Mediation with near insolvent defaulting suppliers: a linear optimisation model to find an optimal outcome

This paper presents a model to describe contractual dispute resolution by mediation in situations where a defaulting supplier is near insolvent. While each party has internal constraints, and if alternate performances are available, such as more costly alternative goods, the proposed approach allows the mediator to find an optimal solution. The notion of optimality is presented as adherence to the initial contract, therefore optimising a value function for the non defaulting party. The proposed model includes describing the evolution over time of each party's perceived constraints using a phasor like approach with a modulation to the core constraints phasing out of the real part and phasing in the imaginary part of complex numbers. The offers related to alternative performances by the defaulting party are modelled by a Gompertz function, being an exponential learning curve of the supplier in regards to the reaction to its offers, limited by another exponential function when approaching its internal constraints. Furthermore, the model takes into account the discount associated to the delay in the delivery time of the alternative performances.