An Inventory Model for Non-Instantaneously Deteriorating Items with Nonlinear Stock-Dependent Demand, Hybrid Payment Scheme and Partially Backlogged Shortages
Md Al-Amin Khan,
Ali Akbar Shaikh,
Leopoldo Eduardo Cárdenas-Barrón,
Abu Hashan Md Mashud,
Gerardo Treviño-Garza,
Armando Céspedes-Mota
Affiliations
Md Al-Amin Khan
Department of Mathematics, Jahangirnagar University, Dhaka 1342, Bangladesh
Ali Akbar Shaikh
Department of Mathematics, The University of Burdwan, Burdwan 713104, India
Leopoldo Eduardo Cárdenas-Barrón
School of Engineering and Sciences, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
Abu Hashan Md Mashud
Department of Mathematics, Hajee Mohammad Danesh Science and Technology University, Dinajpur 5200, Bangladesh
Gerardo Treviño-Garza
School of Engineering and Sciences, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
Armando Céspedes-Mota
School of Engineering and Sciences, Tecnologico de Monterrey, Ave. Eugenio Garza Sada 2501, Monterrey 64849, Mexico
This research work presents an inventory model that involves non-instantaneous deterioration, nonlinear stock-dependent demand, and partially backlogged shortages by considering the length of the waiting time under a hybrid prepayment and cash-on-delivery scheme. The corresponding inventory problem is formulated as a nonlinear constraint optimization problem. The theoretical results for the unique optimal solution are presented, and eight special cases are also identified. Moreover, a salient theoretical result is provided: a certain condition where the optimal inventory policy may or may not involve deterioration. Finally, two numerical examples are provided using a sensitivity analysis to show the validity range of the inventory parameters.