Supply chain optimization of petroleum organization under uncertainty in market demands and prices

A multi-period stochastic planning model has been developed and implemented for a supply chain network of a petroleum organization operating in an oil producing country under uncertain market conditions. The proposed supply chain network consists of all activities related to crude oil production, processing and distribution. Uncertainties were introduced in market demands and prices. A deterministic optimization model was first developed and tested. The impact of uncertainty on the supply chain was studied by performing a sensitivity analysis in which ±20% deviations were introduced in market demands and prices of different commodities. A stochastic formulation was then proposed, which is based on the two-stage problem with finite number of realizations. The proposed stochastic programming approach proved to be quite effective in developing resilient production plans in light of high degree of uncertainty in market conditions. The anticipated production plans have a considerably lower expected value of perfect information (EVPI). The main conclusion of this study is that for an oil producing country with oil processing capabilities, the impact of economic uncertainties may be tolerated by an appropriate balance between crude exports and processing capacities.     

Selection of adequate optimization criteria in chromatographic separations

Computer-assisted optimization of chromatographic separations is still a fruitful activity. In fact, advances in computerized data handling should make the application of systematic optimization strategies much easier. However, in most contemporary applications, the optimization criterion is not considered to be a key issue (Vanbel, J Pharm Biomed, 21:603–610, 1999). In this paper, an update of the importance of selecting adequate criteria in chromatographic separation is presented.     

Optimizing the source distribution in fluid mixing

A passive scalar is advected by a velocity field, with a nonuniform spatial source that maintains concentration inhomogeneities. For example, the scalar could be temperature with a source consisting of hot and cold spots, such that the mean temperature is constant. Which source distributions are best mixed by this velocity field? This question has a straightforward yet rich answer that is relevant to real mixing problems. We use a multiscale measure of steady-state enhancement to mixing and optimize it by a variational approach. We then solve the resulting Euler-Lagrange equation for a perturbed uniform flow and for simple cellular flows. The optimal source distributions have many broad features that are as expected: they avoid stagnation points, favour regions of fast flow, and their contours are aligned such that the flow blows hot spots onto cold and vice versa. However, the detailed structure varies widely with diffusivity and other problem parameters. Though these are model problems, the optimization procedure is simple enough to be adapted to more complex situations.     

Pareto optimal solutions of a cost–time trade-off bulk transportation problem

A cost–time trade-off bulk transportation problem with the objectives to minimize the total cost and duration of bulk transportation without according priorities to them is considered. The entire requirement of each destination is to be met from one source only; however a source can supply to any number of destinations subject to the availability of the commodity at it. Two new algorithms are provided to obtain the set of Pareto optimal solutions of this problem. This work extends and generalizes the work related to single-objective and prioritized two-objective bulk transportation problems done in the past while providing flexibility in decision making.     

Evaluation of the potential of nonlinear gradients for separating a ternary mixture

The potential of applying nonlinear gradients in preparative chromatography is evaluated theoretically and experimentally. The second eluting component of a ternary model mixture is considered as the target component. Systematic gradient resolution experiments were conducted for this mixture using reversed phase chromatography. In preliminary experimental investigations the effect of the mobile phase composition on the specific distribution equilibria was quantified. Concave and convex solvent strength gradients were analysed and compared with conventional linear gradients. Main result of the study is the fact that significant improvement in productivity can be achieved if the gradient shapes are designed carefully.     

Fuzzy profit measures for a fuzzy economic order quantity model

Changing economic conditions make the selling price and demand quantity more and more uncertain in the market. The conventional inventory models determine the selling price and order quantity for a retailer’s maximal profit with exactly known parameters. This paper develops a solution method to derive the fuzzy profit of the inventory model when the demand quantity and unit cost are fuzzy numbers. Since the parameters contained in the inventory model are fuzzy, the profit value calculated from the model should be fuzzy as well. Based on the extension principle, the fuzzy inventory problem is transformed into a pair of two-level mathematical programs to derive the upper bound and lower bound of the fuzzy profit at possibility level α. According to the duality theorem of geometric programming, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs to solve. By enumerating different α values, the upper bound and lower bound of the fuzzy profit are collected to approximate the membership function. Since the profit of the inventory problem is expressed by the membership function rather than by a crisp value, more information is provided for making decisions.     

A proposal for a hybrid meta-strategy for combinatorial optimization problems

In this paper, we propose an algorithm named BDS (Bound-Driven Search) that combines features of exact and approximate methods. The proposed procedure may be seen as a local search algorithm that systematically explores (in a branch-and bound sense) the most promising nodes, thus preventing solutions from being reevaluated. Additionally, it can be regarded as an exact method as it may be able to guarantee that the solution found is optimal. We present the application of this new algorithm to a specific problem domain: the permutation flow shop scheduling problem with makespan objective. The subsequent computational experiments are encouraging, as the algorithm is able to yield exact or near exact solutions to most instances of the problem. Furthermore, the algorithm outperforms one of the best state-of-the-art algorithms for the problem.     

Optimization of supercritical fluid extraction of saikosaponins from Bupleurum falcatum with orthogonal array design

Supercritical fluid extraction (SFE) was used to extract saikosaponins a, c and d from the root of Bupleurum falcatum. An orthogonal array design L₉(3)⁴ was employed as a chemometric method for the optimization of the SFE conditions. The effects of four factors including pressure (30–40 MPa), temperature (40–50°C), ethanol concentration (60–100%) and time (2.5–3.5 h) on the yields of saikosaponins were investigated by a preparative SFE system in the SFE mode. Under the optimized conditions, namely 35 MPa of pressure, 45°C of temperature, 80% of ethanol concentration and 3.0 h of time, the yields of saikosaponin c, saikosaponin a, saikosaponin d, total saikosaponins and SFE extract were 0.16, 0.12, 0.96, 1.24 and 16.48 mg/g, respectively. Determinations of the saikosaponins were performed by HPLC.     

The optimization problem over a distributive lattice

In this paper we give a necessary and sufficient condition for existence of minimal solution(s) of the linear system A * X ≥ b where A, b are fixed matrices and X is an unknown matrix over a lattice. Next, an algorithm which finds these minimal solutions over a distributive lattice is given. Finally, we find an optimal solution for the optimization problem min {Z = C * X | A * X ≥ b} where C is the given matrix of coefficients of objective function Z. This research was completed while the author was a visitor of the Center for Informatics and Applied Optimization, University of Ballarat, Ballarat, Australia.