## 2 Literature Review
Moreover, a review has been presented on the articles related to game theory and optimization methods for several applications of problems. Furthermore, there was a classification into various categories where game theory is useful for increasing the effectiveness of optimization; optimization methods are useful for solving the game theory problems; and a combination of game theory and optimization also may be useful for efficient solving of other classes of problems. The proposed classification was based on four criteria: mainly based on nature of optimization (classic or modern), based on the number of objectives (single or multi), and based on the type of game theory [33]. Subsequently, the reduction of maximum completion time, tardiness, and production cost along with the optimal schedule are generated with the help of GA integrated with Gantt chart (GC) methodology for DMS. A case study of manufacturing scenario with six jobs and twelve machines considered and solved with the proposed GA-GC method [34]. Likewise, resource, management and part agents are considered in a multi-agent-based system to make decisions in a timely manner with proper co-ordination to generate optimal process plans in a distributed scheduling environment [35]. The question lies in how to make the proper choice of action without deviating from the optimal strategy in an uncertain environment that exists in distributional robust optimization problems where the decision maker is not sure about the distribution of uncertainty that exists in the problem. In such a situation, this work gives insight into exploring the alternative ways that help find the distribution of uncertainty by the decision maker, based on the observations found from the experiments. Algorithms are proposed to find the local optima and are derived from a common evolutionary stable strategy to explore their convergence rate by using a mean estimate [36]. A memetic algorithm was discussed for the minimization of makespan for a distributed assembly permutation flow-shop scheduling problem to obtain accurate results [37]. A multi-objective-based mixed-integer programming model was implemented with the consideration of makespan and total traveling distance as objective functions, and a GA-based heuristic approach was proposed to obtain the optimum results in virtual manufacturing cells (VMC) [38]. To solve the scheduling and maintenance planning simultaneously in DMS, an evolutionary-based GA is proposed, and the performance was validated by comparing with the other algorithm [39]. An IPPS problem was solved with the Simulated Annealing (SA) approach that contains the added flexibilities of process, operation, scheduling to optimize the utilization of machines, and production cost in a DMS [40]. A GA was introduced to identify a near-optimal configuration in a manufacturing network. The performance of GA-derived alternate designs is held in comparison with the output of an intelligent search algorithm. A new approach named hybrid of Estimation of Distribution Algorithm (EDA) was employed to increase the profit in forwarding supply chain and to reduce the carbon footprints in a closed-loop supply chain network system [41]. A framework model was presented for the feasibility and merits and their applications of complex networks in advanced manufacturing systems [42]. A particle swarm optimization with a hill-climbing approach was proposed for minimizing the functions that make span and energy consumption in distributed manufacturing systems [43]. To avoid the difficulty of applying the heuristics for the combinatorial nature of problems like crude oil operation scheduling problem, initially, the problem was converted to an assignment problem-related to tanks and distillers, and later a chromosome was implemented, which helps the further application of meta-heuristics like NSGA-II for optimization of refinery schedule. A case study of a china refinery with three distillers and ten charging tankers with multiple objectives was considered and tested successfully [44].