Coordinating production and transportation lotsizes

An extension is introduced to the multi-stage stationary lot-sizing problem with finite production rates by the time-concentrated transportation-process. This representation adequately demonstrates the relations between supplier, carrier and producer. With regard to the reconciliation of the decision variables of these institutional units one differentiates between a pure simultaneous, a pure gradual and two mixed simultaneous-gradual coordination methods. The differences and correspondences of the respective decision variables and the resulting cost functions are demonstrated by means of an analytical examination. Finally, a numerical analysis shows the distinctions in total cost between the pure simultaneous and pure gradual coordination method.