Effects of unequal lot size and variable transportation in unreliable supply chain management

The effect of unreliable players on the supply chain management with a single-setup-multiunequal-increasing-delivery-policy (SSMUID) along with a service-dependent demand and investment is discussed in this model. The manufacturer is unreliable which causes an increase of lead time and shortage. For solving the shortage problem and reducing lead time crashing cost (LTCC), an investment is utilized with the variable backorder price discounts. The number of transportation increases due to the new transportation policy and it causes pollution. Besides the fixed transportation and carbon emission cost (FTCEC), a container dependent carbon emission cost is applied. Some investments for setup cost reduction (SCR), ordering cost reduction (OCR), and quality improvement (QI) are considered. The lead time demand follows a normal distribution. The total cost of the supply chain is optimized and the model is tested numerically. The main intent of this study is to solve the shortage problem which occurs due to unreliability of the manufacturer. The study helps to reduce the unreliability issue of the manufacturer. The objective function is solved by using the classical optimization technique. Numerical results show that the discount for partial backorder enhances the profitability of the manufacturer. The sensitiveness of the parameters are discussed through the sensitivity of analysis and some special cases. Managerial insights provide the applicability of this study among different sectors.