Optimal lower bounds on the contribution margin in the case of stochastic order arrival

In customer order driven production, decisions on the acceptance of customer orders usually have to be based on variable costs and contribution margins (abbreviated CM), since in the short term only these quantities can be influenced. If we assume that customer orders arrive according to a stochastic process and that the decisions on order acceptance have to be made on each order separately, a customer order usually should be accepted only if its contribution margin exceeds a positive lower bound. This paper shows by means of a stochastic model that, under certain assumptions, this lower bound on the contribution margin can be determined using full costing, provided that the available capacity (constant over time) and the arrival process are balanced. This insight justifies, to a certain extent, the use of full costs to support decisions on the short-term production volume, which is a behaviour that can be observed in practice rather frequently. We also demonstrate the extension of the modelling approach to state-dependent lower bounds on the contribution margin.