Continuous review inventory model with lost sale reduction and ordering cost dependent on lead time for the mixtures of distributions

We consider a continuous review inventory system for model involving lost sales reduction through capital investment cost function and the of lead time further which reduces ordering cost. To reduce rate, two forms function, viz. logarithmic power are employed. Two relationships between time, linear considered. develop four models by taking different combinations relationship. Objective study is to total related simultaneously optimizing order quantity, safety factor, fraction shortages during stock-out period that will be length time. The demand assumed follow mixture normal distributions. optimal solution derived developing computer programs using software MATLAB. also provide numerical examples illustrate models.