Towards an integrated framework for supply chain management in the batch chemical process industry

Available online at www.sciencedirect.com

Computers and Chemical Engineering 32 (2008) 650–670

Towards an integrated framework for supply chain management in the batch chemical process industry Luis Puigjaner ∗ , Gonzalo Guill´en-Gos´albez Department of Chemical Engineering, Universitat Polit`ecnica de Catalunya, ETSEIB, Avda. Diagonal 647, G2, E-08028 Barcelona, Spain Received 16 June 2006; received in revised form 26 January 2007; accepted 5 February 2007 Available online 15 February 2007

Abstract There is a large body of work on supply chain (SC) optimization in the chemical process industry (CPI). However, some of the basic aspects of the optimization problem are not adequately handled by the models and solution strategies developed so far in the literature. This paper focuses on the underlying philosophy of our approach to supply chain management (SCM) in the CPI, which aims to overcome the challenges posed by this problem. Two main topics that offer great opportunities for improvement in SCM are discussed. These are the development of modeling approaches and solution strategies that reflect SC dynamics, the inclusion of environmental considerations, and the incorporation of novel business aspects and key performance indicators (KPI) into the existing formulations to enlarge the scope of SC analysis, which is currently rather limited. Our integrated solution strategy for SCM, which covers the aforementioned aspects and implements the ideas and concepts developed in our research, is also presented and its advantages are highlighted in a case study. © 2007 Elsevier Ltd. All rights reserved. Keywords: Optimisation; Supply chain management; Financial management

1. Introduction In recent years, companies have been working to increase their capabilities in a highly competitive market, and this has been greatly helped by advances in information technology. Business management strategies such as enterprise resource planning (ERP), supply chain management (SCM), customer relationship management (CRM) and others are seen as promising solutions by the business management community. The chemical process industry (CPI) is not an exception to this business trend. In fact, the process system engineering (PSE) community is performing a key role in extending system boundaries from chemical process systems to business process systems. Specifically, developing novel modeling approaches and solution strategies for SCM has recently become a major research area in PSE. Interest in this field has been motivated by the idea that the propagation of unexpected and/or undesirable events across the network may be reduced, which would

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Corresponding author. E-mail address: [email protected] (L. Puigjaner).

0098-1354/$ – see front matter © 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2007.02.004

markedly improve the profitability of all the parties involved. Unfortunately, despite the effort made by the PSE community to address the SCM problem, there are still several important aspects that merit further attention. This paper describes the research carried out at our center in recent years in the area of SCM. New areas of research and guidelines for future work are also suggested. Our discussion is divided into three overlapping topics. The first concerns the development of a novel modeling approach to SCM that is able to capture the SC dynamics. This strategy is based on software agents that map the various entities in the SC on a one-toone basis, which allows the manufacturing practices commonly found in industrial scenarios to be easily reproduced. The second is related to extending the scope of SC analysis in pursuit of a holistic approach that enables the combined effects of different decisions taken by the firm to be optimized. Specifically, this paper focuses on the inclusion of environmental and financial considerations at the modeling stage in the SC analysis. Finally, an integrated solution for SCM is offered. This solution merges and implements the aforementioned concepts and ideas and its main advantages and capabilities are highlighted in our discussion of a case study.

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Nomenclature Indices e external suppliers t planning periods Sets FP IP RM

set of states corresponding to final products set of states corresponding to intermediate products set of states corresponding to raw materials

Parameters Coefett technical discount coefficient for payments to external supplier e executed in period t on accounts incurred in period t DttMS technical coefficient for investments in  marketable securities Demst demand of material in state s in time interval t Dempst demand of material in state s in period t dep amount depreciated Divt dividends in period t EttMS technical coefficient for sales of marketable secu rities FCost fixed cost H time horizon ir interest rate MaxCLine upper bound of the credit line MinCash minimum cash Otherst other expected outflows or inflows of cash in period t Pricest price of material in state s in period t StMS marketable securities of the initial portfolio maturing in period t SPricest stock price of material in state s in period t trate tax rate Variables ARect accounts receivable in period t Borrowt total amount borrowed to the credit line in period t Casht cash in period t CLinet debt in period t EPurchet purchases to external supplier e in period t ECasht exogenous cash in period t total amount of money borrowed or repaid to the NetCLine t credit line in period t NetMS total amount received or paid in securities t transactions in period t Payett payments to external supplier e executed in period t on accounts payable incurred in period t  Pledtt amount pledged within period t on accounts receivable incurred in period t Profit profit Purchst amount of material in state s purchased in time interval t

Repayt Salesst Sst Taxes YtMS t ZtMS t

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total amount repaid to the credit line in period t amount of material in state s sold in period t amount of material in state s at the end of period t taxes cash invested in period t in marketable securities maturing in period t security sold in period t maturing in period t

