Management of Pricing Policies and Financial Risk as a Key Element for Short Term Scheduling Optimization Gonzalo Guille ´ n, † Miguel Bagajewicz, ‡ Sebastia ´ n Eloy Sequeira, † Antonio Espun ˜ a, † and Luis Puigjaner* ,† Department of Chemical Engineering - ETSEIB, Universitat Polite ` cnica de Catalunya, Avda. Diagonal, 647, G2, E-08028, Barcelona, Spain, and School of Chemical Engineering and Materials Science, University of Oklahoma, 100 East Boyd Street, T-335, Norman, Oklahoma 73019 In this article the scheduling of batch plants is integrated with pricing decisions. The proposed integrated model simultaneously provides the optimal prices and schedule as opposed to earlier models where prices are usually considered as input data. The main advantages of such formulation are highlighted through a case study where comparison with the traditional approach is carried out. A two-stage stochastic mathematical model is also developed in order to address the uncertainty associated to the demand curve. Finally, financial risk management is discussed. 1. Introduction With the recent trend of building small and flexible plants that follow the market dynamics closer, there has been renewed interest in batch processes. 1 Thus, a high effort to develop different strategies and tools for modeling, simulation, and optimization of these pro- cesses is underway. 2 Nevertheless, in all these develop- ments, significant aspects related to the influence of the currently dynamic environment into the batch plant activity have not been properly studied. One such aspect is related to the way pricing decisions are made in these batch-chemical companies. Industry managers and academia are realizing the strategic importance of the price variable. Pricing strategies consist of selecting the most appropriate price for a particular economic environment or market situation. Traditionally, pricing decisions were the responsibility of the marketing manager who sets a price within the context of his overall market strategy, 3-5 but an effort to integrate pricing strategies with different decision making process is now underway. For instance, Chen et al. 3 analyze a finite horizon, single product, periodic review model in which pricing and inventory decisions are made simultaneously. They also report some articles where price, inventory control, and quality of service (retail and service industries) are integrated. Moreover, issues so far related to the integration of decisions at different levels (scheduling, price determi- nation, etc.) and the associated uncertainty have not been considered. Therefore, while many models have been proposed for scheduling 2,6-8 few are devoted to include uncertainty. 9-14 Sources of uncertainty in sched- uling can be divided into short-term (processing time variations, equipment breakdowns, etc.) and long-term (market trends, technology changes, etc.). For the short- term, reactive scheduling has been used, while some form of stochastic programming has been considered for the long-term. 15 Furthermore, although stochastic models optimize the total expected performance measure, they usually do not provide any control on its variability over the different scenarios; i.e., they assume that the decision maker is risk neutral. However, different attitudes toward risk may be encountered. In general, most decision makers are risk averse implying a major preference for lower variability for a given level of return. In relation to this, Bonfill et al. 16 presented some techniques to manage financial risk in scheduling problems similarly to the way it was done by Barbaro et al. 17 for planning problems. Some of these techniques were also used by Guille ´n et al. 18 for manipulating the financial risk associated to a given supply chain configuration under demand uncertainty. In this work a new strategy for integrating pricing decisions with the scheduling of batch plants and managing the financial risk associated with the consid- eration of the uncertainty associated with the demand curve is introduced. The starting point is the modeling and forecasting of the relationship between product prices and demand aiming at the incorporation of pricing as a decision variable instead of treating it as input data. Once this relation is obtained, it is inte- grated into a scheduling mathematical model in order to simultaneously determine the prices and the associ- ated optimal schedule which maximizes the resulting profit. The capabilities of such model are highlighted through a case study where comparison with the traditional approach applied to fix prices is carried out. A two-stage stochastic formulation is then developed to deal with the uncertainty associated with the demand curve, and the main advantages of the proposed formu- lation are highlighted through comparison with the deterministic approach. A methodology to managing financial risk which relies on the sample average approximation (SAA) method as a way of generating solutions which perform in dissimilar ways under the uncertain environment is next described and applied to our problem. Some risk performance indicators are finally used for assessing the obtained solutions and guiding the decision maker’s choice. 2. Pricing Background Prices are marketing variables often characterized by quick market responses; that is, any decision on pricing * To whom correspondence should be addressed. Tel.: +34 934 016 678. Fax: +34 934 010 979. E-mail: luis.puigjaner@ upc.es. † Universitat Polite `cnica de Catalunya. ‡ University of Oklahoma. 557 Ind. Eng. Chem. Res. 2005, 44, 557-575 10.1021/ie049423q CCC: $30.25 © 2005 American Chemical Society Published on Web 01/08/2005