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Abstract
Inventory acts as a buffer between supply and demand processes to decouple them, as they cannot be matched perfectly. Results of this mismatch can be shortages; failure to meet demand, or overabundant inventories. That is why making the proper inventory decisions is critical. Proper inventory management depends on several factors, among them are whether single or multiple items are considered, the type of demand pattern being deterministic or stochastic, the nature of the supply process, the item shelf life, and the applied shortage policies. The continuous review (s, S) inventory control policy is used to model single class A items under random demand distributions and random replenishment order lead times. A replenishment order is triggered whenever the inventory position drops to or below the reorder level s. The order quantity is large enough to raise the inventory position up to the order up to level S. Analytical models that are used to model and solve this type of inventory control systems have several shortcomings. The models are case dependent; they depend on the type of demand pattern, lead time distribution, and the considered shortage policy. Also assumption like undershoots consideration and the crossing of orders are too difficult to consider, finally, there are too many factors that need to be considered in the same model, which makes it too difficult to solve These reasons have lead to the need of using simulation for modeling and analysis of such systems.
In order to study a system, assumptions are made about how it works. These assumptions compose a model of the system. They usually take the form of mathematical or logical relationships. These relationships are used to understand how the system behaves. If the relationships that compose the model are simple enough, mathematical methods can be used to obtain exact information about the model, this is called analytic solution. However, most real-world systems are too complex to allow realistic models to be evaluated analytically, and these models are better to be studied by means of simulation. Simulation refers to a broad collection of methods and applications to mimic the behavior of a real system. Simulation is used to evaluate a model numerically to estimate the desired true characteristics of the model. If an analytical solution to a mathematical model is available and is computationally efficient, it is usually desirable to study the model in this way rather than via a simulation model. Discrete-event simulation is concerned with modeling the system as it evolves over time by a representation in which the state variables change instantaneously at separate points in time (a countable number of points in time). At these points in time events occur. An event is defined as an instantaneous occurrence that may change the state of the system.
Simulation based optimization is the practice of linking an optimization method with a simulation model to determine the state of certain controllable inputs to a system that will cause system outputs to be at their most favorable or optimal condition. There are different approaches that account for most of the academic literature in simulation optimization, such as gradient and non gradient based approaches and statistical methods. However, none of these approaches has been implemented to develop optimization for commercial simulation software, mainly because these methods generally require a considerable amount of technical sophistication on the part of the user, and they often require a substantial amount of computer time as well. Most commercial simulation optimization
packages are currently dominated by metaheuristic approaches. Thus, in sir optimization practice, such methods appear to take precedence over other IJ metaheuristics are generally fast, robust, and generate multiple alternative s( Although simulation based optimization does not guarantee reaching a global 0] practitioners used the term simulation optimization.
In this thesis, a simulation model of continuous review (s, S) inventory control, constructed in a generic way to satisfy the different assumptions that cannot be mOl the analytical models. A simulation optimization approach is presented, the optil objective is to find the values of sand S that minimize the total replenishment co considered inventory replenishment costs are the ordering, holding, and shortage cc proposed simulation model is developed using the discrete event simulation n software package Arena®. The model performs the following steps, demand arr fulfillment, reviewing the inventory status, placing orders, and receipt. At each transaction, the inventory level is updated by the incoming demand, demand is using the on-hand inventory. If the demand is greater than the supply, the excess becomes shortage. The inventory level is then checked, if a replenishment order is its quantity is calculated and the replenishment order lead time is recor< optimization experiment has been performed. The objective was to find the parameter settings s and S at different levels of system input parameters. The systt parameters were the demand size distribution, time between demands distribution, time distribution.
The results show that the mean demand size has a greater effect on the resull inventory cost as compared to that of the lead time. The effect of lead time significant when associated with high values of mean demand size. The simulate( showed a tendency to increase the safety stock so that the holding cost increases with the increase in the demand size and lead time. The optimal solutions found i the effectiveness of the proposed simulation optimization approach, where the values are obtained without triggering any shortages, except for high values of dem and lead time. Different performance measures about the inventory system can be ’ from the proposed simulation model. Among these are, the safety stock level, iJ replenishment cycle length, and the replenishment quantity. The proposed mode easily modified to apply different shortage policies. The shortage policy can l completely backordering or completely lost sales or mixed backordering and lost achieving a service target.