worker productivity in percent (0 6 x 6 100). This factor directly affects the average task execution times, i.e., all execution times ti,v,1, which are estimated for a single deployed worker, are transformed by using this country-depending transformation percentage. Thus, it holds: 100  ti;v;1 : ð8Þ x • w – Average worker flexibility in percent (0 6 w 6 100). In the following, this parameter characterizes the workers’ ability of coping with complex variants. Specifically, it is assumed that the more flexible workers are, the less larger execution times are additionally increased. Thus, w affects the execution times as follows: 8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g : txi;v;1 ¼

8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g :   100  tx i;v;1 x x þ ð1  GT ðtxi;v;1 ; txi;1 ÞÞ  txi;v;1 ; tx;w i;v;1 ¼ GT t i;v;1 ; t i;1  w

POV ROi with

txi;1

¼

v¼1

txi;v;1

OV ROi

:

ð9Þ

• v – Average teamwork skills in percent (0 6 v 6 100). As mentioned above, all tasks to be executed at the line are performed by working groups. Thus, cooperation skills are crucial to achieve an accelerated execution by the employment of an increased number of workers. These skills can substantially vary between offshore countries. Therefore, the parameter v provides a country-specific cooperation performance measure. It holds: x;w 8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g : tx;w;v i;v;1 ¼ t i;v;1

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8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g : 8w 2 f2; . . . ; MW g:   100 ti;v;w1  ti;v;w  1   tx;w;v ¼ tx;w;v i;v;w i;v;w1 : v ti;v;w1

ð10Þ

• / – Floater availability. Binary parameter indicating whether the considered country enables an employment of floaters. Owing to the demanded flexibility, floaters are comparatively high-skilled employees who have to be specifically educated. However, not all potential offshore countries provide a labor market where these resources are sufficiently available. Hence, if floater employment is not possible in the country in question, / is set to ‘‘false’’. Otherwise, / is ‘‘true’’. • ai;v;w ð1 6 i 6 N ; 1 6 v 6 OV ROi ; 1 6 w 6 MW Þ – Work accuracy of the personnel. As already mentioned above, the accuracy of the task execution considerably affects the attainable efficiency of the assembly line. Moreover, the scrap rate significantly depends on the skills and the experience of the personnel. Thus, the scrap rate is integrated into the assembly line balancing model. For this purpose, ai,v,w determines the average absolute number of accurate executions of task i per 1,000,000 units in the country in question if the vth value of the ROith option is installed by employing w workers. Note that it is assumed that an increased number of workers reduces the probability of failure. On account of mutual assistance, the execution of specific, more complicated tasks can be simplified. Obviously, these effects again depend on the respective teamwork skills of the personnel determined by the factor v. Thus, since the a-values are basically defined for v = 100, it holds: 8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g : avi;v;1 ¼ ai;v;1 8i 2 f1; . . . ; N g : 8v 2 f1; . . . ; OV ROi g : 8w 2 f1; . . . ; MW g: avi;v;w ¼ ai;v;w1 þ

v  ðai;v;w  ai;v;w1 Þ : 100

ð11Þ

In order to simplify the following calculations, it is assumed that all defective items are remanufactured by just placing them on the conveyor belt for a second time. Hence, the production process is stretched by C additional time units for each defective item. 3.5. Restrictions A generated assembly line layout is feasible if it fulfills all the restrictions itemized below. Domains of the variables to be determined: 8i 2 f1; . . . ; N g : 8m 2 f1; . . . ; Mg : si;m 2 f0; 1g ^ wm 2 f0; . . . ; MW g ^ fm 2 f0; . . . ; MW g ^ wm þ fm 2 f0; . . . ; MW g ^ fm 6 /  MW :

ð12Þ

Each task is unambiguously assigned to a single station: 8i 2 f1; . . . ; N g :

M X

si;m ¼ 1:

ð13Þ

m¼1

The worker employment and the task assignment have to be consistent, i.e., a task can be executed only at a station where a worker is employed and vice versa: ! N N X X 8m 2 f1; . . . ; Mg : si;m 6 GT ðwm ; 0Þ  N ^ wm 6 GT si;m ; 0  MW : ð14Þ i¼1

i¼1

The task assignment complies with the existing precedence constraints: 8i 2 f1; . . . ; N g : 8j 2 Ci :

M X m¼1

m  si;m 6

M X m¼1

m  sj;m :

ð15Þ

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Empty stations are only allowed at the end of the line: ! ! N N X X 8m 2 f1; . . . ; M  1g : GT si;mþ1 ; 0 6 GT si;m ; 0 : i¼1

497

ð16Þ

i¼1

wm workers and fm floaters can avert each possible work overload in the mth station "m 2 {1, . . . , M}: 8 9
i2S m

