Pseudo Order Consideration in Available to Promise (Atp)

In this paper we provide an analytic model for order promising for available-to-promise (ATP) in an assemble-to-order production environment. A distinguishing feature of our model is its inclusion of pseudo orders, which are unconfirmed customer orders, whose quantity level is uncertain. Our objective function maximizes a weighted sum of expected profit and service, where service is a concave function of the confirmed orders' fill rates. There are convex production costs. We derive the optimal solution structure: some orders are not filled at all, others are 100% filled and one order is partially filled. The solution for the confirmed order quantities and pseudo order capacity reservation level can be found by solving a system of equations. We also provide a numeric study