Refinery Planning under Uncertainty

Abstract

This paper presents a novel approach to refinery planning under uncertainty. To calculate the expectation of plant revenues, which is the main difficulty of the problem, loss functions are derived and applied. Different standard loss function approximation methods are compared and integrated into the planning model. The results show that the piecewise-linear approximation of the loss function can obtain good accuracy with improved solution speed. A general formulation for revenue and cost calculations is proposed by considering uncertainty in both the raw material and the product demand. To handle possible unmet customer demands, the hard-to-specify penalty functions of the two-stage programming are avoided and replaced by two of the decision maker's service objectives, namely, confidence level and fill rate. Confidence level, which is the probability of satisfying customer demands, is commonly used in chance-constrained programming. However, fill rate, which is the proportion of demands that are met by a plant, is a greater concern of most managers. In this paper, fill rates are effectively calculated using the loss function. The maximum plant profit that satisfies certain fill rate objectives can then be obtained. Case studies show that a planning strategy that satisfies certain confidence level objectives might be overly lenient compared to a strategy that satisfies a fill rate objective. Because very few refinery planning models consider the influences of uncertainty, case studies including realworld large-scale refinery planning problems are used to illustrate the effectiveness of the proposed approach.

A multiperiod nonlinear programming approach for operation of air separation plants with variable power pricing

“…Furthermore, contractual obligations may place constraints on the amount of demand that must be met. As described by Li et al 8 and Nahmais et al, 9 we use the loss function to evaluate the expected revenue and, assuming a Type 2 service level, formulate probabilistic fill-rate constraints on customer demands. In this section, we describe the necessary changes to the multiperiod formulation and show how the solution is affected by increasing demand uncertainty.…”

“…The numerical integration of the standardized loss function can be expressed by piecewise polynomial functions. 8 Since we are now considering the expected value for product sales, the inventories are expected values as well, as defined by, I i;n ¼Ŝ i;n À h i;n À r i;n LŜ i;n À h i;n r i;n ! " # ; i 2 P; n 2 1; 2; 3; 4 ð Þ :…”

“…Two types of customer service levels have been described, 8,9 where customer satisfaction is measured by whether or not actual customer demands are met in a given interval. The Type 1 service levels (called confidence levels) have been adopted in the application of chance-constrained programming, 8,17 and can be written as…”

“…Furthermore, the problem size can grow prohibitively large as the number of scenarios is increased. As in our previous work, we have adopted the loss function developed in Li et al 8 and Nahmias 9 to quantify the expected profit in terms of production rates and uncertain customer demands. To model contractual obligations, a Type 2 service level, as described in Li et al 8 and Nahmias, 9 is assumed, and the fill-rate expression is used to constrain customer satisfaction levels.…”

“…As in our previous work, we have adopted the loss function developed in Li et al 8 and Nahmias 9 to quantify the expected profit in terms of production rates and uncertain customer demands. To model contractual obligations, a Type 2 service level, as described in Li et al 8 and Nahmias, 9 is assumed, and the fill-rate expression is used to constrain customer satisfaction levels. This treatment allows decision makers to quantify the interaction between demand uncertainty levels and fill-rate constraints.…”