Optimisation of the stock structure of a single stock item taking into account stock quantity constraints, using a Lagrange multiplier

• Autorzy: Krzyżaniak Stanisław

Identyfikatory

DOI

10.17270/J.LOG.2022.730

• Języki publikacji: EN

Abstrakty

EN

Background: Optimisation in the area of stock management is most often performed in relation to cycle stock. The classic example here is the Harris-Wilson formula for calculating the economic order quantity. Often these models are not subject to any constraints imposed on the optimised quantities. However, in practice, taking such constraints into account is important. The application of the so-called Lagrange multiplier is helpful here, but the examples of its application usually refer to the multi-position sets of stock items (e.g. the search for the optimum structure of stock of material groups in the case of capital constraints). This paper attempts to optimise the structure of the stock (cycle stock vs. safety stock) for a single stock item. Methods: To achieve the objective of determining the optimum stock structure for the various conditions under which stock replenishment is implemented, a general model has been built, a component of which is a Lagrange function containing the constraint conditions for the solution. Next, this model has been implemented in the form of an EXCEL spreadsheet application. Results: The result of solving the optimization task based on the proposed model is a system of equations, the solution of which (with the help of the EXCEL application) allows to determine the optimum value of the Lagrange multiplier, on the basis of which the components of the inventory structure and other related quantities (service level indicators and costs, such as stock replenishment, stock maintenance and stock deficit costs) are calculated. This has been illustrated using a fictitious example, which at the same time made it possible to observe certain general relationships between the adopted constraints and the recorded quantities. Conclusions: Two types of conclusions can be presented. The first type concerns the approach itself. The possibility of determining the optimum structure of the stock (cycle stock vs. safety stock) depending on various values characterising the adopted stock replenishment system as well as the adopted limitations has been demonstrated. The second type of conclusions results from the presented example of application of the method for the assumed ranges of changes of selected quantities.

Słowa kluczowe

EN

stock optimization; Lagrange multiplier; service level; stock related costs

PL

optymalizacja zapasów; mnożnik Lagrange'a; poziom usług; koszty związane z zapasami

• Wydawca: Wyższa Szkoła Logistyki
• Czasopismo: LogForum
• Rocznik: 2022
• Tom: Vol. 18, no. 2
• Strony: 261--269
• Opis fizyczny: Bibliogr. 11 poz., rys., tab., wykr.

Twórcy

autor

Krzyżaniak Stanisław

• Poznań School of Logistics, Poznań, Poland

Bibliografia

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• 2. Fergany H. A., Gomaa M. A., Probabilistic Mixture Shortage Multi-Source Inventory Model with Varying Holding Cost Under Constraint. Delta Journal of Science. Vol. 39 (2018) 9-17. https://dx.doi.org/10.21608/djs.2018.138901
• 3. Harris F.W. (1913), How many parts to make at once, “Factory, The Magazine of Management”, Vol. 10, No 2, February 1913.
• 4. Hoswari S. et al (2020). Comparison Study about Inventory Control System from Some Papers in Indonesian Case Study. IOP Conf. Ser.: Mater. Sci. Eng. 852 012110.
• 5. Korponai, J., Toth, A.B. and Illes, B. (2017), Effect of the Safety Stock on the Probability of Occurrence of the Stock Shortage, Proceedings of 7th International Conference on Engineering, Project, and Production Management, Procedia Engineering, 182, pp. 335-334. https://doi.org/10.1016/j.proeng.2017.03.106
• 6. Kowiger H. (2012), Wybrane problemy dotyczące optymalizacji funkcji użyteczności (in Polish) - Selected problems of utility function optimization, Research Bulleting of Szczecin University. Studies and Papers of the Faculty of Economic Sciences and Management no 26 of 2012, pp. 225-237
• 7. Krzyżaniak S (2017). An attempt towards a model approach to choosing a stock replenishment system under conditions of independent demand. Research Journal of the University of Gdańsk. Transport Economics and Logistics. Vol. 68 (2017), str. 39-48.
• 8. Lukitosari V. et al (2019) Minimizing cost and backorder risk through customer priority on spares inventory. Journal of Physics.: Conf. Ser. 1218 012061. https://doi.org/10.1088/1742-6596/1218/1/012061
• 9. Samak-Kulkarnia, S.M. and Rajhansb, N.R. (2013), Determination of Optimum Inventory Model for Minimizing Total Inventory Cost. Proceedings of Chemical, Civil and Mechanical Engineering Tracks of the 3rd Nirma University International C onference on Engineering (NUiCONE 2012), Procedia Engineering, 51, pp. 803-809. https://doi.org/10.1016/j.proeng.2013.01.115
• 10. Tempelmeier, H. (2000), Inventory Service-Levels in the Customer Supply Chain. OR Spectrum, 2000, 22(3), pp. 361-380.
• 11. Yassa R. I, Ikatrinasari Z. F. (2019) Determination Of Multi-Item Inventory Model With Limitations Of Warehouse Capacity And Unit Discount In Leading Garment Industry In Indonesia. International Journal of Mechanical and Production, Engineering Research and Development (IJMPERD), ISSN(P): 2249-6890; ISSN(E): 2249-8001, Vol. 9, Issue 2, Apr 2019, 161-170

Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).