###### Abstract  
The selection of products to be offered on the market is a critical decision-making process encountered in all industry sectors. It is not just a matter of maximizing profit or optimizing the utilization of corporate resources but also specifically concerns determining a product portfolio that is most suitably aligned to corporate strengths and that appeals to the most attractive and emerging markets. Hence, corporate competencies such as strategic management and production capabilities must be taken into account concurrently. Starting from this point of view, a twofold decision support system (DSS) has been developed. On the one hand, a theory of constraints (TOC)-based analytic hierarchy process (AHP) approach, including a taboo search algorithm, has been developed in order to derive the right product mix for maximizing the total profit amount by considering the bottleneck problem. On the other hand, a GE/McKinsey screen matrix is added to this consolidated approach to support decision-makers in the formulation of product portfolio strategies. The DSS provides a platform to compare outputs coming from the preceding two processes, which allows for the refinement of the solution. The proposed DSS is executed with a problem dataset from the industry to test its accuracy and reliability. product mix problem; theory of constraints; analytical hierarchy process; product portfolio; strategic management; tabu search +
Footnote †: journal: Applied sciences  
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Footnote 1: institutetext: Institute for Transport Planning and Logistics, Hamburg University of Technology, 21071 Hamburg, Germany; [PERSON]ESS]  
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priority are selected, regardless of the time spent on bottlenecks [5]. The TOC-derived heuristic, however, proposes that product lines should be selected according to their ratio of throughput per time spent on system constraints [2; 9; 10; 11; 12; 13]. The situation, however, is more complex than it seems. The challenges faced are categorized by the multitude of bottlenecks, the dominance rule adopted in the sequencing of products, and production over integer quantities. If demand exceeds the capacity of the production system, more than one bottleneck may exist. Although it is argued that TOC-derived heuristics are successful in single-bottleneck environments [6; 13; 14; 15; 16], [PERSON] [17] demonstrated that a TOC-derived heuristic may not lead to the optimal solution, even in single-bottleneck environments. Some of the researchers focused on multi-bottleneck systems [4; 5; 6; 7; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18]. However, algorithms developed to solve PMP have failed in multi-bottleneck environments since all decisions are made based on the most capacitated constraint, namely, the dominant bottleneck. In determining a product mix, previous researchers merely used the priorities assigned to products by the dominant bottleneck. Considering only one bottleneck in decision-making and ignoring the importance of other ones may distort the solution because only part of the information is used [1]. The initial TOC-based traditional algorithms were presented by [PERSON] and [PERSON] [6] and [PERSON] [13]. They asserted that TOC-derived heuristics could lead to an optimal solution via an integer linear programming (ILP) model. This assertion was also supported by [PERSON] [7], [PERSON] [19], and [PERSON] [20]. Although PMP can be formulated as an ILP model, as the number of products increases, the difficulty of solving the ILP model increases exponentially [1]. Following these developments, a series of approaches were propounded, such as the revised algorithm [4], dominance rule-based algorithm [21], and advanced heuristics such as genetic algorithms [22; 23] and the tabu-search (TS) [24], providing new policies to deal with the combinatorial complexity of PMP with multiple constrained resources. The revised algorithm tries to improve the solution using an iterative decrease and increase process.