The maximum total processing time at station m is calculated in Formula (17). In order to determine the time required for the most complex variant at station m, the maximum contributions of all relevant options are iteratively added. Consequently, the value with the longest processing time of the respective relevant option is determined in each iteration. 3.6. Assembly line control issues As already mentioned above, the personnel planning is based on worst case considerations. Specifically, the size of the floater pool is determined by the minimal number of floaters that prevents work overload even in the most extreme scenario. This scenario is characterized by the simultaneous production of the most complex variant constellation in each station. However, by using a sophisticated assembly line control (see Bock et al., 2006 for details), a considerable number of these negative scenarios can be avoided. By tuning the job sequence, modifying the worker and task assignment as well as implementing flexible overlapping areas between the stations, many capacity bottleneck constellations can be eliminated. However, an accurate estimation of these line-dependent reductions proves to be a complex task. Thus, in order to examine the consequences of various values, two additional parameters are introduced. • b – Assumed F is the number of floaters necessary to cope with the described worst case scenario, then the control abilities of the line allow a reduction to b Æ F [–]. • c – Assumed FTimes(L) is the duration during which a floater is employed at the line, then the control abilities of the line attain a reduction to c Æ FTimes(L) [–]. Note that all activities of a sophisticated assembly line control require flexible human resources. Consequently, the flexibility degree w introduced above, is applied again to provide a country-oriented specification (bw, cw). Thus, it holds: bw ¼

100  b 100  c ^ cw ¼ : w w

ð18Þ

3.7. Objective function A generated assembly line layout L is solely rated by its personnel costs AC(L). These are estimated for an average planning horizon in which P product units are manufactured. ! M X w w ACðLÞ ¼ WOF  FTimesðLÞ  c þ ðWF  WOF Þ  P  C  b  F þ WW  wm m¼1

þ OFFL  NO OFFL PRODðLÞ:

ð19Þ

Note that the line has to account for the entire floater wages during the duration determined by the abbreviation FTimes(L)

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2 M 6X FTimesðLÞ ¼ P  4

1 2 S RO jY m j fm X F p1 ðoÞ;v oA 4 m @@  ð1  nm ðf ; v1 ; . . . ; vjS RO ÞÞ m j P o¼1 f ¼1 m¼1 ðv1 ;...;v RO Þ2S C m jS m j 2 31313   X 5A5A5:  nm ðf  1; v1 ; . . . ; vjS RO f  tx;w;v Þ 4 i;vpm ðROi Þ ;minfwm þf ;MW g m j X

00

ð20Þ

i2S Tm

In this calculation, the minimum number of floaters that ensures a timely work execution is sought for all stations and their respective relevant option value configurations. More precisely, it is tested, whether f employed floaters are sufficient to avert an overload if f  1arenot.  In this calculations, the used binary function nm f ; v1 ; . . . ; vjS RO 2 f0; 1g indicates whether a work over mj  is manufactured by employing f load can be expected in station m if the variant configuration v1 ; . . . ; vjS RO m j additional floaters      C : n f ; v ; . . . ; v 2 S 8m 2 f1; . . . ; Mg : 8f 2 f0; . . . ; fm g : 8 v1 ; . . . ; vjS RO RO 1 m m jS m j m j 0 1 X x;w;v ti;vp ðRO Þ ;minfwm þf ;MW g ; C A: ð21Þ ¼ GT @ i2S Tm

m

i

Furthermore, the expected number of defective items in each period can be determined by ! M Y NO OFFL PRODðLÞ ¼ P  1  PROB ACC PRODm :

ð22Þ

m¼1

By assuming a stochastic independence between the different tasks, the probability of an accurately produced item in station m can be estimated as follows: 8m 2 f1; . . . ; Mg : PROB ACC PRODm 1 2 00 RO Sm j jY fm    X X F p1 m ðoÞ;vo A 4 @@  ¼ 1  nm f ; v1 ; . . . ; vjS RO m j   P f ¼1

o¼1

v1 ;...;v

jSRO m j

2S C m

2 3131    Y avi;v pm ðROi Þ ;minfwm þf ;MW g 5A5A:  nm f  1; v1 ; . . . ; vjS RO 4 m j 1; 000; 000 T

ð23Þ

i2S m

The cost rate for defective items (OFFL) is determined by a theoretical expansion of the working time for one takt. Therefore, the personnel resources are employed for C additional time units ! !  PM M X FTimesðLÞ  WOF m¼1 wm  WW þC : ð24Þ OFFL ¼ fm  ðWF  WOF Þ þ P 2P m¼1 Note that the average costs for floater employment during the repairing steps are calculated in the last summand. Since the respective product item is produced for a second time, only the tasks that are incorrectly processed in the first instance or tasks that are successors of a task that was incorrectly processed in the first instance have to be repeated. Therefore, it is assumed that 50% of the tasks of an incorrectly processed product item have to be repeated on the average. It is worth mentioning that this simplified cost calculation does not comprise any costs caused by incorrect handling of material. If these costs are identified as additional significant factors, the model has to be extended accordingly. 4. Balancing solution approaches In order to find efficient assembly line layout constellations, a specifically designed Tabu Search approach is applied (for an introduction to Tabu Search, see Glover and Laguna, 1997). This procedure is completely

