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Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Applied Mathematical Modelling, Volume 33, Issue 11, November 2009, Pages 4201–4214
This paper shows how to model a problem to find optimal number of replenishments in the fixed-order quantity system as a basic problem of optimal control of the discrete system. The decision environment is deterministic and the time horizon is finite. A discrete system consists of the law of dynamics, control domain and performance criterion. It is primarily a simulation model of the inventory dynamics, but the performance criterion enables various order strategies to be compared. The dynamics of state variables depends on the inflow and outflow rates. This paper explicitly defines flow regulators for the four patterns of the inventory: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. It has been discussed how to use suggested model for variants of the fixed-order quantity system as the scenarios of the model. To find the optimal process, the simulation-based optimization is used.
نتیجه گیری انگلیسی
The model of the inventory control as the discrete system control can be successfully used as a general dynamic model for analyzing inventory dynamics over a finite time horizon in the case of the fixed-order quantity system. When developed in a spreadsheet (tables and charts) it is a great tool for both academics and professionals to better understand dynamics of the inventory on the day by day basis. This model clearly distinguish the law of dynamics, control domain and performance criterion. It is very useful when one analyzes the business decision environment: firstly, establish the law of dynamics; secondly, determine the control domain; thirdly, define an objective function which will be incorporated into the performance criterion. After that, one can perform “what if” analyzes or a meta-heuristics search in order to find the optimal solution which can be simulated and analyzed. The proposed model explicitly defines mathematical relations of the inventory inflow YI and outflow YO for each of possible inventory patterns: discrete inflow – continuous/discrete outflow and continuous inflow – continuous/discrete outflow. The mathematical relation for the inventory inflow YI reflects inventory policy to replenish items whenever stock falls below defined level. The mathematical relation for the inventory outflow YO reflects the model assumption that the demand is known and at a constant rate (continuous or discrete). The main constraint for the control domain secures non-negativity of the stock. Additional constraint can be easily added in order to describe resource scarceness, without corrupting the law of dynamics. Also, the objective function of the performance criterion J can be modified, without corrupting the law of dynamics. Modifications of the objective function can include costs divergences or new costs introduction. Various inventory decision environments can be described by combining the nature of circumstances variables: constant or variable throughout time horizon, independent or dependent on each other. A set of classical inventory models is obtained by modifying EOQ model: Production order quantity model, Quantity discount model, Inventory model with planned shortages, etc., with specific techniques for solving each of their problems. All of them can be presented by the discrete-time system as the scenarios of the special cases of the inventory dynamics. Working with the model of discrete system control, the limitations of the classical model are overcome. The model and searching method are separated. The various searching methods can be used over the model, The presented algorithm of the “total search” finds an optimal discrete process (X, p, u) very fast because there are “just a few discrete process-candidates”. If the model is developed in a spreadsheet, there is no advantage of the simplicity of the classical EOQ model. Moreover, problem of optimal control of discrete system is well structured and there are meta-heuristics algorithms with provably good run times and with provably good or optimal solution quality. As the search methods (meta-heuristics algorithms) are rapidly developing and computers are faster than ever (and will be), the time has come to use simulation-based techniques of the optimal control of discrete system in respect to inventory control both in the education and in professional work.