An AHP-based decision-making tool for the solution of multiproduct batch plant design problem under imprecise demand

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Abstract

This paper addresses the problem of the optimal design of batch plants with imprecise demands in product amounts. The design of such plants necessarily involves the way that equipment may be utilized, which means that plant scheduling and production must form an integral part of the design problem. This work relies on a previous study, which proposed an alternative treatment of the imprecision (demands) by introducing fuzzy concepts, embedded in a multi-objective Genetic Algorithm (GA) that takes into account simultaneously maximization of the net present value (NPV) and two other performance criteria, i.e. the production delay/advance and a flexibility criterion. The results showed that an additional interpretation step might be necessary to help the managers choosing among the non-dominated solutions provided by the GA. The analytic hierarchy process (AHP) is a strategy commonly used in Operations Research for the solution of this kind of multicriteria decision problems, allowing the apprehension of manager subjective judgments. The major aim of this study is thus to propose a software integrating the AHP theory for the analysis of the GA Pareto-optimal solutions, as an alternative decision-support tool for the batch plant design problem solution.

Introduction

While quantitative consideration of uncertainty in the design of continuous processes has received increased attention in recent years [1], considerably less attention has been granted to this feature in the context of batch processing. Yet, this issue is of particular relevance for contemporary multiproduct batch operations due to the high degree of uncertainty arising from the complexity and typically incomplete information about the involved chemical/physical steps, the heavy reliance on timely and appropriate operator initiated actions, the need to process multiple products in the same facility as well as the relative volatility of the demands for the specialized products typically produced according to the batch mode [2].

The growth of specialty chemicals, food products and pharmaceutical industries aroused the current focus on the batch plant design problem. In the conventional optimal design of a multiproduct batch chemical plant, a designer specifies the production requirements for each product and total production time for all products. The number, required volume and size of parallel equipment units in each stage are to be determined in order to minimize the investment cost. Such an approach formulates the optimal design problem as a single-objective mixed-integer nonlinear programming (MINLP) problem [3], [4], [5], [6], [7], [8], [9], [10].

However, in real world applications, the chemical engineers often need to make decisions when faced with competing objectives [11]. For instance, the optimal design of a multiproduct batch chemical plant not only accounts for the investment cost minimization, but also for operation cost minimization, makespan minimization and/or revenue maximization. All those objectives might be considered simultaneously [10].

In this framework, this study introduces a new design approach to maximize the net present value (NPV) and two other performance criteria, i.e. the production delay/advance with respect to a fixed date and a flexibility criterion. This design problem becomes a multi-objective optimization problem (MOOP). Multi-objective optimization is a natural extension of the traditional optimization of a single-objective function. If the multi-objective functions are commensurate, combining all the objectives within a single-objective function enables the use traditional optimization techniques. However, if the objective functions are incommensurate, or competing, then an accurate weight factor tuning is necessary to get a good scaling of the criteria involved in the optimized single-objective function.

Besides, the competition between several objectives causes lack of complete order for MOOPs. For instance, in an optimal design problem, the simultaneously required minimization of the investment cost and maximization of the revenue, can lead to antagonist configurations. Pareto optimality or non-inferiority is therefore used to define an optimal solution to MOOPs [12].

On the other hand, the key point in the optimal design of batch plants under imprecision concerns the modeling of demand variations. The market demand for products resulting from the batch industry is usually changeable, and at the stage of conceptual design of a batch plant, it is almost impossible to obtain the precise information on the future product demand over the plant lifetime. Nevertheless, decisions must be taken on the plant capacity. This capacity should be able to balance the product demand satisfaction and extra-capacity in order to reduce the loss on the excessive investment cost or than on market share due to the varying product demands [13].

The most common approaches treated in the dedicated literature represent the demand uncertainty with a probabilistic frame by means of Gaussian distributions. Yet, this assumption does not seem to be always a reliable representation of the reality, since in practice the parameters are interdependent and do not follow symmetric distribution rules, which leads to very complex conditional probabilities computations.