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depicted in the present section. In order to conduct the search process starting from a feasible constellation, the procedure commences with a simple determination of an initial solution. Specifically, following the node numbering that is determined after sorting the nodes topologically (Cormen et al., 2001) all tasks are iteratively assigned to stations. For this purpose, stations are opened in ascending order and filled as long as the maximum number of assignable workers is able to guarantee a timely processing. Thereby, the first task that does not fit into the currently considered station, causes the opening of a new station. 4.1. The applied neighborhood In order to modify the existing solution in each move, different operations are tested. As provided by the meta-strategy Tabu Search, the best move in the neighborhood found, which is currently not blocked by a tabu state, is executed. Note that an existing tabu state is neglected only if this move leads to an improvement of the best currently known solution (this is frequently denoted as the improved-best aspiration criterion (Glover and Laguna, 1997)). The entire neighborhood of the Tabu Search procedure comprises the application of the following operations. • Task exchange: This kind of operations modifies an existing solution through the exchange of two tasks. Specifically, if the existing precedence and capacity constraints approve, two selected tasks currently assigned to different stations are exchanged. Note that in both affected stations, the restriction of the total work content (Restriction (17)) has to be fulfilled afterwards. • Task move: A task move assigns a task to another station at the line. Again, such an alternative is examined only if it complies with the existing precedence and capacity restrictions (Restrictions (15) and (17)). • Station splitting: In order to provide a more flexible move generation, stations can be split in two new ones at any inner task position. For this purpose, the tasks currently assigned to the station in question are iteratively examined in their current order. Note that within each solution, every task unambiguously possesses a position at the line. Therefore, station assignments are subsequences of one or more tasks that comply with the predetermined precedence constraints. Obviously, this operation can only be applied to stations comprising more than one task. • Station unification: This is the counterpart to the station splitting operation. By applying this routine to a station, it is tested if this station can be unified with its larger numbered neighbor. Since task positions are not affected, the completion of this operation can only fail in case of a violation of the Restriction (17). For an efficient move handling of complex instances, the Tabu Search algorithm applies all operations of this neighborhood only to a specific subsequence of consecutive tasks in a currently considered solution. More precisely, only tasks belonging to this subsequence can be moved into a new position or interchanged with another task along the line. In contrast to this selective source determination, the destination of an applied move or exchange operation is not restricted and is thus possible at the entire line. Moreover, station splittings or station unifications can be applied only to stations whose current assignment comprises tasks of the subsequence in question. After the completion of each move, the subsequence currently under consideration is cyclically changed. A neighborhood window is used for this purpose. By covering a contiguous partial solution, it determines the neighboring tasks that are currently under consideration for an application of the operations in each move. In the performed computational tests, the size of the window (sw) was always determined as a proportion of the total number of tasks (N). Specifically, it holds sw 2 {N/32, N/16, N/8, N/4, N/2}. Depending on the current performance of the conducted search process, the Tabu Search procedure switches between different states. By varying the size and structure of the applied neighborhood, these states substantially affect the searching process. In State 1, a neighborhood window size of max{1, N/32} tasks is predetermined. State 2 makes use of sw = max{1, N/16}, State 3 of sw = max{1, sw = N/8}, State 4 of sw = max{1, N/4}, and State 5 applies a neighborhood window size of sw = max{1, N/2} tasks. The search commences in the initial State 1. A state increment from i to i + 1 is always performed when a predetermined number of moves (mtrans,1) has failed to improve the best currently known solution. But, when this happens again in the fifth state, the window size is set to the maximum sequence length N. In contrast to the States 1–5, where the best found operation of all types is implemented, the higher numbered States 6–9 are single typed.

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Thus, the best found task exchange is implemented in State 6, the best found task move in State 7, the best found station split in State 8, and finally the best found station unification in State 9. Here again, a state transition to the neighboring larger numbered state is conducted when a predetermined number of moves (mtrans,2) has failed to improve the best currently known solution. In contrast to this, each improvement of the best known solution found in the States 6–9 induces a return to the initial state. In order to prevent cyclical computations, a Tabu List is applied. After performing a move, its resulting objective function value modulo 100,000 is blocked for 35 moves. For this purpose, an integer array TL is maintained throughout the search process. For i 2 N with 0 6 i 6 99,999, the entry TL(i) provides the move number when a currently blocked operation becomes available again. Note that in the jth move (j < TL(i)), all operations resulting in a constellation with an objective function value o, which fulfills the equality (o modulo 100,000) = i, are blocked. Consequently, after performing the mth move, which leads to an objective function value v, TL(v modulo 100,000) is set to m + 35. Since no operation is blocked in the beginning, all entries of the array are initialized with 1. The move execution of the Tabu Search procedure stops after the elapse of a predetermined time limit Tmax. This time limit is set in compliance with the complexity of the instance to be solved. 4.2. Evaluation of a solution found After modifying the currently considered solution, the respective objective function value has to be adapted accordingly. For this purpose, only the contributions of the affected stations at the line are examined. This recalculation commences with the determination of the costs of floater employment. Specifically, in order to sum up floater activity at the line, each value configuration of the options relevant to the station in question is examined. Since the quantity of assigned floaters as well as the quantity of workers are unspecified at this time, they are simultaneously set here. For this purpose, it is first tested whether there are configurations in that floater employment may be reasonable. This can only be the case if 1. (WOF  WF) < WW, and if nP o P x;w;v 2. o2S RO max j1 6 v 6 OV > C. T EqðROi ; oÞ  t o i2S i;minfv;OV RO g;1 m m i

