## 6 Existing Work on DEH Algorithms  
After describing the DES approach and using it to model and simulate complex systems, [PERSON] et al. [10] noticed that it could be combined with heuristics to solve NP-Hard optimization problems with synchronization requirements. This section summarizes some contributions utilizing BR-DEH algorithms. Thus, the aforementioned authors proposed a solution approach for a home service routing problem. In the home service routing problem, operators are assigned several customer homes to visit, and vehicles distribute them among homes. Because of new placed service requests and cancellations, home assignments and routes are dynamic and should be updated during the day. The solution approach supports planners in assigning operators and defining vehicle routes dynamically. In addition, this approach benefits from a defined event list to construct vehicle routes and operator-homes assignments during the day, which allows for minimizing the number of required vehicles. Similarly, [PERSON] et al. [31] used a BR-DEH approach to solve the omnichannel vehicle routing problem. In the problem, a retail store is replenished, and online-customers orders should be picked up and delivered. The solution approach utilizes the BR-DEH methodology to construct solutions that are refined using a local search operator. The approach found promising solutions for most of the problem instances. Another transportation problem is solved by [PERSON] et al. [42]. In their problem, a container should be delivered on or before a given deadline. This container is transported along a network of hubs by trucks. One truck could transport only one container, and the containers could be stored temporarily at any hub. A BR-DEH algorithm is employed to solve the problem by specifying which containers are selected to be temporarily transported from a hub, as well as which containers have to be stored at hubs until future notice. Then, a biased-randomized behavior is introduced into the heuristic to construct several variants of the deterministic solution. In order to propose an approach to handle the problem, an iterated local search framework integrates the biased-randomized heuristic to find the most promising solutions in short computation times. As discussed in Section 5, problems in manufacturing are good candidates to be solved using the BR-DEH approach. For example, [PERSON] et al. [32] use this methodology to solve a flow-shop problem in the semiconductor industry. Jobs are processed by machines based on job type, and these jobs could be batched along the production line. In an extension to the problem, job priorities of being processed on machines in the flow-shop problem are considered. Similarly, [PERSON] et al. [34] used a DEH algorithm to recommend a solution that minimizes the production makespan. In addition, the solution approach utilizes biased randomization to construct several solutions and Monte Carlo simulation to evaluate the solutions. Another manufacturing problem involves the re-entry and re-processing of parts on machines. This problem considers re-entry cycles of jobs due to quality issues. Thus, the same machine that processed the job in the first cycle should handle it for the second cycle. This problem is modeled as a flow-shop problem, and [PERSON] et al. [33] defined a discrete-event list to manage the defined constraints in the problem. In addition, the authors integrated a biased-randomized procedure to find a solution in a short computational time. A dynamic ride-sharing problem arises in the context of edge computing in smart cities and the integration of the Internet of Things. The dynamic ride-sharing problem refers to one of the routing problems related to smart cities, in which a driver uses a private car to pick up riders along a route. However, after departing from the origin (after defining the initial route), new ride requests and traffic conditions might influence decisions regarding defined routes. Thus, the routes should be dynamically updated with the changes along the route.