# Newsboy problem with birandom demand

### Abstract

Estimation of accurate product demand in a single period inventory model (SPIM) is an essential prerequisite for successfully managing the supply chain in large and medium merchandise. Managers/ decision makers (DMs) often find it difficult to forecast the exact inventory level of a product due to complex market situations and its volatility caused by several factors like customers uncertain behavior, natural disasters, and uncertain demand information. In order to make fruitful decisions under such a complicated environment, managers seek applicable models that can be implemented in profit maximization problems. Many authors studied SPIM (also known as newsboy problem) considering the demand as a normal random variable with fixed mean and variance. But for more practical situations the mean demand also varies from time to time yielding two-folded randomness in demand distribution. Thus, it becomes more difficult for DMs to apprehend the actual demand having two-folded random/birandom distribution. A blend of birandom theory and newsboy model has been employed to propose birandom newsboy model (BNM) in this research to find out the optimal order quantity as well as maximize the expected profit. The practicality of the projected BNM is illustrated by a numerical example followed by a real case study of SPIM. The results will help DMs to know how much they should order in order to maximize the expected profit and avoid potential loss from excess ordering. Finally, the BNM will enhance the ability of the managers to keep parity of product demand and supply satisfying customers’ needs effectively under uncertain environment.

### Downloads

### References

Abdel-Malek, L. L., & Otegbeye, M. (2013). Separable programming/duality approach to solving the multi-product Newsboy/Gardener Problem with linear constraints. Applied Mathematical Modelling, 37(6), 4497-4508.

Agrawal, V., & Seshadri, S. (2000). Impact of uncertainty and risk aversion on price and order quantity in the newsvendor problem. Manufacturing & Service Operations Management, 2(4), 410-423.

Cao, G., & Shan, D. (2013). The effect of exit strategy on optimal portfolio selection with birandom returns. Journal of Applied Mathematics. Article ID 236579, 1-6.

Chen, S. P., & Ho, Y. H. (2013). Optimal inventory policy for the fuzzy newsboy problem with quantity discounts. Information Sciences, 228, 75-89.

Ding, S. (2013). Uncertain multi-product newsboy problem with chance constraint. Applied mathematics and computation, 223(15), 139-146.

Gallego, G. & Moon, I. (1993). The distribution free newsboy problem: review and extensions. Journal of Operational Research Society, 44(8), 825-834.

Gallego, G. (1992). A minmax distribution free procedure for the (Q,R) inventory model. Operations Research Letters, 11(1), 55-60.

Gler, M. G. (2014). A note on: The effect of optimal advertising on the distribution-free newsboy problem. International Journal of Production Economics, 148, 90-92.

Hadley, G. W. (1963). Analysis of inventory systems, Prentice-Hall, New Jersey, USA.

Kamburowski, J. (2014). The distribution-free newsboy problem under the worst-case and best-case scenarios. European Journal of Operational Research, 237(1), 106-112.

Kamburowski, J. (2015). On the distribution-free newsboy problem with some non-skewed demands. Operations Research Letters, 43(2), 165-171.

Lee, C. M., & Hsu, S. L. (2011). The effect of advertising on the distribution-free newsboy problem. International Journal of Production Economics, 129(1), 217-224.

Liu, Z. (2013). The Common Formula on Birandom Variable Variance. International Conference on Information Technology and Applications (ITA), IEEE, 486-488.

Mahoney, J. F., & Sivazlian, B. D. (1980). Probability of Shortage for Erlang Distributed Demand in a (σ,S) Inventory Problem. SIAM Journal on Applied Mathematics, 38(1), 156-162.

Maity, S., Roy, A., & Maiti, M. (2015). A modified genetic algorithm for solving uncertain constrained solid travelling salesman problems. Computers & Industrial Engineering, 83, 273-296.

Natarajan, K., Sim, M., & Uichanco, J. (2017). Asymmetry and ambiguity in newsvendor models. Management Science, 64(7), 2973-3468.

Pando, V., San-Jos, L. A., Garca-Laguna, J., & Sicilia, J. (2013). A newsboy problem with an emergency order under a general backorder rate function. Omega, 41(6), 1020-1028.

Peng, J., & Liu, B. (2007). Birandom variables and birandom programming. Computers & Industrial Engineering, 53(3), 433-453.

Sun, Y., & Guo, Z. (2017). Optimal Inventory Policy for Newsboy Problem Based on Fuzzy Random Demand. In Proceedings of the Fourth International Forum on Decision Sciences. Uncertainty and Operations Research. Springer, Singapore.

Tadikamalla, P. R. (1978). Applications of the Weibull distribution in inventory control. Journal of the Operational Research Society, 29(1), 77-83.

Tao, Z., & Xu, J. (2013). An equilibrium chance-constrained multiobjective programming model with birandom parameters and its application to inventory problem. Journal of Applied Mathematics. Article ID 382620, 1-12.

Tavana, M., Shiraz, R. K., & Hatami-Marbini, A. (2014). A new chance-constrained DEA model with birandom input and output data. Journal of the operational research society, 65(12), 1824-1839.

Vipin, B., & Amit, R. K. (2017). Loss aversion and rationality in the newsvendor problem under recourse option. European Journal of Operational Research, 261(2), 563-571.

Wang, G., Tang, W., & Zhao, R. (2012). A birandom job search problem with risk tolerance. Journal of Applied Mathematics, Article ID 161573, 1-12.

Wang, Y., Fan, J., Xu, Y., Sun, W., & Chen, D. (2017). Designing management strategies for carbon dioxide storage and utilization under uncertainty using inexact modelling. Engineering Optimization, 49(6), 1024-1039.

Watt, R., & Vzquez, F. J. (2017). An analysis of insurance demand in the newsboy problem. European Journal of Operational Research, 259(3), 1064-1072.

Xu, J., & Ding, C. (2011). A class of chance constrained multiobjective linear programming with birandom coefficients and its application to vendors selection. International Journal of Production Economics, 131(2), 709-720.

Xu, J., & Zhou, X. (2009). A class of multi-objective expected value decision-making model with birandom coefficients and its application to flow shop scheduling problem. Information Sciences, 179(17), 2997-3017.

Xu, J., Tu, Y., & Zeng, Z. (2012). A nonlinear multiobjective bilevel model for minimum cost network flow problem in a large-scale construction project. Mathematical Problems in Engineering. Article ID 463976, 1-40.

Xu, J., Zhang, Z., & Mookerjee, V. S. (2013). Applying birandom MODM model to navigation coordinated scheduling: a case study of Three Gorges Project. Transport, 28(2), 140-157.

Yan, L. (2009). One type of optimal portfolio selection in birandom environments. Modern Applied Science, 3(6), 126.

Zhang, W., Li, J., Zhang, R., & Chen, Y. (2017). Impact of Emergency Order in Price-Dependent Newsvendor Problems. Asia-Pacific Journal of Operational Research, 34(02), 1750001.

Zhang, Z., & Xu, J. (2013). A multi-mode resource-constrained project scheduling model with birandom coefficients for drilling grouting construction project. International Journal of Civil Engineering, 11(1), 1-13.

Zhou, M., Lu, S., Tan, S., Yan, D., Ou, G., Liu, D.,& Zhu, X. (2017). A stochastic equilibrium chance-constrained programming model for municipal solid waste management of the City of Dalian, China. Quality & Quantity, 51(1), 199-218.

*Decision Making: Applications in Management and Engineering*,

*2*(1), 1-12. Retrieved from https://dmame.rabek.org/index.php/dmame/article/view/24