Acta Univ. Agric. Silvic. Mendelianae Brun. 2013, 61(7), 2221-2227 | DOI: 10.11118/actaun201361072221

Functions of several variables analysis applied in inventory management

Martina Janková, Veronika Novotná, Tereza Varyšová
Institute of Informatics, Brno University of Technology FBM, Kolejní 2906/4, 612 00 Brno, Czech Republic

In many cases a retailer is not capable of settling an invoice immediately upon receiving it and is given an option by the supplier to settle the invoice within a definite period. The retailer can sell the goods before the deadline, accumulate revenue and earn interest. If the retailer is not able to meet his obligations within the deadline, he is charged an interest. This paper introduces a newly constructed model which enables a retailer to set an optimal price of goods under permissible delay in payments, and to determine the maximum term of payment. The model is based on the assumption of time-dependent demand and has been developed for non-deteriorating goods. The paper further analyzes a situation in which the retailer sell all the goods in time, and a situation in which the deadline was not met. Theoretical results are demonstrated by an illustrative example.
The authors of the paper used methods of analysis and synthesis, and the method of mathematical analysis (differential calculus of multivariable functions, solution of ordinary differential equations).
The model suggested in the paper can be expanded in the future. One option is generalization of the model, allowing for the lack of goods, bulk discounts, etc.

Keywords: inventory management, EOQ model, non-deteriorating goods, local extremes, multivariable functions
Grants and funding:

This paper was supported by grant FP-S-13-2148 'The Application of ICT and Mathematical Methods in Business Management' of the Internal Grant Agency at Brno University of Technology.

Received: August 17, 2013; Published: December 24, 2013  Show citation

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Janková, M., Novotná, V., & Varyšová, T. (2013). Functions of several variables analysis applied in inventory management. Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, 61(7), 2221-2227. doi: 10.11118/actaun201361072221
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    References

