277776 An Integrated Production and Distribution Model for the Optimal Operation of Industrial Gas Supply-Chains
In this work, we address the problem of determining optimal operational level decisions for the coordinated production and distribution of industrial gas supply-chains. In this industry, cryogenic air separation processes are used to produce oxygen, nitrogen, and argon both as gaseous and liquid products. Air separation units consume large amounts of electricity, mainly due to the operation of the compressors used at different stages of the process. Depending on the equipment configuration used, alternative operation modes with different efficiencies and energy requirements are available at each plant. Thus, the main driver of the production cost is the cost of electricity, which prices fluctuate during the day either on an hourly or on a peak/off-peak basis, depending on the pricing scheme adopted. Gaseous and liquid customers of industrial gases are usually served by pipeline or truck delivery, respectively, and the transportation cost needed for truck deliveries is the main variable cost of the distribution side. Both the frequency of deliveries to a given customer and the selection of routes supplying product to multiple customers should be considered in order to reduce this cost. Besides, distribution capacity depends not only on the availability of trucks, trailers, and drivers but also on the inventory levels of liquid products at each plant. Thus, at any given time the connection between production and truck-distribution is given by the available amount of liquid products stored at the plants. The replenishment of storage tanks in customer locations must be secured by an appropriate distribution schedule.
On the production side, previous work addressing the minimization of production costs in air separation plants has been proposed by Ierapetritou et al.  and Karwan and Keblis . Ierapetritou et al.  developed a two-stage stochastic formulation where uncertainty in the power prices is considered within a given portion of the optimization horizon. Karwan and Keblis  developed a mixed integer mathematical formulation embedded in a rolling horizon procedure to minimize the cost of running an air separation unit under a real time pricing (RTP) scheme. They also conducted simulation studies to assess the robustness of the production plans obtained. On the distribution side, several publications tackle the estimation of the delivery scheduling costs for different purposes through the use of truck routing heuristics or continuous approximations. In one of the most recent papers, You et al.  developed a mixed-integer linear programming model to integrate long term planning decisions of sizing storage tanks at customer locations with the estimation of the delivery costs at the operational level. In order to solve large-scale instances, they develop a first approach based on a two-level decomposition strategy and the second one based on a continuous approximation method. In a recent effort to model both production and distribution within a holistic approach, Glankwamdee et al.  developed a simplified linear production and distribution planning model for industrial gas supply chains. In order to account for uncertainty, they extended this formulation both via a minmax model and a two-stage stochastic program, and tested the effectiveness of the proposed methods using simulation. However, only time-aggregated planning decisions were considered and neither plant mode selection nor vehicle routing details are included in the model.
The main goal of this contribution is to assess the benefits of optimal coordination for production-distribution in an industrial gases supply-chain, with the same level of accuracy on both sides. A mixed-integer linear programming (MILP) formulation minimizing the overall cost of production and distribution over a limited time horizon (7 to 14 days) is presented. The problem involves the production of gaseous and liquid products at multiple plants, and the distribution of liquid products to multiple customers through alternative routes using a limited number of trucks. On the distribution side, multiple depots are considered, and trucks at a given depot can deliver product from multiple sources. Besides, in order to ensure customer storage replenishments, product can be purchased from an alternative source. As the number of sources and customers increase, the selection of the alternative routes to be included in the formulation becomes a critical issue, and special methods to choose the routes are evaluated. The proposed methodology has been successfully tested on small and medium-size examples with a limited number of products, plants, customers, depots, trucks, and routes. Clusters of customers are considered for the larger problem instances. Comparison of different levels of coordination on the production-distribution supply-chain shows that significant benefits can be obtained with a higher coordination among all plants/depots in order to fulfill the shared customer demands.
 Ierapetritou M. G., Wu D., Vin J., Sweeney P., Chigirinskiy, M. Cost minimization in an energy-intensive plant using mathematical programming approaches. Industrial and Engineering Chemistry Research. 2002; 41:5262–5277.
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