Obviously, an employment of floaters is reasonable only in this constellation. Consequently, if at least one of these two restrictions is not fulfilled, only ordinary workers will be employed at the station in question. In the following, this configuration is denoted as the floater-less case. In this specific configuration, it only remains to determine the number of workers to be employed. For this purpose, the minimum number of workers wmin m is calculated first. It is determined as the minimum number of workers necessary for meeting the maximum execution time at the considered mth station within the predetermined takt time C. Hence, the total number of assigned workers can be selected out of the interval ½wmin m ; MW  in the floater-less case. Note in this connection that an increased number of workers, i.e., wm > wmin m , may result in reduced offline costs due to a decreased scrap rate. Thus, the tradeoff between wage increases and accuracy improvements has to be examined. For this purpose, all remaining alternatives are compared and the constellation resulting in the least costs is implemented. However, this alternative is not necessarily the optimal constellation. This is concluded because the applied offline rate OFFL depends on the total number of workers and floaters employed at the line as well as on the actual floater employment for coping with impending work overload. Consequently, the allocation of personnel at each station again influences the factor OFFL. However, these effects had never been observed in preliminary computational tests. Hence, recalculations of OFFL, which would be necessary for an optimal personnel assignment, were omitted. Therefore, in order to evaluate alternative worker assignments at the station in question, the offline rate OFFLpd is applied. It results from the solution provided by the last iteration. Note that apart from the floater-less case, OFFLpd is also applied to the configuration where both restrictions are fulfilled. When both restrictions itemized above are fulfilled, the personnel planning calculation becomes significantly complicated. More precisely, the ratio of floaters and workers has to be determined additionally in this case. Therefore, both parameters fm and wm have to be simultaneously specified while it holds

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fm þ wm 2 ½wmin m ; MW . Analogous to the floater-less case, again all possible value configurations for fm and wm are explored. However, while the number of employed workers is fixed in the floater-less case, it is no longer the case for explored configurations with fm > 0. Here, the temporary floater assignments depend on the complexity of the respective variants. Consequently, an accurate calculation of FTIMES and NO_OFFL_ PROD(L) has to comprise all possible value configurations of the respective relevant options at the affected stations. For each of them, the number of assigned workers and floaters is determined to derive the contributions to FTIMES and NO_OFFL_PROD(L), respectively. Thus, FTIMES and the scrap rate PROB_ACC_ PRODm are simultaneously calculated. Subsequently, the resulting costs for each feasible configuration of fm þ wm 2 ½wmin m ; MW  are compared. In order to prepare this subsequent comparison, two arrays are maintained throughout the exploration process. Providing an entry for each feasible configuration of fm þ wm 2 ½wmin m ; MW , intermediate results for FTIMES and NO_OFFL_PROD(L) are continuously updated. After completing the exploration, the results stored in both arrays are evaluated and the best found configuration is selected eventually. The examination process of all value configurations of the options respectively relevant to each affected station is carried out in a stack-oriented manner. Specifically, each entry on this stack represents the value of a specific relevant option that is currently considered. Hence, the examination begins with a null vector. While increasing the stack entries iteratively, it is always tested whether the currently generated subsolution can be completed to a constellation where work overload is possible (i.e., at least two workers are required to avert an impending work overload). If not, the exploration of the underlying subtree can be skipped. This results from the fact that these variant configurations are manufactured without any floaters. Consequently, the number of assigned workers is one for all these cases. Therefore, their total contribution to the parameters FTIMES and NO_OFFL_PROD(L) can be directly calculated. Note that these bounding rules may substantially reduce the computational effort. Since the parameters FTIMES and the scrap rate are already updated at this stage, the objective function value can be directly calculated afterwards. For this purpose, Formula (19) is used. Note that the offline rate OFFL is updated accordingly beforehand. 5. Computational results The intentions of the conducted computational tests are twofold. First, it should provide a performance evaluation of the proposed offshoring decision support system. Second, the measured results should be used to obtain basic cognitions concerning the main attributes that may drive the profitability of offshoring decisions. However, before these drivers can be identified, the test environment and the simulated configurations are briefly introduced. 5.1. Test environment and simulated configurations In the following, an examination of offshoring decisions is conducted by the means of a direct comparison of country-specific variable manufacturing costs. These costs are estimated for utilizing an assembly line layout generated by the Tabu Search approach. In order to conduct this comparison examplarily, a set of different theoretical country configurations is introduced in the following. Apart from a configuration representing a high-wage country (in the following denoted by the abbreviation HWC), several competing offshore countries are additionally generated. Altogether three groups of configurations are introduced (see Table 1 for details). Among them, HWC is characterized by a wage level of 100%. This country represents a configuration that may be found in a highly industrialized country, as for instance the United States. Here, the human resources are assumed to have the maximum skill level of 100%. The countries of the second group are denoted as A-countries and offer a wage cut of 50% compared to HWC. Here, two different country configurations (A1 and A2) are distinguished in order to analyze the impact of lower personnel skills. Finally, the B-group represents countries with a wage level of only 25% and further decreasing personnel skills. The configurations B1 and B2 are introduced to indicate different personnel skills. Note that all these configurations are not based on real countries but represent a thinkable pattern (cf. Hogan (2004) or Section 1 in this paper).

