## 4 Simulation Models and Sustainability: Characterization
### Discrete Event Simulation (DES)  
Discrete event simulation originally appeared in the late 1950s, and it has slowly increased in popularity to become the most widely utilized of the traditional operational research methodologies across a wide range of industries, including manufacturing, travel, banking, health, and beyond. A discrete event system (DES) is a discrete-state and event-driven system in which the state changes only as a result of discrete events occurring across time. Event-based modeling refers to the representation of the information of the discrete event system using an event graph. The representation of temporal and logical relationships between the event is called an event graph [81]. An event graph consists of a set of event nodes and directed edges with two types of edges described as scheduling edges and canceling edges. An event-based model allows the system to evolve through a sequence of events such that an event is described as a change in the state of the model. A discrete event modeling is defined, in contrast to continuous modeling, as the system that changes discretely at certain points in time [82]. As the events taking place in the system are random, therefore, any description of the system using differential equations is not possible; thus, the requirement of the event graphs is warranted. The components of DES include the following items  
* System State: The collection state variables which, at a given time, describe the state of system;
* Simulation clock: It describes the current time in the system;
* Event list: List made up of list of events taking place at a given time in the system;
* Statistical counters: Variables that have statistical system data stored in them;
* Initialization routine: An algorithm whereby the simulation is initialized at time zero;
* Timing routine: An algorithm that draws up sequence of events with time;
* Event routine: Algorithm that updates the system state after an event has occurred;
* Library routines: Random observation generator from probability distributions;
* Report generator: Algorithm that estimates the optimal measures and stores them as reports;
* Main program: This is an an algorithm that, using the timing routine, determines the next event and thence shifts the control to the event sequence and updates the system. The magnified and data-dependent view of DES implies that its application in manufacturing SCs is generally limited to the operational level. Nonetheless, some instances where DES finds its use at strategic-tactical level of operations include: design of new facilities [83], improvement of warehouses and distribution centers [84; 85], changes in staffing and operating rules, and effect of investments on facility operation [86; 87], among others. DES has historically been invoked in the case of sustainability through the lens of optimisation such that sustainability was conceived as a sub-problem of optimization. The earlier approaches to sustainability using DES were limited as \"optimization of multiple objectives was not very common in manufacturing simulation\" [88]. The evolution of DES software rendered them useful in the case of complex systems such as logistics, healthcare, military strategy, and profit optimization. One of the major issues applying DES for sustainability can be attributed to limited computing power in the past. The limited size of memory limited the size of the models that could have been developed. The clock speed also limited the simulations that could be run. However, in the recent past, there has been a steep increase in the computing power available to researchers and practitioners. Following this, a number of studies appeared where DES was applied in the case of sustainability assessment. The use of DES for modeling sustainable operations in manufacturing SCs has been carried along two major themes. Firstly, those problems that deal with the material flow in industrial and their allied operations and, secondly, those dealing with energy flows in the operations.