Abstract
As is known, the problem of determining economically justified volumes of supplies in the theory and practice of logistics management plays a key role in ensuring the efficient operation of both individual enterprises and supply chains. Logistics, which is the science of effective management of material, information and financial flows in the field of production and circulation, is closely related to such sections of operations research as mathematical programming, inventory management theory, schedule theory, queuing theory and more. Many tasks of logistics are directly related to the optimal management of stocks of raw materials, semi-finished and finished products, as well as the construction of an optimal schedule for delivery of finished products to points of consumption with the participation of trunk transport. Thus, since the issues of optimal inventory management are of paramount importance in logistics, it means the importance of inventory theory in the design and operation of various logistics systems. The article is devoted to substantiation of expediency and efficiency of additional costs of a supply firm for advertisement with the aim to its profit increasing on the fixed planning horizon under supposition that the expected demand at point of destination may be controlled by firm. For this problem solving the modification of classical Wilson’s model from inventory control theory is used to maximize the total profit of firm for sailing the good, taking into account ordering, delivery and storage of good costs on the planning horizon and additional cost for advertisement of good. It is assumed that buying/sailing prices of good are known, as well as daily expenses for storage of good at warehouse. It is supposed also that demand for the good is an increasing function of advertisement costs. The case of linear dependence of demand on advertisement cost is studied in details. For this particular case the optimal value of ordering party of good and optimal value of cost for advertisement are found in evident form. It is shown also that above optimization model may be generalized for the case of several kinds of good. Restrictions on the capacity of the warehouse for storage of goods and restrictions on the financial resources available to the company allocated for advertising activities are taken into account. A convex optimization problem is obtained, which can be solved numerically using the Excel application package.
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