A supply chain management in a single-vendor and a single-buyer integrated inventory model with backorders under imperfect production system

Lead time is an essential factor in any supply chain and inventory management system. In stochastic inventory models, lead time is often viewed as a prescribed constant or a random variable that is not subject to control. In many practical situations, lead times can be controlled by paying additional investment. Using this viewpoint, notion of the crashing cost into stochastic inventory model, in which lead time can be controlled by additional investment. Many researchers have developed various analytical inventory models we have considered the piecewise linear function. So in this proposed model, we derive the mathematical model which is developed by incorporating three types of lead time crashing cost functions (i) exponential function, (ii) polynomial function and (iii) negative exponential function. An integrated inventory model is recognized to find the optimal solutions of order quantity, lead time, total cost for buyer, total cost for vendor and the total number of deliveries from the single-vendor to the single-buyer in one production run. A solution process is suggested for solving the proposed model and numerical examples to illustrate the feature of the proposed model, and examined the effect of the key parameters on the optimal solution and managerial implications are discussed. Numerical examples show that this model offers significant improvements over existing models. A computer code using the software Matlab is developed to derive the optimal solution. The main contribution of this paper is developing a mathematical model and an effective solution procedure to find the optimal solution. Finally, a graphical representation of the computational algorithm is represented by a flowchart in each model. © 2017, © 2017 Northeastern University, China.