Involvement of controllable lead time and variable demand for a smart manufacturing system under a supply chain management

The concept of controllable lead time and variance is critical issues for the smart supply chain management. This study concerns about variable lead time and variance under controllable production rate and advertise-dependent demand. Managers of any supply chain always improve their performance by reducing lead time and its variance. This paper explores and quantifies these benefits of such lead time reduction for commonly used lot size quantity, production rate, safety factor, reorder point, advertisement cost, vendor's setup cost. Instead of expected total cost equations, this study provides an exact total cost equation built on an inherent relationship between on-hand inventory and backorder. The marginal value analysis on lead time and its variance achieve more accurate results. The analytical results show that the total supply chain cost is a convex function of both lead time and variance. In other words, the cost savings on both lead time and its variance reduction decrease when lead time becomes larger. Two continuous investments are implied to reduce setup costs and improve the reliability of the production process. The expected backorder and inventory for the buyer uniformly distributed throughout reorder point. Moreover, a smart production process is developed under stochastic demand and flexible production rates. The global optimality of the cost function and decision variables are validated through classical optimization. The numerical examples confirm analytical results and sensitivity analysis is provided for different parameters. Some special cases along with graphical representations are given to validate the model.