A unified EOQ model with financial constraints and market tolerance

We consider the general EOQ (with partial backorders) paradigm to study factors related to the recent financial crisis. Upstream, there are financial constraints, which first limit the available capital per replenishment and second impose the prepayment (in full or partial) of the quantity ordered. Downstream, the concept of market tolerance is operationalized, permitting here backorders to occur at no-cost for a fixed time period (directly analogous to upstream payment credit). For the resulting system, we present an exact unified model of the total average profit/cost. Optimal profit/cost and respective decision variables (i.e. order cycle and shortage period) are subsequently obtained in closed form. Interestingly, by appropriately relaxing the solution of the unified system, the solution of several (some previously studied) EOQ-type models prevails. Finally, analytical and computational results reveal the impact that each factor (individually and jointly) has on system optimal solution and on the behavior of the respective optimizers.