## 2 A Division of Manual Labor, Assembly and Production Lines
### Generalizations of the SALBP and Complexity of These Problems
The deterministic ALBP is formulated as follows. A set of assembly operations is specified: \(V=\{1,2,\ldots,n\}\). For each operation, a fixed processing time (duration) is given along with the digraph \(G=(V,A)\), which determines the partial strict order on the set \(V\) of assembly operations. The deterministic ALBP is to assign assembly operations, \(V\), to the ordered set of workstations \((S_{1},S_{2},\ldots,S_{m})\), such that the precedence relations given in the digraph \(G=(V,A)\) are not disturbed and the objective function would take the optimal value. The deterministic SALBP is well-studied, and many exact, approximate and heuristic algorithms have been developed for these problems (see [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52]). This section is focused on designing and balancing assembly lines with possible deviations from normal manufacture conditions. The article [2] presents the exact algorithms for solving the SALBP. In the article [42], the authors divided the published algorithms for solving the ALBP into two groups. The first group includes precise algorithms that guarantee the optimal solution to the ALBP, and the second group includes heuristic algorithms that lead to some acceptable solution to the ALBP, not necessarily optimal. This article contains an overview of heuristic algorithms used for the ALBP, an efficiency comparison of algorithms for solving the ALBP and an overview of the exact and approximate algorithms for solving the multi-model ALBP. The article [43] compared the procedures proposed for solving the SALBP-1. The article [44] presents a hybrid artificial intelligent algorithm, which realizes an artificial immune system in combination with a simulated annealing algorithm. The algorithm aims at enhancing the performance of an artificial immune system via incorporating simulated annealing in order to achieve a global optimum for assembly conveyers with a rather large number of assembly operations. The new algorithm was implemented on a mechanical assembly composed of seven parts joined by connectors. The algorithm was effective in achieving an optimum with a restricted CPU time compared to other artificial intelligent algorithms. The article [45] describes the application of a differential evolution algorithm to the SALBP. This algorithm is an evolutionary one, similar to a genetic algorithm for global optimization over continuous spaces. The extensive experimental work over public benchmark test instances showed the effectiveness of this algorithm. In most investigated SALBP, smoothing workstation loads were considered. In the work [46], a differential evolution algorithm was developed for minimization of the workload smoothness index in the SALBP-2. The parameters were optimized based on the Taguchi method. To validate the algorithm, the computational experimental results were compared with other published heuristics. The comparison indicated the effectiveness of the new algorithm. An optimization of the numerical parameters has been addressed in order to minimize a workload smoothness index. After presenting a mathematical model, a differential evolution algorithm was developed to minimize the smoothness index. Some advantages were based on a suitable mutation, which ensures the search diversity and enhances the effectiveness based on properties of the objective function. The values of numerical parameters in the developed algorithm have been tuned based on the sizes of the tested instances. A detailed statistical experiment showed that except for one from the medium-sized problems, the levels of other numerical parameters influenced the efficiency of the addressed algorithms for other problems. The computational results indicated supremacy of the algorithm over tested heuristics for small, medium and large instances. The article [47] is devoted to supply chain designing and conveyer balancing.