A multi-item inventory system with expected shortage level-dependent backorder rate with working capital and space restrictions

In this paper, a new multi-item inventory system is considered with random demand and random lead time including working capital and space constraints with three decision variables: order quantity, safety factor and backorder rate. The demand rate during lead time is stochastic with unknown distribution function and known mean and variance. Random constraints are transformed to crisp constraints with using the chance-constrained method. The Minimax distribution free procedure has been used to lead proposed model to the optimal solution. The shortage is allowed and the backlogging rate is dependent on the expected shortage quantity at the end of cycle. Two numerical examples are presented to illustrate the proposed solution method.