Lot-size reorder-point system with deterministic variable parameters, Erlang-distributed supplier’s capacity and Logarithmic normal-approximated LTD

Here, a mixed backorder and lost sale inventory system with stochastic lead time demand and supplier’s availablecapacity is proposed. Lead time and ordering cost parameters are considered to be controllable with extra investment.In order to fit some real and practical environment, lead time demand uncertainty is approximated by log-normaldistribution to provide a right skewed distribution. Also, it is considered that supplier’s available capacity follows aspecific gamma distribution. On the basis of the mentioned characteristics for the proposed system, a mathematicalmodel is proposed and a solution algorithm is developed to find optimal solution. Also, a sensitivity analysis is carriedout with respect to important system’s parameters.