Multiple Optima in Gasoline Blend Planning Shefali Kulkarni-Thaker and Vladimir Mahalec* School of Computational Engineering and Science, McMaster University, Hamilton, Ontario, Canada L8S 4L7 ABSTRACT: Gasoline is produced by blending several diﬀerent components in ratios such that the blended mixture meets the required quality speciﬁcations. The blender produces diﬀerent batches of gasoline by switching operation from one grade of gasoline to another. Blend planning horizon usually spans 10 to 14 days. Blend plan optimization minimizes the total blend costs by solving a multiperiod problem, where demands need to be satisﬁed in each period and some inventory is carried into the future time periods to meet the demands. Since blend component production is determined by a longer range reﬁnery production plan, inventory carrying costs are not included in the objective function. It is shown that nonlinear programming (NLP) as well as mixed integer nonlinear programming (MINLP) solvers lead to diﬀerent blend recipes and diﬀerent blend volume patterns for the same total cost. The new algorithm described in this work systematically searches for multiple optimum solutions; this opens the way for blend planners to select from diﬀerent blend plans based on additional considerations (e.g., blend more of regular gasoline earlier in the planning horizon thereby creating an opportunity to meet more demand for it in early periods) instead of having to use only one solution that varies with the choice of the solver. Inherent structure of the proposed algorithm makes it well suited for implementation on parallel CPU machines. 1. INTRODUCTION Gasoline blending produces several diﬀerent grades of gasoline by blending various intermediate reﬁnery streams. Costs of intermediate streams (blend components) depend on the cost of operating the process units that produce them. Each grade of gasoline has diﬀerent speciﬁcations that vary with season and the geographical location of the target market. Gasoline quality speciﬁcations are inequalities, that is, a speciﬁc property either has to be greater than or equal to the speciﬁcation (e.g., octane number greater than or equal 91) or less than or equal to the speciﬁcation (e.g., Reid vapor pressure less than 11). Since components for blending gasoline are complex mixtures of many diﬀerent chemical compounds, it is possible to meet the same product speciﬁcations by using diﬀerent blend recipes while using the same components. These diﬀerent blend recipes will result in gasoline batches (mixtures of components) that are closer or further away from the constraints. An optimal percentage of components in a blend (optimal blend recipe) is computed in such a manner that the product quality speciﬁcations are satisﬁed, while minimizing the cost of the blend. Gasoline costs are largely driven by the cost of high octane components. Hence, if a batch of gasoline is blended even slightly above the minimum required octane, there is a signiﬁcant loss of proﬁt. An average reﬁnery can lose millions of dollars per year 1 if it blends consistently 0.1 octanes above the minimum required octane (e.g., 91.1 vs 91.0). Such economic importance of gasoline blending has made it a subject of research for the last several decades. Simpliﬁed gasoline blending system is shown in Figure 1. The components for gasoline blending are stored in separate storage tanks; that is, there is a separate tank for each component. Materials from the component tanks are blended in ratios that correspond to the speciﬁed blend recipe. Blending is carried out in a blend header, a device where gasoline components are mixed. In order to simplify the model, and without losing accuracy of the results, one can think of blending occurring in the tank that contains the respective grade of gasoline. The total amount of gasoline to be blended over the planning horizon is determined from the supply commitments to the customers. Since shipments of diﬀerent grades are uneven from day to day, the blender operates in multibatch mode: for example, produce a batch of midgrade gasoline, then a batch of premium gasoline, etc. Switching from one gasoline grade to another requires calibration of analytical instruments; that is, there is a setup time that reduces the total blend-capacity. From the blender, the produced gasoline is sent to the product storage tanks. Product shipments (in batches) are from the storage tanks to pipelines or trucks or ships. Simplistic approach to gasoline blending would be to add together all expected product shipments (for each grade separately) and compute how much additional gasoline needs to be produced for each grade and also compute the corresponding optimal blend recipes for each grade. However, such an approach most of the time does not produce feasible solutions, since product shipments vary over the planning horizon and there are limits on the storage of blend components and the storage of the gasoline products. Hence, gasoline blending must consider when speciﬁc products need to be delivered along the blending time horizon, production rates, and properties of blend components, as well as the blender capacity and the inventory constraints. Work process currently prevalent in the industry to optimize gasoline blending consists of the following: • Blend planningminimize total cost of all blends over a multiperiod horizon. ◦ Blend planning time horizon is divided into periods (discrete time representation). Received: August 29, 2012 Revised: June 20, 2013 Accepted: June 21, 2013 Published: June 21, 2013 Article pubs.acs.org/IECR © 2013 American Chemical Society 10707 dx.doi.org/10.1021/ie3011963 | Ind. Eng. Chem. Res. 2013, 52, 10707−10719