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Table 1 Predetermined parameters for the different countries Parameter setting for high-wage and offshore countries

HWC A1 A2 B1 B2

Wage level

Productivity x

Flexibility w

Team skills v

Accuracy Factor

Floaters av.? /

100 50 50 25 25

100 90 90 80 80

100 90 80 70 70

100 90 90 80 80

1,000,000 998,500 998,000 997,000 997,000

Yes Yes Yes Yes No

In accordance with the following parameter setting, altogether 10 basic problem instances have been randomly generated: N 2 f105; 221g; P 2 f205; 296g; C 2 f162; 193g; t1 2 f69:53; 78:72g: In order to provide reliable equipartitions, all instance generation processes make use of a random number generator that is based on the principles described in detail by Park and Miller (1988). In order to analyze the impact of the complexity of the variant program in detail, 5 different groups of variant programs (or complexity groups) were combined with these problem instances. Specifically, the complexity groups SC (= Small Complexity Level), MC (= Moderate Complexity Level), NC (= Normal Complexity Level), HC (= High Complexity Level), and EC (= Extreme Complexity Level) were respectively generated in accordance with the parameter setting depicted in Table 2. Note that each defined complexity group altogether comprises 10 randomly generated instances of variant programs. These variant program instances complement the 10 basic problem instances. All the 50 resulting problem instances were again recombined with three additional parameter constellations representing different control abilities of the line. Specifically, the parameters b and c vary between b = c = 1.0 (no control abilities), b = c = 0.5 (moderate control abilities), and finally b = c = 0.25 (comprehensive control abilities). Thus, altogether 150 completed instances evolve. All these resulting balancing problems were solved by applying the Tabu Search algorithm described in Section 4. This procedure was coded in C++ on an AMD Athlon XP1800+ Personal Computer using 512 MB DDR DRAM. In order to provide a comparison of sophisticated line layouts in all considered configurations, the proposed Tabu Search procedure was applied as long as substantial improvements were expected. Hence, according to the results achieved by preliminary analyses, the available computational time was restricted to 1000 seconds for the complexity groups SC, MC, and NC. Additionally, it was extended to 1800 seconds for the more complicated groups HC and EC. 5.2. Evaluation of the planning procedure In this section, the performance of the proposed planning procedure is analyzed. For this purpose, Table 3 provides the results attained for the HWC and the offshore countries of the category A. These results are focused on the configurations with a high and a small complexity level of the variant program. By examining the measured results, it becomes obvious that the Tabu Search procedure was able to substantially improve the initial solution independent of the respective specific country constellation. Owing to the fact that the Table 2 Parameter setting of the generated variant program groups Group

SC MC NC HC EC

Parameter setting of the variant program groups Number of variants (r)

Work content variety (q)

r 2 [8; 108] r 2 [50; 9.3312 · 104] r 2 [192; 6.77376 · 106] r 2 [4.92804 · 107; 8.0362533888 · 1013] r 2 [7.776 · 108; 5.0345463168 · 1017]

q 2 [9.346; 11.229] q 2 [8.525; 15.101] q 2 [12.37; 18.104] q 2 [15.196; 20.921] q 2 [20.438; 24.758]

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Table 3 Comparison of the average initial and average best solutions for various scenarios Scenario

Initial solution

Best solution F.

Total costs

S.

Red. (%)

S.

W.

W.

F.

