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.

Highlights

  • The classical newsboy problem (CNP) aims at determining the optimal order quantity of products, which minimize the expected total cost and / or maximize the Adhikary et al./Decis

  • The characteristics of a single period inventory model (SPIM) become more complicated due to complex market situations and its volatility caused by several factors like customers uncertain behavior

  • Gallego and Moon (1993, 1994) analyzed distribution-free newsboy problems where decision makers (DMs) have no idea about the demand distribution

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Summary

Introduction

The classical newsboy problem (CNP) aims at determining the optimal order quantity of products, which minimize the expected total cost and / or maximize the. Vipin and Amit (2017) proposed a loss aversion SPIM under alternative option and proved the rationality of the decision maker to predict the order quantity by imposing loss aversion in the newsboy model with the change of selling price and purchase cost factors They showed the models based on utility functions perform better in forecasting the rational behavior due to loss aversion. Many more real life applications can be found in the following literature: a multi-objective birandom inventory problem (Tao and Xu, 2013), a birandom multi-objective scheduling problem (Xu et al, 2013) in ship transportation, optimal portfolio selection with birandom returns(Cao and Shan, 2013), a modified genetic algorithm (Maity et al, 2015), chance-constrained programming model for municipal waste management with birandom variables (Zhou et al, 2015), and the CCUS (carbon capture, utilization, and storage) management system in birandom environment (Wang et al, 2017).

Birandom Variable
Expected Value of birandom variables
E Pr t dt Pr t dt
Birandom Simulation
Mathematical Formulation
Numerical Example
A Case Study
Conclusion
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