A cost‐effective model for the gasoline blend optimization problem

Abstract

Gasoline blending is a critical process with a significant impact on the total revenues of oil refineries. It consists of mixing several feedstocks coming from various upstream processes and small amounts of additives to make different blends with some specified quality properties. The major goal is to minimize operating costs by optimizing blend recipes, while meeting product demands on time and quality specifications. This work introduces a novel continuous-time mixed-integer linear programming (MILP) formulation based on floating time slots to simultaneously optimize blend recipes and the scheduling of blending and distribution operations. The model can handle non-identical blenders, multipurpose product tanks, sequence-dependent changeover costs, limited amounts of gasoline components, and multi-period scenarios. Because it features an integrality gap close to zero, the proposed MILP approach is able to find optimal solutions at much lower computational cost than previous contributions when applied to large gasoline blend problems.

Successive LP Approximation for Nonconvex Blending in MILP Scheduling Optimization Using Factors for Qualities in the Process Industry

“…The common linearization practice, shown in the inequality constraints and , considers the feed or component properties as fixed or constant ( v̅ i , p , t and w̅ i , p , t ) and the properties of the blended product are replaced by lower ( v̅ j , p , t L and w̅ j , p , t L ) and upper ( v̅ j , p , t U and w̅ j , p , t U ) bounds of property specifications. ,,, In these linear constraints and the property variables of the blend cannot be exactly calculated since they are approximate or surrogate quality balances modeled as inequalities. This means there are slacks and/or surpluses in the quality calculation modeled as factor flows (factor times flow), except when the constraint is binding or active; then the corresponding slack and/or surplus is zero.…”

“…Large-scale blend scheduling optimization problems found in the process industries are prohibitively expensive to solve in full-space mixed-integer nonlinear programming (MINLP) approaches since the initial steps of the binary variable relaxation in a nonlinear problem (NLP) are highly degenerate (i.e., many nondifferentiated solutions). To overcome this problem, the main strategy in the literature is to naturally decompose the quantity–logic–quality phenomena into a two-stage solution procedure. − In these algorithms, the scheduling assignments in quantity–logic relationships are solved first in a mixed-integer linear problem (MILP) by neglecting the nonconvex blending constraints commonly referred to as pooling . Then a quantity–quality NLP problem is solved for fixed discrete or binary logic decisions found previously.…”

“…Since planned recipes are known to be gross estimates, factors can play a vital role to better manage the blend recipe uncertainties using more timely process quantity and quality data, i.e., updated information within the planning time period. When applying or proxying LP factors for quality in MILP problems, this can drastically reduce the MILP-NLP gap in the two-stage or phenomenological decomposition 5 as more quality information is programmatically transferred to the logistics optimization. If this surrogate formulation of quality information (LP factors) is neglected in the MILP problem, many degenerate logistics solutions may occur with very close or similar MILP objective functions for different sets of quantity and logic decisions such as source to sink assignments and flow sizings.…”

Gasoline Blend Planning under Demand Uncertainty: Aggregate Supply–Demand Pinch Algorithm with Rolling Horizon

“…Their original large MINLP problem formulation, where nonlinearity comes from nonlinear blending properties, is replaced by a sequential MILP approximation. Cerdá et al presented a novel continuous-time MILP formulation based on floating time slots to simultaneously optimize both blend recipes and scheduling operations. Their proposed approach computes optimal solutions at much lower computational costs compared to other previous work.…”

Scheduling and Feed Quality Optimization of Concentrate Raw Materials in the Copper Refining Industry

“…However, in the literature, the main strategy of blending and scheduling optimization for considering the several stages of storage, mixing, and movement of raw materials involved in the logistics and feed quality operations is to decompose the MINLP model into the solutions of MILP and NLP programs. − In such an MILP–NLP decomposition approach, the quality information from the mixing of streams is neglected in the MILP step, which might produce infeasibilities in the NLP subproblems if the discrete assignments found in the MILP do not allow the matching of the quality constraints of the NLP. Alternatives in the literature for approximating the nonlinearities of blending in the MILP before solving the NLPs make use of (a) piecewise McCormick envelopes to linearly under- and overestimate the bilinear terms, − (b) multiparametric disaggregation, and (c) augmented equality balances as cuts of quality material flows .…”