Total costs

HWCSC/0.25 HWCSC/0.5 HWCSC/1.0

46.1 46.1 46.1

120.4 120.4 120.4

14.9 14.9 14.9

216,459,023 222,008,103 233,106,263

56.8 64.5 79.8

56.8 64.5 80.6

59.8 43.8 7.8

127,580,855 154,187,424 169,813,752

41.1 30.7 27.9

HWCHC/0.25 HWCHC/0.5 HWCHC/1.0

46.3 46.3 46.3

82 82.1 82.3

55.4 55.3 55.1

162,564,362 181,620,921 219,536,881

50.2 56.8 75.2

50.3 56.8 76

76.1 59.8 28.6

116,983,410 143,722,774 162,911,385

27.5 20.6 26.0

A1SC/0.25 A1SC/0.5 A1SC/1.0

70.2 70.2 70.2

114.1 114.2 114.3

71.7 71.6 71.5

138,135,107 152,823,424 176,210,685

75.2 83.8 93

75.2 83.8 93

83.4 58.4 24.4

92,342,345 108,144,948 117,516,114

31.7 28.5 33.4

A1HC/0.25 A1HC/0.5 A1HC/1.0

72.4 72.4 72.4

86.9 86.9 86.9

99.8 99.8 99.8

110,096,086 126,355,578 152,370,765

72.6 77.4 89.4

72.6 77.4 89.4

97.1 82.7 55.3

87,215,609 102,424,637 116,691,597

19.8 18.3 23.2

A2SC/0.25 A2SC/0.5 A2SC/1.0

78.3 78.3 78.3

117.7 117.8 117.8

86.8 86.7 86.7

152,805,606 171,514,575 193,875,632

81.9 89.1 100.3

81.9 89.1 100.4

90.7 69.1 37.1

152,805,606 124,134,052 135,159,632

29.5 26.7 30.3

A2HC/0.25 A2HC/0.5 A2HC/1.0

80.3 80.3 80.3

93.4 93.4 93.4

115.1 115.1 115.1

126,481,987 147,884,186 173,566,826

77.7 84.9 98.9

77.7 84.9 98.9

112 93.9 62.9

100,667,384 120,474,320 134,840,082

19.5 17.9 22.0

Used abbreviations: S. = number of stations; W. = number of workers; F. = number of floaters; Red. = average cost reduction in percent.

HWC-constellation was assumed to have the maximum worker skills, the largest cost reductions were attained there. However, an increase in complexity of the considered variant program substantially restricts the efficiency of the applied optimization process. For instance, as depicted in Table 3, a cost reduction of about 41% was possible for the constellation HWCSC/0.25. This improvement rate was reduced to only 27.5% for the scenario HWCHC/0.25. Note that this complexity-induced loss of efficiency occurred in all tested combinations of countries and control abilities. This can be mainly explained by the fact that a higher complexity within the variety program substantially restricts the flexibility of the applied searching process and consequently the Tabu Search procedure as well. Obviously, a higher number of option values and an increased variety complicates the task allocation process. Since the maximum task execution time over all selectable values of the relevant option is decisive for a possible assignment, higher complexity results in an increased number of longer tasks. Thus, the solution procedure either results in constellations with an increased number of stations or compensates the increased capacity demand by assigning additional workers or floaters. The latter case is mostly preferred. Particularly, if there are comprehensive control abilities (e.g., constellations with b = c = 0.25) and if work overload scenarios occur on an irregular basis, temporarily assigning additional staff becomes a very promising alternative. Consequently, it can be stated that independent of the initial solution, the proposed Tabu Search Heuristic provides sophisticated line layouts. This was underlined not only by significant improvement rates but also by additional analyses focusing on the structure of the generated solution constellations. For instance, slight modifications of the control ability factors b and c directly lead to respective adaptations of the generated solutions. Consequently, if it is assumed that these abilities are only slightly reduced, the Tabu Search algorithm responds with line layouts that comprise an increased number of stations. This results from the fact that an assignment of floaters becomes more costly under these modified circumstances. Additionally, it should be noticed that the Tabu Search algorithm is able to achieve substantial improvements of the best solution found even in the later steps of the examination process. This can be interpreted as an indicator for a globally acting searching process. Altogether, it was validated that both, the application of the proposed problem model and the Tabu Search procedure that was specifically designed for it, provide a sophisticated decision support for arrangements of mass customization manufacturing systems. Note that in reasonable time, the algorithm attains efficient

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results even for extreme variant programs comprising more than 503 quadrillions(!) of different variants. Consequently, it provides a promising base for the following analysis that examines the benefit of offshoring decisions. This analysis makes suggestions on the basis of a direct comparison of alternative line arrangements in different competing countries. Particularly the impact of the generated complexity of the variant program should be examined for various configurations. 5.3. Analysis of offshoring decisions In this section, a the results that were achieved for the generated competing locations are compared. For this purpose, the cost reductions in percent attained by hypothetically relocating the considered mass customization manufacturing system from HWC to the generated offshore countries (Tables 4 and 5) are analyzed in detail. This analysis particularly covers an examination of the impact of the variant program complexity on those cost reductions. The first conclusion is that the more comprehensive the assumed control abilities of the line (indicated by the parameters b and c) are, the more flexible the assembly line design process becomes. Especially the configuration b = c = 0.25 substantially reduces the costs of flexible floater assignments. Hence, in order to handle bottleneck scenarios more efficiently, sophisticated line layouts, which were generated for these cases, significantly increase the size of the floater pool. This becomes obvious by examining the results of the best solutions found depicted in Table 3. Here, a strong correlation between the control abilities and the size of the floater pool can be observed. However, as described in detail in Section 5.2, each increase in complexity reduces this flexibility substantially. More precisely, it restricts the possibilities of the solution procedure of finding a suitable task assignment. Independent of the amount of assumed control abilities, the Tabu Search procedure responds to it by an amplified floater allocation (c.f. Table 3). But, for efficiently utilizing this measure, two important prerequisites have to be fulfilled. First, the line has to possess enhanced control abilities that reduce the floater costs. Second, according to the existing worker skills, there have to be remaining capacities for reducing the task execution times by employing additional workers at the affected stations. Obviously, both conditions are more likely to be fulfilled by the HWC-configuration. Therefore, it can be expected that Table 4 Average percentage of cost reductions attained by offshoring from HWC to A-countries for various configurations A-offshore countries Complexity

