Alternative Quantitative Approaches forDesigning Modular Services: A ComparativeAnalysis of Stewards Partitioning and TearingApproachHans Corsten, Ralf Gssinger, and Hagen Salewski1 ProblemModularisation is a possibility to design work sharing services which gains increas-ing attention in the field of service research (cf. 2, pp. 221; 3, pp. 811). The basicconcept is to merge single tasks of the underlying service into service modules insuch a way, that costs are minimised and that the service supplier is simultaneouslyenabled to serve a heterogeneous spectrum of customer needs. Because of the inte-grated nature of the co-production of services by service supplier and customers, therelevant costs are coordination costs1, which arise when interdependent tasks are tobe fulfilled by different actors, or when these tasks are not completely complemen-tary. In the context of service production, tasks can be combined to service modulesup to such a module size, that existing interdependencies are still minimal in termsof coordination costs. Higher coordination costs only occur, if interdependent tasksare assigned to different modules and when the activities, which different actors areresponsible for, need do be adjusted.To support the decisions in the design of service modules, different quantitativeapproaches are suggested (cf. 5, pp. 1675; 6, pp. 40), which are based on themodel of Design Structure Matrices (DSM). On the basis of DSM, partitioning al-gorithms can be utilized to identify modules. A technique, which is often used, is thepartitioning and tearing approach described by D. V. Steward. However, the perfor-mance of this approach has not been examined in adequate detail. This contributionaims at a test-based evaluation of Stewards approach. The performance of Stew-Hans Corsten and Hagen SalewskiDept of Business Administration and Production Management, University of Kaiserslautern,Gottlieb-Daimler-Strae 42, 67663 Kaiserslautern, Germany, e-mail: corstenwiwi.uni-kl.de,salewskiwiwi.uni-kl.deRalf GssingerDept of Business Administration, Production and Logistics, University of Dortmund, Otto-Hahn-Strae 6, 44227 Dortmund, Germany, e-mail: Ralf.Goessingertu-dortmund.de1The case, that single tasks cause direct costs of work sharing, is not considered.385B. Hu et al. (eds.), Operations Research Proceedings 2010, Operations Researrch Proceedings,DOI 10.1007/978-3-642-20009-0_61, Springer-Verlag Berlin Heidelberg, 2011386Hans Corsten, Ralf Gssinger, and Hagen Salewskiards approach is compared with the partitional clustering approach by J. Reichardt,which aims at the detection of structures in large networks. Both approaches needto be modified to solve the presented problem. To evaluate the performance, thestandard criteria solution time and solution quality are used. Additionally, the influ-ences of the DSMs composition are considered and the effects of size, structure,and density of the matrix are examined.2 ApproachesModularisation is realised by the assignment xv.m(xv.m 0,1) of tasks v (v =1,.,V) for a specified service path2to modules m (m = 1,.,M;M V). Theassignment should ensure thatthe relevant coordination costs between ordered modules, which are provided foreach task combination v and v?as elements av.v? 0 of the DSM A V V,are minimised; the order of the modules is enforced by the range of the indicesm and m?in the objective function,the number of tasks in one module cannot exceed the coordination capacity of anactor and each module must exceed a given number of tasks which represent theminimum capacity utilisation of this actor, andthe set of all tasks must be decomposed completely into disjoint modules.These requirements can be modelled as a quadratic assignment problem withV M decision variables and 2M+V constraints.Min! K =M1m=1Mm?=m+1Vv=1Vv?=1xv.mxv?.m?av.v?s.t.:Vv=1xv.m SmaxmVv=1xv.m SminmMm=1xv.m= 1vxv.m 0,1v,mThe optimal solution of the model can be found by applying exact methods forsmall DSM sizes only.2Since only specified service paths are considered, the combination of tasks of a path can only bepartial services. A construction of service modules has to be made across all paths. However, thisdistinction is not kept up in this paper and the term module is used instead.Alternative Approaches for Designing Modular Services387Stewards approach (cf. 6, pp. 40) is a two-step heuristic designed for binaryDSMs. In the first step, partitioning, interdependent service tasks are combined insuch a way, thatonly one-directional dependencies remain between modules,modules contain as few tasks as possible, andmodules are in an order which minimises the total number of dependencies topreceding service modules.After partitioning, the internal structure of the resulting modules is analysed, andtearing of internal dependencies is used to create an internal order of the servicetasks. The tearing described by Steward leads to unfavourable small modules. Forthis reason, the tearing was enhanced a by a system grid a