Modeling of the ordering process for piecewise-linear demand with saturation

V. M. Bure   ; V. V. Karelin   ; L. N. Polyakova   ; I. V. Yagolnik

Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 13 (2017) no. 2, pp. 138-146

Résumé

This article discusses the behavior of trading companies when the demand function for a product is a piecewise linear function with some pre-defined level of saturation. As a result of special marketing research the demand function is determined. It is assumed that the following scheme is used. The ordered product is divided into two parts. The first batch will arrive immediately and will be sold within a certain period of time up to $T_1$. The second batch of goods will be delivered only at time $T$ and this batch will be sold with reduction in price as follows from deficit of the goods. The consideration of a such a scheme for the sale stems from the fact that, first, commercial enterprises have limited capacity and can not accommodate the entire volume of products ordered, and secondly, the manufacturer may not offer the entire ordered quantity at the initial time. An important feature of this problem is selection of parameters which are subsequently optimized. For trading firms the moment time $T_1$ has very high importance because trading companies have sold the first batch and received money. After this moment the trading firms will pay to the manufacturers, and manufacturers can to continue the activities. The time moment $ T_1$ is important for trading firms, as it will allow them to fulfill various financial obligations associated with the payment of loans and other expenses. Time $T$ is also important, so this will mean the successful completion in full of selling all these goods. Refs 16. Fig. 1.

Détail

Keywords: the level of product inventory, piecewise linear demand, the goods deficit, reduction.

Bibliographie

[1] Giri B. C., Sharma S., “Optimal ordering policy for an inventory system with linearly increasing demand and alowable shortages under two levels trade credit financing”, Oper. Res. Intern. J., 16 (2016), 25–50 | DOI

[2] Aggarwal S. P., Jaggi C. K., “Ordering policies of deteriorating items under permissible delay in payments”, J. Oper. Res. Soc., 46:5 (1995), 658–662 | DOI | Zbl

[3] Dave U., “Letters and viewpoints on “economic order quantity under conditions of permissible delay in payments””, J. Oper. Res. Soc., 46:5 (1985), 1069–1070 | DOI

[4] Chen S. C., Teng J. T., Skouri K., “Economic production quantity models for deteriorating items with up-stream full trade credit and down-stream partial trade credit”, Intern. J. Prod. Econ., 155 (2013), 302–309 | DOI

[5] Giri B. C., Sharma S., “An integrated inventory model for a deteriorating item with allowable shortages and credit linked wholesale price”, Optim. Lett., 37 (2015), 624–637 | DOI | MR

[6] Goyal S. K., “Economic order quantity under conditions of permissible delay in payments”, J. Oper. Res. Soc., 36:4 (1985), 335–338 | DOI

[7] Huang Y. F., “Optimal retailer's ordering policies in the EOQ model under trade credit financing”, J. Oper. Res. Soc., 54:9 (2003), 1011–1015 | DOI | Zbl

[8] Huang Y. F., Hsu K. H., “An EOQ model under retailer partial trade credit policy in supply chain”, Intern. J. Prod. Econ., 112:2 (2008), 655–664 | DOI

[9] Jamal A. M. M., Sarker B. R., Wang S., “An ordering policy for deteriorating items with allowable shortages and permissible delay in payment”, J. Oper. Res. Soc., 48:8 (1997), 826–833 | DOI | Zbl

[10] Khanra S., Ghosh S. K., Chaudhuri K. S., “An EOQ model for a deteriorating item with time dependent quadratic demand under permissible delay in payment”, Appl. Math. Comput., 218:1 (2011), 1–9 | MR | Zbl

[11] Khanra S., Mandal B., Sarkar B., “An inventory model with time dependent demand and shortages under trade credit policy”, Econ. Model., 35 (2013), 349–355 | DOI | MR

[12] Maihami R., Abadi I. N. K., “Joint control of inventory and its pricing for non-instantaneously deteriorating items under permissible delay in payments and partial backlogging”, Math. Comp. Model., 55:5–6 (2012), 1722–1733 | DOI | MR | Zbl

[13] Bure V. M., Karelin V. V., Polyakova L. N., “Probabilistic model of terminal services”, Applied Mathematical Sciences, 10:39 (2016), 1945–1952 | DOI

[14] Polyakova L. N., Karelin V. V., “On a continuous method for minimizing of nonsmooth functions”, Intern. conference stability and control processes in memory of V. I. Zubov (SCP), Proceedings, eds. L. A. Petrosyan, A. P. Zhabko, Saint Petersburg University, Saint Petersburg, 2015, 338–341

[15] Polyakova L., Karelin V., “Exact penalty functions method for solving problems of nondifferentiable optimization”, Cybernetics and physics, 3:3 (2014), 124–129 | MR

[16] Polyakova L. N., “On the method of exact penalty quasidifferential functions”, Journal of Computational Mathematics and Mathematical Physics, 41:2 (2001), 225–238 (In Russian) | Zbl