A single-vendor multi-buyer integrated model with controllable lead time and quality improvement through reduction in defective items

Abstract

This paper presents a single-vendor multi-buyer integrated inventory model with an imperfect production system of the vendor. The expected demand of each buyer is assumed to be dependent on selling price while lead-time demand of each buyer is assumed to be normally distributed. Further, each buyer's lead time can be reduced at an added crash cost. We extend the model by assuming that the vendor invests money in order to improve the quality of the product and reduce the percentage of defective items. The objective is to determine the optimal values of the decision variables involved so that the average total profit of the system is maximised. We relax the assumption of normality to treat the model with distribution-free approach, where only the mean and standard deviation of lead-time demand are known. Optimal results are obtained for a numerical example and effects of the key parameters are included to illustrate the results of the proposed model.

Keywords:

• inventory
• supply chain
• integrated model
• vendor–buyer model
• defective item
• lead-time reduction
• investment function

Acknowledgements

The authors are thankful to the anonymous reviewers for their comments and constructive suggestions which have helped in improving the quality of the paper.

Additional information

Funding

The first author gratefully acknowledges the financial support (postdoctoral fellowship) provided by the National Board for Higher Mathematics (NBHM) [grant number 2/40(15)2012/R&D-II/8017] for carrying out this work.