Decision support with ill-known criteria in the collaborative supply chain context

In the field of Supply Chain Risk Management, the attitude of managers toward risk affect the tactical decision-making process in collaborative supply chains under an uncertain environment, concerning especially capacity levels, lot-sizing rules, purchasing strategies, production scheduling,…, etc. The issue can be formulated as a sequential decision problem under uncertainty where the customer decisions affect the decisions made by the supplier. In this paper we deal with two kinds of uncertainties. The first one is the uncertainty on the indicators of performance (which are not comparable) used by the decision maker to choose a solution (for example: service quality or inventory cost). Hence, we propose an approach based on subjective probability to evaluate the probability that a decision is optimal for the first actor and the probability that it is optimal for both. From these two evaluations, we propose a ranking function to help the first actor to take into account the second one when selecting a decision. The second kind of uncertainty pertains to the demand. A classical criterion under total uncertainty is Hurwicz criterion where a weight expresses a degree of pessimism. Nevertheless, the degree of pessimism is itself ill-known. Thus, it becomes difficult to take into account the behavior of the actors. Hence, we propose an approach based on possibility theory and the so-called pignistic transform, which computes a subjective probability distribution over the criteria. Then, we apply the method used for uncertain criterion. This approach is illustrated through an example and an industrial case study.