Optimization model for long range planning in the chemical industry

This paper presents a multiperiod MILP model for the optimal selection and expansion of processes given time varying forecasts for the demands and prices of chemicals. To reduce the computational expense of solving these long range planning problems, several strategies are investigated which include the use of integer cuts, strong cutting planes, Benders decomposition and heuristics. These procedures, which have been implemented in the program MULPLAN, are illustrated with several example problems. As is shown, the proposed model is especially useful for the study of a variety of different scenarios. UNIVERSITY LIBRARIES CARNEGtE-MELLQN UNIVERSITY PITTSBURGH, PENNSYLVANIA 15213 Chemical companies are increasingly concerned with acquiring and managing more efficiently the resources that they will need to survive and prosper in a very competitive environment. Therefore, they must evaluate their options from two perspectives. First, they must assess the potential benefits of new resources when these are used in conjunction with existing processes, but accounting for their effect over the long term. Second, companies must identify and assess the potential impact on their business of important uncertainties in the external environment. Included are uncertainties regarding demand, prices, technology, capital, markets, and competition. In selecting new resources, companies should seek to develop long term strategies for hedging against these uncertainties, and to provide contingency plans to be put into effect as the uncertainties are revealed. Therefore, due to increasing competition, changing economic environment and fluctuating demands of chemicals, there is an increasing need of quantitative techniques for planning the selection of new processes, the expansion and shut-down of existing processes, and the production of chemicals (see Hirshfeld, 1987). Uncertainties in planning models â e, however, difficult to handle. Random coefficients are often replaced by their expected values in the planning models which might lead to misleading solutions (Kallberg et al> 1982). Using a single deterministic value other than the mean can also lead to large inaccuracies (Birge, 1982). In these cases, a stochastic optimization model for random coefficients should be ideally used for the planning model. However, since stochastic programs are in general very difficult and expensive to solve, an alternative approach is to use a deterministic multiperiod optimization model. This model can be used to account for predicted changes over a given time horizon and also to account for a finite number of different scenarios which can be associated with discrete probabilities. A rather large number of papers has been reported in the Operations Research literature on capacity expansion problems in several areas of application. A recent survey can be found in Luss (1982), In the chemical engineering literature dynamic programming has been applied to chemical plant expansions (Roberts, 1964), but this decomposition technique becomes quite ineffective for large scale problems. Alternative approaches include the NLP formulation by Himmelblau and Bickel (1980), the multiperiod MILP formulation by Grossmann and Santibanez (1980), the goal programming approach of Shimizu and Takamatsu (1985) and the recursive MILP technique by Jimenez and Rudd (1987). However, these approaches are often limited to the size of problems that they can handle. It is the purpose of this paper to present a multiperiod MILP model for long range planning that can be used either in a strictly deterministic fashion or as an approximation to the stochastic optimization problem. Several solution strategies which include the use of integer cuts, strong cutting planes and Benders decomposition, are presented for reducing the computational expense of solving the MILP problem. These strategies, which have been implemented in the computer program MULPLAN, will be illustrated with several example problems. Problem Statement The specific problem that is addressed in this paper assumes that a given network of processes and chemicals is given. This network includes an existing system as well as potential new processes and chemicals. Given are also forecasts for prices and demands of chemicals, as well as investment and operating costs over a finite number of time periods within a long range horizon. The problem then consists of determining the following items that will maximize the net present value over the given time horizon: a) Capacity expansion and shut-down policy for existing processes; b) Selection of new processes and their expansion capacity policy; c) Production profiles; d) Sales and purchases of chemicals at each time period. Linear models are assumed for the mass balances in the processes, while fixed-charge cost models are used for the investment cost. Also, limits on the investment cost at each time period can be specified, as well as constraints on the sales and purchases. As will be shown in the next section, the above problem can be formulated as a multiperiod MILP problem. Multiperiod MILP Model A network consisting of a set of NP chemical processes that can be interconnected in a finite number of ways is assumed to be given. The network also involves a set of NC chemicals which include raw materials, intermediates and products. This network can then be represented by two types of nodes: one for the processes and the other for the chemicals. These nodes will be interconnected by a total of n streams to represent the different alternatives that are possible for the processing, as well as the purchases and sales from different markets. Also, a finite number of NT time periods is considered where prices and demands of chemicals vary, as well as the investment and operating costs of the processes. The objective function to be maximized is the net present value of the project over the specified horizon consisting of NT time periods. It will be assumed for the modelling that the material balances in each process can be expressed linearly in terms of the production rate of the main product, which in turn defines the capacity of the plant. As for the investment costs of the processes and their expansions, it will be considered that they can be expressed linearly in terms of the capacities with a fixed charge cost to account for the economies of scale. In the formulation of this problem the variable Qit represents the total capacity of the plant of process i that is available in period t, t=l,NT. The parameter Qio represents the existing capacity of a process at time t=0. QEit represents the capacity expansion of the plant of process i which is installed for starting its operation in period t. If yit are the 0-1 binary variables which indicate the occurrence of the expansions at each time period and for each process, the constraints that apply are