A deteriorating inventory model for determining optimal replenishment run time with failure rework and shortage

Abstract

Many researchers focused on economic production quantity model for defective/deteriorating items under the assumptions (a) all the defective items can be reproduced as serviceable items (b) all the deteriorating items can be detached from inventory through screening process (c) shortages are not permitted. In an actual manufacturing environment, due to controllable or uncontrollable factors, some of the defective items may not be reproduced as serviceable items and due to human error or other factors, the internally deteriorated items may pass on to customers which will make negative impact on corporate image. This paper investigates an imperfect production inventory model with imperfect inspection of deteriorating items and failure rework under finite planning horizon. This system consists of m replenishment runs with failure rework and shortage. The main objective is to determine the optimal replenishment run time, optimal economic production quantity and optimal replenishment cycle time with the aim of minimising the total cost of the model. A solution procedure with an algorithm is proposed and a numerical example is provided to the theoretical results and to highlight the managerial insights.

KEYWORDS:

• Multi-replenishment run
• failure rework
• defective items
• internally deteriorating items
• penalty cost
• scrap cost

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

T. Sekar

Mr T. Sekar is a research scholar, Department of Mathematics, Gandhigram Rural Institute – Deemed to be University, Gandhigram – 624302, Tamil Nadu, India. He received his B. Sc degree from Govt. arts college karur, Bharathidasan University, M. Sc and M. Phil degree from National College, Trichy, Bharathidasan University, Tamil Nadu, India. His research interests are in the field of inventory management and control, optimization techniques and their applications.

R. Uthayakumar

Dr R. Uthayakumar was born in Dindigul, India, in 1967. He received the PhD degree from the Gandhigram Rural Institute – Deemed to be University, Gandhigram, Tamil Nadu, India, in 2000. Currently, he is a Professor & Head, Department of Mathematics, Gandhigram Rural Institute – Deemed to be University, Gandhigram. He has done research in the area of functional analysis. His current research interests are primarily in the field of optimization and the Theory of Fractal Analysis. He is also interested in finding out the general mathematical model in the field of inventory management and supply chain. To his credit, he has published many research articles in the area of inventory management and supply chain in reputed international journals. Moreover, he is guiding many scholars in the above said areas.