Subject The article considers various mathematical models for managing stock inventories. Objectives The aims include to obtain a multi-product model to manage inventories with random deliveries of multiple periodicity with minimum working capital, to analyze and compare it with the model by the Kulakovs, and to build models based on real data. Methods Our own multi-product model to manage inventory with multiple periodicity is built assuming that at the beginning of the cycle only the first resource is fully purchased, the remaining resources are initially purchased in shares and then additionally purchased within the cycle. The volume of resource supply is not limited, the frequency of supply of all resources is multiple. The model rests on accounting equations at the initial point in time, and also at the time of additional purchase of resource deficit. Results We constructed a multi-product model of stock management with an arbitrary volume of supplies and multiple periodicity. We compared it with the model by the Kulakovs and made a real-data model for the VostokAvtoTrans branch of TOO VostokTsvetMet (Republic of Kazakhstan). Conclusions The offered model enables to save more than twenty percent of working capital as compared with the model by the Kulakovs.
Buchan J., Koenigsberg E. Nauchnoe upravlenie zapasami [Scientific Inventory Management]. Moscow, Nauka Publ., 1967, 423 p.
Sviridova O.A. [Mathematical models and methods of inventory control. Types and classifications]. Logistika = Logistics, 2010, no. 4, pp. 21–22. URL: Link (In Russ.)
Kuznetsov D.N., Tolstykh S.S. [Stochastic model of multi-stage management of multistock inventories]. Upravlenie obshchestvennymi i ekonomicheskimi sistemami, 2007, no. 1. (In Russ.) URL: Link
Volobueva E.Yu. [Possibility of optimizing the order volume and sales price in the supply chain]. Logistika = Logistics, 2010, no. 3, pp. 36–37. URL: Link (In Russ.)
Sokolov G.A., Volobueva E.Yu. [The Markov model of optimizing the product delivery process with a single-step consumer value]. Logistika = Logistics, 2012, no. 11, pp. 46–48. URL: Link (In Russ.)
Volobueva E.Yu. [The stochastic model of optimizing the order volume and sale price in the supply chain based on profitability criterion]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2012, no. 2, pp. 81–87. URL: Link (In Russ.)
Brodetskii G.L., Volobueva E.Yu. [Supply chains management in terms of many criteria under conditions of random demand]. Logistika = Logistics, 2012, no. 3, pp. 32–35. URL: Link (In Russ.)
Brodetskii G.L., Gusev D.A., Kuleshova E.S. [The algorithm of multi-criterial distribution of goods in the warehouse network]. Logistika = Logistics, 2014, no. 8, pp. 24–28. URL: Link (In Russ.)
Kosorukov O.A., Sviridova O.A. [Taking into Account the Demand Uncertainty while Optimizing the Inventory Management]. Logistika = Logistics, 2012, no. 6, pp. 12–13. URL: Link (In Russ.)
Lukinskii V.S., Vorob'eva N.I. [Modified economic order quantity (EOQ) model with discounts]. Logistika = Logistics, 2015, no. 4, pp. 54–59. (In Russ.)
Lukinskii V.S., Lukinskii V.V., Maevskii A.G. [Building a model to calculate an economic batch quantity taking into account the deficit]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2014, no. 1, pp. 43–54. URL: Link (In Russ.)
Rozhkov M.I. [Simulation modeling of logistic networks of suppliers in the motor industry]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2012, no. 2, pp. 40–49. URL: Link (In Russ.)
Pilipchuk S.F., Radaev A.E. [Formation of the optimal system of freight delivery using the simulation modeling tools]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2013, no. 6, pp. 43–52. URL: Link (In Russ.)
Vinogradov A.B. [Using the modified method of economic trade-offs for conflict resolution in the internal supply chain]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2009, no. 4, pp. 33–44. URL: Link (In Russ.)
Lukinskii V.V., Katkova E.V. [Analyzing the methods of selecting logistics intermediaries]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2014, no. 2, pp. 49–56. URL: Link (In Russ.)
Vorob'eva N.I., Lukinskii V.S., Lukinskii V.V. [Economic order quantity model: Analysis and directions of further development]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2014, no. 3, pp. 42–53. URL: Link (In Russ.)
Valeeva A.F., Valeev R.S., Tarasova T.D., Gazizova E.I. [On uniform product delivery to various clients taking into account the solution of problems related to inventory management, routing and warehousing]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2015, no. 2, pp. 53–58. URL: Link (In Russ.)
Bochkarev A.A., Bochkarev P.A. [Selecting suppliers and optimizing the size of delivery lot under changing demand]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2014, no. 1, pp. 37–42. URL: Link (In Russ.)
Yampol'skii S.M., Shalamov A.S. [A logistics approach to current assets management automation of a trading company]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2013, no. 4, pp. 65–70. URL: Link (In Russ.)
Kulakova Yu.N. [Evaluating the normalization factor in the multi-product model of enterprise inventory management model subject to equal frequency and equal cost of delivery]. Logistika i upravlenie tsepyami postavok = Logistics and Supply Chain Management, 2012, no. 3, pp. 76–83. URL: Link (In Russ.)
Kulakov A.B., Kulakova Yu.N. [Multi-product model of control of the reserves of enterprise with the deliveries to the equal periodicity]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2013, no. 29, pp. 58–62. URL: Link (In Russ.)
Kulakova Yu.N., Kulakov A.B. [Study of normalization factor behavior in a multiproduct inventory model for delivery of two kinds of goods with multiple periodicities]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2014, no. 10, pp. 44–54. URL: Link (In Russ.)
Mitsel' A.A., Alimkhanova D.A. [A multi-product model to manage inventory with even frequency of delivery]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2015, no. 40, pp. 55–66. URL: Link (In Russ.)
Dzenzelyuk N.S. [The methodology of adaptive management of inventories in conditions of a nonstationary market]. Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Ser.: Ekonomika i menedzhment = Bulletin of South Ural State University. Series Economics and Management, 2011, no. 21, pp. 27–31. URL: Link (In Russ.)
Kulakova Yu.N., Kulakov A.B. [A multiproduct inventory control model for supply of two types of goods at random interval between deliveries]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2017, vol. 16, iss. 6, pp. 1152–1169. (In Russ.) URL: Link
Mitsel' A.A., Stavchuk L.G. [A three-product model to manage inventory with random demand]. Ekonomicheskii analiz: teoriya i praktika = Economic Analysis: Theory and Practice, 2017, vol. 16, iss. 3, pp. 561–572. (In Russ.) URL: Link