An alternative treatment of the imprecision is constituted by using fuzzy concepts [14]. This approach, based on the arithmetic operations on fuzzy numbers, differs mainly from the probabilistic models insofar as distribution laws are not used. It considers the imprecise nature of the information, thus quantifying the imprecision by means of fuzzy sets that represent the “more or less possible values”. A previous work [15] proposed the integrated use of the above-mentioned fuzzy concepts into a Genetic Algorithm (GA) for the treatment of multi-objective batch plant design problems, since this stochastic optimization method is particularly well suited to tackle imprecise, multi-objective applications.

But the huge number of Pareto-optimal solutions emerging from the GA naturally leads to the question of choosing the best configuration, i.e. the most adapted to any manager's wishes. As a result, multicriteria decision-making techniques should be employed in solving this issue. A common approach is the analytic hierarchy process (AHP [16], [17], [18]). For this purpose, the results generated by the multi-objective, fuzzy GA are treated in this study by the conventional AHP, which shows the effectiveness and some unique advantages.

The use of AHP as an additional decision-support tool, for different kinds of problems, was highlighted in previous studies: for instance, its application to criteria evaluating postal service efficiency was carried out by Chan [19]. Furthermore, the combination of fuzzy logic and AHP concepts has already proved to be consistent for the treatment of multicriteria problems. The Fuzzy Extended Analytic Hierarchy Process (FEAHP) was proposed on problems of critical decision identification, including risk factors, for the development of an efficient system for global supplier selection [20] (the criteria being quality, service performance and supplier's profile).

The paper is organized as follows. Section 2 is devoted to a brief description of a study antecedent, the integration of fuzzy set theory within a multi-objective Genetic Algorithm (MOGA). Section 3 presents an overview of the AHP while Section 4 details its application to the treated batch plant design problem. This application is then illustrated by some typical results in Section 5. Finally, the conclusions on this work are drawn.

Section snippets

Fuzzy logics

The emergence of electronic commerce and business-to-business applications has, in a recent period, considerably changed the dynamics of the supplier–customer relationship. Indeed, customers can change more rapidly their orders to the suppliers and many enterprises have to organize their production even if the demand is not completely known at short term. On the other hand, the increasing need for integration and optimization in supply chains leads to a greater sensitivity to perturbations due

AHP method overview

The AHP is a systematic analysis technique developed for multicriteria decision [27]. Its operating mode lays on the decomposition and structuring of a complex issue into several levels, rigorous definition of manager priorities, and computation of weights associated to the alternatives. The output of AHP is a ranking indicating the overall preference for each decision alternative.

Preliminary design of the analysis

As mentioned in the AHP outline section, the steps of the method implementation are (i) the determination of the main and secondary objectives, in order to define the hierarchy; (ii) the incorporation of the decision-maker's preferences, in order to finally (iii) generate the priority tables that will support the computations finally providing a ranking of the alternatives.

Computational results

This section deals with the results obtained with the above-developed methodology. Let us recall that, apart from the decision matrices defined by the decision-maker, the basic information on which lies the study is constituted by the non-dominated solutions brought out by the GA.

However, the asymmetrical shape of the uncertain demand shape must be underlined, since these data will have implications on the final result. This choice is justified by the fact that, in real industrial cases, a

Conclusions

This study addresses the issue of multicriteria batch plant design under imprecise demands. The optimization carried out in previous studies with an adapted Genetic Algorithm (GA) provided a huge number of non-dominated solutions, which requires an additional treatment. This new step was implemented through the well-known analytic hierarchy process (AHP), in order to account for the subjective judgments of any manager. Besides, the resulting fuzzy results are decomposed into essential elements

References (32)

  • J. Balasubramanian et al.

    Scheduling optimization under uncertainty—an alternative approach

    Computers and Chemical Engineering

    (2003)
  • L. Wang et al.

    Selection of optimum maintenance strategies based on a fuzzy analytic hierarchy process

    International Journal of Production Economics

    (2007)
  • G. Zeng et al.

    Optimization of wastewater treatment alternative selection by hierarchy grey relational analysis

    Journal of Environmental Management

    (2007)
  • Grossmann IE. Optimal design of multiproduct batch plants. CACHE process design case studies, vol. 6,...
  • I.E. Grossmann et al.

    Optimum design of multipurpose chemical plants

    Industrial Engineering and Chemical Process Design and Development

    (1979)
  • F.C. Knopf et al.

    Optimal design of batch/semicontinuous processes

    Industrial Engineering and Chemical Process Design and Development

    (1982)
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