Chair: Lazaros Papageorgiou, UCL (University College London), United Kingdom
Scheduling under Uncertainty: A multiparametric programming approach
Richard Oberdieck (firstname.lastname@example.org), Efstratios N. Pistikopoulos (email@example.com)
In this contribution, we highlight the connection between the areas of scheduling under uncertainty, model predictive control and multiparametric programming. In the classical approach a schedule for a given process is generated assuming nominal values for all states and parameters of the system. The resulting mixed-integer linear programming (MILP) problem is then solved for optimality offline. However, many process states and parameters such as demand or energy pricing vary with time, and might cause the generated schedule to be suboptimal or even infeasible. Therefore, a receding horizon framework similar to model-predictive control (MPC) has been proposed, where a state-space representation of the problem is solved at each time step for the current realization of the states of the system, and a new schedule is generated. This however requires the online solution of the MILP problem until the next time step, which even for medium sized problems becomes computationally infeasible. Here, we present a multiparametric programming approach to link scheduling under uncertainty with a receding horizon framework. The key features of such a formulation are (i) posing the scheduling problem under uncertainty and a receding horizon policy as a multiparametric MILP (mp-MILP) problem, and (ii) developing efficient solution strategies for general mp-MILP problems. Recently, we developed an efficient two-stage method which is able to solve general mp-MILP problems, including uncertainty present in the left-hand side of the constraint matrix, by decomposing the problem into a master Mixed-Integer Nonlinear Programming (MINLP) and a slave multiparametric linear programming (mp-LP) problem. The presence of non-convexities is dealt with using suitable relaxation techniques, and the problem is solved for ε-convergence by appropriate tightening of the relaxation. Additionally we devised a novel branch-and-bound approach which relies on branching the integer variables and suitable fathoming procedures. The non-convex terms are thereby kept, enabling us to retrieve the exact solution of general mp-MILP problems, however excluding left-hand side uncertainty. Several numerical examples are presented to highlight the potential of the new approach.
Keywords: Multiparametric Programming, Receding Horizon, Scheduling under Uncertainty
Multi-period stochastic optimization model for integrated CCS supply chain under carbon price uncertainties
Nasim Elahi (firstname.lastname@example.org), Nilay Shah (email@example.com)
The previous CCS supply chain models are steady-state or the very few multi-period models cannot make simultaneous decisions for all parts of an overall optimal CCS chain. We have developed a multi-period spatially explicit least cost optimization model of an integrated CO2 capture, transportation and storage infrastructure. The investment and operational decisions made at each phase result in an overall minimum cost solution subject to design and operational constraints. The model is formulated as a mixed integer linear programming (MILP) problem within GAMS. The coding flexibility allows for exploring the effects of the anticipated changes in any of the economic or operational parameters, future energy system changes or storage sites’ leasing conditions on the network performance. A case study is devised with reference to 18 biggest sources in the UK and 10 sinks in the surrounding seas up to year 2050. The results indicate the Humber emitters are connected to the Southern North Sea sinks via a shared network of pipelines. Another network connects several emitters across the UK to the East Irish Sea. To consider the future uncertainties, the deterministic model is modified to become a non-flexible probabilistic CCS network optimization tool where the solution is on average an optimal strategy. A scenario was devised to investigate the future UK CCS network layout under carbon price uncertainties. It was found for a 2-phase horizon, CCS first enters the portfolio at carbon prices $72 in 2015 and $87 in 2025. For carbon prices $152 and $184, CCS becomes the only mitigation option.
Keywords: Multi-period supply chain optimisation, carbon dioxide capture and storage, de-carbonisation
Sustainable Supply Chain Planning under a Colaborative Perspective
Ana Amaro (firstname.lastname@example.org), Ana Barbosa-Póvoa (email@example.com)
Current requirements on sustainable development have been introducing important SC operability requirements and companies begin to realise the need to embed sustainability into SC operations namely through the implementation of green practices as well as by the improvement of recovery, recycling, remanufacturing and other closed loop processes and products. A major challenge is then placed on the supply chain network configuration and on its operability. Following these motivations, a new model formulation is proposed to help the decision making process at the planning level of industrial supply chains. The proposed approach accounts for the trade between sustainability and economical decision criteria and focus on the optimization of the collaborative forward flows of products in order to enhance sustainability conditions with a profitable SC planning strategy. A single level formulation that relies on a discrete time approach is proposed where different topological, operational and processing constraints are integrated while accounting for both the sustainability indicators and the economic performance criteria. A Mixed Integer Linear Model (MILP) formulation is obtained which is implemented in the GAMS language and solved using the CPLEX solver. Different networks and operational characteristics are studied. A set of planning scenarios is used to study the impact of different assignment strategies for the material flows’. These account for the trade-off between sustainability indicators such as energy savings and economic indicators such as costs. The model applicability is shown through the solution of an industrial case-study.
Keywords: Supply chain, optimal planning, sustainability