Offshoring to A1 Control ability factors b = c =

Offshoring to A2 Control ability factors b = c =

0.25%

0.5%

1.0%

0.25%

0.5%

1.0%

SC MC NC HC EC

28.11 27.53 27.75 25.84 24.56

30.44 30.32 30.69 29.15 27.00

31.25 31.06 30.57 28.70 30.30

18.48 18.20 17.39 14.39 11.47

20.33 19.99 19.51 16.74 13.54

21.03 21.24 20.28 17.64 21.17

Average

26.76

29.52

30.38

15.99

18.03

20.28

Table 5 Average percentage of cost reductions attained by offshoring from HWC to B-countries for different configurations B-offshore countries Complexity

Offshoring to B1 Control ability factors b = c =

Offshoring to B2 Control ability factors b = c =

0.25%

0.5%

1.0%

0.25%

0.5%

1.0%

SC MC NC HC EC

33.66 31.71 28.80 24.70 20.01

38.95 38.24 35.83 33.53 30.71

41.21 41.61 39.29 38.25 41.37

11.66 8.68 4.38 1.90 1.89

26.86 25.00 21.49 20.20 18.31

33.32 32.77 29.83 29.55 34.67

Average

27.78

35.46

40.35

4.95

22.38

32.03

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the planning process carried out for this configuration attains a higher flexibility compared to the other configurations. According to the calculated cost reductions illustrated in Tables 4 and 5, the increased flexibility of the planning process substantially reduces the increase of variable costs for HWC. Specifically, offshoring (from HWC) to A1 results in average cost reductions of between 31.25% and 24.65%. For A2, these reductions are diminished to between 21.24% and 11.47%. Note that both A-countries possess a substantially lower wage level of only 50%. Additionally, by offshoring to B1, a cost decline of between 40.61% and 20.01% is obtained. Finally, reductions of between 34.67% and 1.89% were achieved for B2. Since the B-countries attract companies through a wage reduction of 75%, these results give a first impression of the considerable impact of the available worker skills in the offshore country. Consequently, neglecting this impact may result in unexpected declines of the intended savings of wages. Thus, the remaining cost reductions may not even compensate for the additional offshoring-dependent costs caused by transportation, supply chain control, or contracting in those cases (for details, see Hogan, 2004). In order to avoid such unmeant developments, applying an integrated approach that enables a detailed analysis of this tradeoff seems to be recommendable. By analyzing the average cost reductions depicted in Tables 4 and 5, it is obvious that the impact of a varying complexity level substantially increases with reduced worker skills and comprehensive control abilities. Specifically, while the difference between largest and smallest cost reduction is only of 2.5% for the configuration (A1, 1.0), this difference rises over 13.5% if comprehensive control abilities are assumed for the B-countries (B1/B2, 0.25). Therefore, attaining substantial reductions of variable costs highly depends on the complexity of the produced variant program if a line with comprehensive control abilities is offshored to a country that only provides the employment of workers with moderate skills. However, if the line grants only poor control abilities, or if the skill level of the workers in the offshore country becomes comparable to the one in HWC, this impact is substantially lower.

Fig. 1. Clustering of the impact of different variant program complexity levels on offshoring decisions.

