Stohastistic Modeling and Optimization of Industrial Stock

The nonlinear stochastic model of updating of industrial stocks is considered in the paper. The purposes of work are: 1. To define an optimum strategy of updating of industrial stocks and reductions of the expenses connected to their storage; 2. To combine the modeling process with the real information describing the process of industrial stocks management in real time; 3. To take to account the nonlinearity dependences of factors of the model; 4. To construct the management process in online regime. In the first scenario for incidental values modeling is used traditional methods, in particular, the method of the reverse transformation the Bellman’s method (receipt-refusal). In the second scenario of modeling the authors have used modeling methods that allow to consider specific characteristics of changes of value P order frequency (is measured as units of orders per unit of time), namely, irregularity of consumption intensity, different lengths of intervals between order points, inability to select an appropriate rule of distribution of value P for the whole modeling time interval. For resolving the problem under given conditions, the method of imitation modeling was applied, which allows to develop (imitate) different options of organization of the process of stock management, taking into account the aforementioned specific characteristics of the particular scenario. BASIC MODEL OF STOCK MANAGEMENT In any stock management system the level of stock changes in accordance with the respective cyclical model. The reduction of the level of stock is determined by the demand. At a specific moment, to replenish the stock after a definite period of time, termed delivery lead-time, a new order is made; the order is received and the stock is increased. After that a new stock cycle begins. To simplify stock management modeling a, number of conditions are established: 1) The demand for products is constant. If the consumption coefficient is constant, then the stock level is also reducing at a constant rate. 2) It is assumed that delivery time is known and is a constant value, which means that the order may be made at the point corresponding to definite time parameters and stock amount (replenishment level) values, which ensure receipt of the required stock at the moment when stock level is 0; 3) Stock-out is not allowed; 4) A definite y amount of raw materials and materials is ordered during the stock cycle time. The basic model of stock management is presented in fig. 1. All stock cycles are equal. The maximum amount of raw materials and materials available in stock correspond to order amount y. Figure 1. Scheme of the basic stock management model A model has to be developed to describe costs over the whole stock storage period; the length of the period is not important – it may range from one day up to a year etc. In the particular case a period of one year is chosen and the following system designations are used: D annual demand for product; Co variable costs of one order, n units / 1 order; Ch variable storage costs per one existing stock unit, n units per product unit per year; C acquisition price of one existing stock unit, n units per year; y order size in product units. If the demand for the products is D units per year, but the size of each batch is y number of units, the annual demand is D/y. The annual cost of an order (Ca) is equal with the costs of one order multiplied with the number of orders made in a year: