A fuzzy scenario-based optimisation of supply network cost, robustness and shortages

Supply network (SN) robustness has become an important issue in SN management. In this paper, we refer to SN as robust, if it maintains its performance in the presence of uncertainty in SN parameters, namely uncertain changes in customer demand. A customer forecasts its demand in terms of requested quantity and time of delivery. This forecasted demand can be changed until a certain time. After that, the customer is committed to its demand. However, a manufacturer has to order materials in advance to produce its product without knowing the exact changes in customer demand. The materials can be ordered either from a standard supplier, or, from an emergency supplier, if there is not enough material in stock and/or there is not enough time for a delivery from the standard supplier. We define a new concept of fuzzy scenarios that comprise uncertain changes in customer demand. These changes are specified by linguistic terms and modelled using fuzzy numbers. The robustness of an SN is measured in a novel way as the variance of costs incurred in all fuzzy scenarios. This means that the robust SN maintains its cost in the presence of uncertain changes in customer demand. A novel fuzzy multi-objective optimisation model is developed, which determines quantities of materials to be ordered by a manufacturer from a standard supplier and times of ordering. The objectives considered simultaneously embed all fuzzy scenarios and include the minimisation of total SN cost, the maximisation of robustness and the minimisation of shortages. Various experiments are carried out to analyse the relationship between SN parameters and SN performance. Results obtained by applying the SN model demonstrate that robustness can be increased and shortages can be decreased, but, as expected, at a higher SN cost. In the case of the high ratio of the unit purchase cost from the emergency supplier to the unit surplus cost, a considerable increase of robustness and a decrease of shortages can be achieved. Finally, it is shown that the model can be applied to large-scale SNs