    1. ABAD, P. L., JAGGI, C. K, 2003: A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive. International Journal of Production Economics, 89, 2: 115-122. ISSN 0925-5273. DOI: 10.1016/S0925-5273(02)00142-1 Go to original source...
    2. ALONZO, P., DI SANZO, S., 2011: Unemployment and hysteresis: A nonlinear unobserved components approach, Studies in Nonlinear Dynamics and Econometrics, 15, 2: 1-25. ISSN 1558-3708. Go to original source...
    3. BANERJEE, A., 2005: Concurrent pricing and lot sizing for make-to-order contract production. International Journal of Production Economics, 93, 0: 189-195. ISSN 0925-5273. DOI: 10.1016/j.ijpe.2004.06.017 Go to original source...
    4. BHUNIA, A. K., MAITI, M., 1997: Deterministic inventory models for variable production. Journal of The Operational Research Society, 48, 2: 221-224. ISSN 0160-5682. DOI: 10.1057/palgrave.jors.2600343 Go to original source...
    5. BOUCEKKINE, R., SAGLAM, R., VALLEE, T., 2004: Technology adoption under umbodiment: a two-stage optimal control approach, Macroeconomic Dynamics, 8, 2: 250-271, ISSN 1365-1005. DOI: 10.1017/S1365100503030062 Go to original source...
    6. DAVE, U., 1985: On "economic order quantity under conditions of permissible delay in payments" by Goyal, Journal of the Operational Research Society, 36: 1069. ISSN 0160-5682. DOI: 10.1057/jors.1985.186 Go to original source...
    7. DOŠLÁ, Z., KUBEN, J., 2012: Diferenciální počet funkcí jedné proměnné, 1. vyd. Brno: Masarykova univerzita, p. 209, ISBN 8021058145.
    8. FEDERGRUEN, A., HECHING, A., 1999: Combined pricing and inventory control under uncertainty. Operations Research, 47, 3: 454-475. ISSN 0030-364X. DOI: 10.1287/opre.47.3.454 Go to original source...
    9. FEWINGS, D. R., 1992: A credit limit decision model for inventory floor planning and other extended trade credit arrangement. Decision Science, 23: 200-220. ISSN 1540-5915. DOI: 10.1111/j.1540-5915.1992.tb00384.x Go to original source...
    10. GOYAL, S. K., 1985: Economic order quantity under conditions of permissible delay in payments, Journal of the Operational Research Society, 36, 4: 335-338. ISSN 0160-5682. DOI: 10.1057/jors.1985.56 Go to original source...
    11. HARADA T., 2010: Path-dependent economic growth with technological trajectory, Economics of Innovation and New Technology, 19, 6: 521-538. ISSN 1043-85. DOI: 10.1080/10438590903166412 Go to original source...
    12. HWANG, H., SHINN, S. W., 1997: Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments, Computers and Operations Research, 24, 6: 539-547. ISSN 0305-0548. DOI: 10.1016/S0305-0548(96)00069-X Go to original source...
    13. CHANG, L.Y. OUYANG, J. T., 2003: An EOQ model for deteriorating items under supplier credits linked to ordering quantity. Applied Mathematical Modelling, 2003, 27: 983-996. ISSN 0307-904X. DOI: 10.1016/S0307-904X(03)00131-8 Go to original source...
    14. CHEN, X., SIMCHI-LEVI, D., 2006: Coordinating inventory control and pricing strategies: The continuous review model. Operations Research Letters, 34, 3: 323-332. ISSN 01676377. DOI: 10.1016/j.orl.2005.04.012 Go to original source...
    15. CHU, P., CHUNG, K. J., LAN, S. P., 1998: Economic order quantity of deteriorating items under permissible delay in payments. Computers and Operations Research, 25, 12: 817-824. ISSN 0305-0548. DOI: 10.1016/S0305-0548(98)00006-9 Go to original source...
    16. IOANA, A., MIREA, V., BĂLESCU, C., 2010: Economic processes study through Fuzzy Logic, Journal of Economic Computation And Economic Cybernetics Studies And Research, 2010, 2, 129-138. ISSN 0424-267X.
    17. JABER, M. Y., OSMAN, I. H., 2006: Coordinating a two-level supply chain with delay in payments and profit sparing. Computers & Industrial Engineering, 50, 4: 385-400. ISSN 0360-8352. DOI: 10.1016/j.cie.2005.08.004 Go to original source...
    18. JAMAL, A. M. M., SARKER, B. R., and WANG, S., 1997: An ordering policy for deteriorating items with allowable shortage and permissible delay in payment. Journal of the Operational Research Society, 48, 8: 826-833. ISSN 0160-5682. DOI: 10.1057/palgrave.jors.2600428 Go to original source...
    19. KHALEB, E., HAYMAN, W., 2013: Reinvestigating the relationship between ownership structure and inventory management: A corporate governance perspective. International Journal of Production Economics. 143, 1: 207-218. ISSN 0925-5273. Go to original source...
    20. KHOUJA, M., 2000: Optimal ordering, discounting, and pricing in the single-period problem. International Journal of Production Economics, 65, 2: 201-216. ISSN 0925-5273. DOI: 10.1016/S0925-5273(99)00027-4 Go to original source...
    21. LAU, A. H. L, LAU, H. S., 2003: Effects of a demand-curve's shape on the optimal solutions of a multi-echelon inventory/pricing model. European of Journal Operational Research, 147: 530-548. ISSN 0377-2217. DOI: 10.1016/S0377-2217(02)00291-6 Go to original source...
    22. LIAO, H. C., TSAI, C. H., SU, C. T., 2000: An inventory model with deteriorating items under inflation when a delay in payment is permissible. International Journal of Production Economics, 63, 2: 207-214. ISSN 0925-5273. DOI: 10.1016/S0925-5273(99)00015-8 Go to original source...
    23. MADDAH, B., BISH, E. K., 2004: Joint pricing, assortment, and inventory decisions for a retailer's product line. Naval Research Logistics, 54, 3: 315-330. ISSN 1520-6750. DOI: 10.1002/nav.20209 Go to original source...
    24. MANNA, S. K., CHAUDHURI, K. S., 2001: An economic order quantity model for deteriorating items with time-dependent deterioration rate, demand rate, unit production cost and shortages. International Journal of Systems Science, 32, 8: 1003-1009. ISSN 0020-7721. DOI: 10.1080/00207720119195 Go to original source...
    25. MCNELIS, P. D., 2003: Nonlinear phillips curves in the Euro area and USA? Evidence from linear and neural network models, Computational Intelligence for Financial Engineering, Proceedings. IEEE International Conference. Hong Kong, New Zone Creative Centre, 145-149, ISBN 0-7803-7654-4 Go to original source...
    26. MEHTA, D., 1998: The formulation of credit policy models. Management Science, 15, 1: 30-50. ISSN 0025-1909. DOI: 10.1287/mnsc.15.2.B30 Go to original source...
    27. NENES, G., 2010: Inventory Management of multiple items with irregular demand: A case study, European Journal of Operational Research, 205, 2: 313-324, ISSN 0377-2217. DOI: 10.1016/j.ejor.2009.12.022 Go to original source...
    28. POLATOGLU, L. H., 1991: Optimal order quantity and pricing decisions in single-period inventory systems. International Journal of Production Economics, 1991, 23: 175-185. ISSN 0925-5273. DOI: 10.1016/0925-5273(91)90060-7 Go to original source...
    29. SCHWEITZER, P. J., SEIDMANN, A., 1991: Optimizing processing rate for flexible manufacturing systems. Management Science, 37, 4: 454-466. ISSN 0025-1909. DOI: 10.1287/mnsc.37.4.454 Go to original source...
    30. SHARKER B. R., JAMAL, A. M., WANG, S., 2000: Optimal payment time under permissible delay for products with deterioration. Production Planning & Control, 24, 11: 380-390. ISSN 0953-7287. DOI: 10.1080/095372800232117 Go to original source...
    31. SILVER, A. E., 1990: Deliberately slowing down output in a family production context. International Journal of Production Research, 28, 1: 17-27. ISSN 0020-7543. DOI: 10.1080/00207549008942681 Go to original source...
    32. STEJSKAL, L., STÁVKOVÁ, J.: Consumer decision making simulation. Acta univ. agric. et silvic. Mendel. Brun., 2009, 57, 3: 147-152. ISSN 1211-8516 Go to original source...
    33. TENG, J. T., 2002: On the economic order quantity under conditions of permissible delay in payments. Journal of the Operational Research Society, 53, 8: 915-918. ISSN 0160-5682. DOI: 10.1057/palgrave.jors.2601410 Go to original source...
    34. WENG, Z. K., 1995: Modeling quantity discount under general price-sensitive demand functions: Optimal policies and relations. European Journal of Operational Research, 86: 300-314. ISSN 0377-2217. DOI: 10.1016/0377-2217(94)00104-K Go to original source...
    35. YOU, P. S., HSIEH, Y. C., 2007: An EOQ model with stock and price sensitive demand. Mathematical and Computer Modelling, 45, 7: 933-942. ISSN 0895-7177. DOI: 10.1016/j.mcm.2006.09.003 Go to original source...
    36. ZHANG, T., 2012: A Monte Carlo Analysis for Stochastic Distance Function Frontier, Inzinerine Ekonomika-Engineering Economics, 2012, 23, 3: 250-255. ISSN 1392-2785. Go to original source...

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