A newsboy problem for an inventory system under an emergency order: a modified invasive weed optimization algorithm

Abstract

The newsboy problem has numerous applications for decision making in manufacturing and industrial environments. This paper presents a practical newsboy problem for an industrial system under both supplier quantity discounts and budget constraints where the storage space is stochastic and described using a normal distribution function. In this industrial system, when a shortage occurs, two strategies of the lost sale condition and the emergency order are available for the vendor as an option to fill the occurred shortage. This paper seeks to find the optimal order quantity for each product as well as to choose either the lost sale condition or the emergency order. The objective is to maximize the expected total profit of the vendor under uncertain demand and the stochastic storage space. As the proposed problem is NP-hard, a modified invasive weed optimization algorithm (IWO) is developed. The advantage of the proposed IWO is that it is capable of solving the proposed problem with both binary and continuous decision variables. As there is no benchmark available in the literature, an efficient genetic algorithm is designed to solve the problem and to compare the results obtained using IWO. Then, the algorithms are tuned using the response surface methodology and their performances are analyzed statistically. Finally, the applicability of the proposed approach and the solution methodologies are demonstrated. A sensitivity analysis on the number of products and discount segments indicates they have a significant impact on the vendor’s tendency in choosing either the emergency order or the lost sale condition.

Keywords:

• Inventory control
• newsboy problem
• emergency order
• invasive weed optimization
• lost sale condition

JEL Classification:

• C02
• C12
• C25
• C44
• C62

Acknowledgements

The authors would like to acknowledge the efforts and the consideration of the editor and all of the anonymous reviewers for their valuable comments and suggestions to improve the quality of the paper.