Capacity choices under uncertainty for infrastructure sharing synergies: a robust optimization formulation

Industrial symbiosis (IS) implemented in eco-industrial parks (EIP) are based on resource substitution synergies (use of waste materials or fatal energy as inputs) and infrastructure sharing synergiesnotably local decentralized energy generators like combined heat and power (CHP) plants. Implementation of the former is enhanced by synergistic opportunities in the latter. The value of infrastructure sharing is brought by the intensification of use of an assetamong several partnersleveraging economies of scaleonthe cost of capacity. Initial investors must specify ex-ante arrangements (cost sharing and access price) to commit toward investments in infrastructure capacity. In this way we propose a model that investigates the decision of an actor (or a group of actors) choosing a level of infrastructure capacity so as to set a plug-and-play offer to 1 potential entrant. The latter has a capacity requirement which is uncertain beforehandso that min-max regret criterionis appropriate to model this decision problem. Capacity cost exhibits sub-additive property so that there is room for profitable overcapacity setting. The entrant's willingness-to-pay for the access to the infrastructure depends on its standalone cost and the capacity gap that must be completed in case the available capacity is insufficient ex-post (the back-up cost). Since initial capacity choices are driven by the foresights on future entrant's willingness-to-pay we derive the back-up cost function which helps us to define the investor's objective function. We first show that the regret function is decreasing and convex in the entrant's capacity needs for capacity above the entrant's requirements. This function is increasing and convex for values below. We then derive the general form of robust solutions. Dependingon the initial requirements volumes, economies of scales and back-up cost assumptions different capacity levels are set.