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However, independent of these configurations and except for one specific constellation (the case b = c = 1.0, EC), it can be stated that a high complexity level within the production program correlates negatively with the attainable cost reductions, and vice versa. Obviously, this correlation is strengthened by comprehensive control abilities of the line and lower worker skills in the offshore country. Note that this correlation cannot be observed for the configuration characterized by lacking control abilities (indicated by the extreme parameter configuration b = c = 1.0) and an extreme complexity level in the variant program (EC). By analyzing the line structure generated for the HWC, it becomes obvious that the executed planning process cannot maintain its higher flexibility in this specific configuration compared to the one conducted for the offshore countries. Even here, extreme complexity in combination with lack of control abilities lead to inefficient constellations. Therefore, the HWC-configuration substantially loses competitiveness. In order to generalize the obtained results for strategic management, Fig. 1 illustrates the general impact of different complexity levels on the benefit of offshoring. Here, the measured cost reduction attained for each specific complexity level is compared with the average cost reduction for all tested constellations. More precisely, the respective complexity-induced differences between both cost reductions are calculated for all combinations of the two following factors: the country constellation (i.e., the worker skills provided there) and the level of control abilities of the line. In order to identify substantial deviations, these differences are clustered for each considered combination of worker skill level and assumed control ability level of the line. Based on these calculations, the resulting impact clustering explicitly confirms the implications made above. Altogether, it can be stated that, ceteris paribus, the larger the complexity of the production program is, the more unworthwhile offshoring a mixed-model assembly line with comprehensive control abilities becomes. Vice versa, the more the complexity of the variant program is reduced, the more profitable becomes offshoring. Particularly, this correlation is significantly strengthened for offshore countries that offer only a moderate level of worker skills but at the same time have exceptionally low labor costs. Hence, companies attracted to offshoring through these low wage levels are strongly hold to examine these tradeoffs carefully. Note that this consideration is solely based on personnel costs and therefore does not yet incorporate any additional material consumption. This may be resulting out of, e.g., an increased scrap rate in the offshore country. Obviously, if these costs are significant, the model has to be extended accordingly. 6. Summary and conclusions In this present paper, a new approach that provides detailed offshoring decision support for mass customization manufacturing processes is generated. It is focused on specific manufacturing processes where theoretically a large number of variants has to be simultaneously produced on the same mixed-model assembly line. In order to provide an appropriate estimation of the resulting manufacturing costs, the layout of the mixedmodel assembly line was respectively generated for competing locations. This approach is the first one that provides a detailed analysis of the tradeoff between lower worker wages and additional manufacturing costs caused by reduced worker skills. Note that these kinds of tradeoffs characterize many offshoring decision problems. Apart from validating the efficiency of the introduced balancing approach, the conducted computational tests reveal that particularly the complexity of the variant program has a significant impact on cost reductions attainable by offshoring. Particularly, companies that consider offshoring to a country that provides only low worker skills should examine these dependencies thoroughly. Note that since these offshore countries provide exceptionally low wage levels, many companies are attracted and thus have to face this problem. Owing to the fact that the presented results are already promising, future research will extend the proposed approach mainly in two directions. Obviously, all cognitions obtainable by an application of the introduced approach are solely based on the appropriateness of the applied mixed-model assembly line balancing. Thus, on the one hand, future research will validate the assumptions of the proposed balancing model more comprehensively. Particularly, this work will mainly address a better understanding of realistic values for the used control ability factors b and c. By applying a corresponding real-time oriented control approach, specific scenarios that are more likely to occur during the production process can be simulated. Based on such a kind of simulations, a more reliable estimation of factors could be provided. Note that the measured results indicate a strong relevance of the size of these factors to the attainable costs reductions. Thus, their exact determination

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would substantially improve the significance of the attained results. Obviously, the extreme constellation b = c = 1.0 is unrealistic. Its assumption of the total lack of line control abilities clearly underestimates the comprehensive possibilities of applicable control measures (Bock et al., 2006). However, note that for an exact determination of the control factors, a layout-specific calculation has to be provided. Obviously, its integration into the proposed balancing approach is a challenging field of future research. Apart from specifying the model assumptions and parameters, the second direction of future research will focus on further improving the algorithm. Note that the appropriateness of the proposed approach depends on the finding of sophisticated layout constellations. On account of the complexity of the applied problem model, finding optimal constellations is unrealistic. Thus, the rating of a location considered for offshoring strongly depends on the efficiency of the applied search heuristic. In order to substantially attain efficiency gains, a parallelization of the proposed procedure seems to be promising. Currently, Local Area Networks (LAN), which connect modern personal computers, can be found in almost all companies. However, only ordinary office communications or text processing programs are executed in these networks. Obviously, these applications use only a small fraction of the available computational capacity. Consequently, in order to increase the computational performance, the use of the available off-peak times of the processors is recommendable. Specifically, these off-peak times can be used, for instance, to generate more sophisticated layouts by simultaneously exploring different parts of the solution space. In order to efficiently handle the unpredictable background load caused by the simultaneous use of the LAN by ordinary office applications, specific load balancers were designed. It has been shown that their integration into the conducted searching process results in substantial improvements of the yielded solution quality (Bock and Rosenberg, 2000). Note that even under extreme adversarial conditions, these improvements were attained with a considerable reliability. References Askin, R.G., Zhou, M., 1997. A parallel station heuristic for the mixed-model production line balancing problem. International Journal of Production Research 35, 3095–3105. Becker, C., Scholl, A., 2006. A survey on problems and methods in generalized assembly line balancing. European Journal of Operational Research 168, 694–715. Blecker, T., Abdelkafi, N., Kaluza, B., Kreutler, G., 2004. A Framework for understanding the interdependencies between mass customization and complexity. 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