Greek symbols φ face value of accounts pledged

2. A multi-agent system for SCM Many of the approaches developed in the past in the area of SCM are not able to consider the delays associated with the information that flows through a real SC. These approaches, which usually involve using mixed integer modeling techniques to address SC planning decisions, assume that the orders placed by customers are immediately known by the entire SC and that the demand is satisfied as it arrives to the system. We believe that these kinds of models are not as insightful as those in which the dynamic features of the SCs are explicitly taken into account. Specifically, at the operational level, models that capture the SC dynamics are particularly appealing because they assist managers in understanding complex interactions between system states, data, and decision variables. Another limitation of the tools that are available for SCM is that they have traditionally focused on myopic methods for manufacturing sites, logistics and distribution tasks rather than on approaches that consider all of these methods simultaneously. Specifically, a large body of literature in PSE is concerned with the analysis of manufacturing plants and the computation of optimal scheduling plans in terms of predefined criteria (usually makespan, cost or profit) that satisfy a demand that comes directly from a customer. M´endez, Cerd´a, Grossmann, Harjunkoski, and Fahl (2006) offer a detailed review of these types of models. However, the approaches devised to date neglect important aspects of the problem, such as the buffering effect, demand distortion and storage costs, which are all due to the distribution channels through which the materials flow. Neglecting these aspects may result in either infeasible or suboptimal solutions for the entire SC. The first task undertaken by our group to bridge this gap was the design and construction of a dynamic simulation model of a generic SC. The aim was to represent and model interactions between the components of a generic SC network in a functional way, with the aim of further obtaining a decisionmaking tool for SCM. With this goal in mind, Mele, Espu˜na, and Puigjaner (2002) proposed a dynamic approach to SCM based on the development of a stochastic discrete event-driven system model of an SC that contemplated several network nodes. This model included all the entities belonging to the SC as independent and well-defined objects that were represented by a collection of states and transitions. In the system envisaged, the

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Fig. 1. Framework for stochastic simulation.

SC is considered to be a decentralized system in which there is no global coordinator and every one of its entities makes decisions locally. The framework for the stochastic discrete event simulator is shown in Fig. 1. It includes the following elements: • State variables that describe a system at given points in time, that is, the simulation outputs. • The simulation model, which includes the equations or other relationships describing how the state variables change over time as a function of decisions or external events. • The sampling tool, which provides a representative sample from the multi-variate probabilistic distribution that characterizes the uncertain parameters. The stochastic discrete event model was implemented in MATLAB® (Works, 2004). A variety of case studies that contemplated several aspects and operation modes (inventory control policies, selection of suppliers, demand uncertainty, etc.) were solved with the aim of analyzing the impact of different manufacturing policies on the behavior of the chain and also to demonstrate the validity of this kind of representation. The initial discrete event simulation model later evolved into an SC simulator that used software agents as the building paradigm. The effectiveness of these kinds of tools for solving complex problems led to software agents being used to model and optimize the SC operation. SC networks are truly complex systems whose good performance relies on coordinating a number of entities. For this reason, approaches that consider the SC in terms of agents and discrete event-based simulation may be better suited to this kind of problem (Banks, 1998; Julka, Karimi, & Srinivasan, 2002a). These approaches model not only the dynamics of the individual components but also the interactions between them and, since they mimic the natural structure of an SC and the interacting mechanism of its entities, they have the additional advantage of being easily reconfigurable when the chain structure changes. Furthermore, agents are a very effective technique for designing distributed SC systems over the Internet, which is a very important channel for doing business and sharing business-related information in a seamless manner.

Given these advantages, multi-agent systems have in the last few years become a promising tool for solving SC problems (Chen et al., 1999; Goodwin, Keskinocak, Murthy, Wu, & Akkiraju, 1999; Julka, Karimi, & Srinivasan, 2002a, 2002b; Sauter, Parunak, & Goic, 1999). Moreover, they are a natural result of advances in the field of dynamic simulation. Compared with the many efforts to design other kinds of approaches to SCM, research on agent-based systems is still very limited, especially in the CPI sector, and usually focuses on partial problems, such as cooperative decision support or distributed simulation. Very few studies have addressed both these problems simultaneously. Furthermore, many agent-based systems suffer from a lack of optimization skills. To avoid this, external optimization tools must be used to eliminate the need for a random trialand-error search and to allow the optimization procedure to be automated. During these last years, part of our research effort has been devoted to developing our own multi-agent framework for SCM. The structure of the proposed system is shown in Fig. 2. It consists of a system of real agents, a central agent, a simulator and a set of modules. This is an ambitious framework that aims to cover the entire range of management tasks that must be accomplished by an SC network. A brief overview of the multi-agent system is provided next. Its main parts are the following: • Real agents. They are software agents that work in a computer network. Each one maps one real-world entity or node in the SC network, communicates with it, and stores all the data concerning this entity. Depending on the SC manager or decision-maker, the real agent system can solve particular problems, update its database, suggest improvements, and so forth. • Real central agent. It can make decisions based on certain SC models and built-in procedures, and then test the conclusions over the simulation model. One of the procedures for the central agent to make decisions is to run experiments using the simulation model. The central agent manages the information stored in the network and makes decisions over the real SC network. It is also through the central agent that the external customers and suppliers communicate with the system and negotiation processes are carried out. This exchange of information may be done on the Internet. • Simulated agents. They make up an SC simulator that emulates the behavior of the real-world SC and therefore the real agent system. The central agent can use the simulator to test the effects of the decisions over the entire SC before the latter is implemented in the real environment. The simulator can be used by the central agent or by managers, who can use the simulator as a stand-alone application. The simulated agents have an operational model that emulates the behavior of the entities in a real-world SC. • Modules. Both the simulator and the real agents may use some of the modular tools that the framework provides to perform specific tasks. The modules may be demand forecasters, negotiation algorithms, optimization packages, scheduling software, performance index evaluators, and so on.

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Fig. 2. Multi-agent framework.

Both the system of real agents and the system of simulated agents comprise two categories of objects: software agents and messages. Of the agents that take part in this system (see Fig. 3), the emulation agents represent the physical entities, facilities or nodes in the real-world SC, such as suppliers, customers, manufacturing plants, distribution centers, etc. Each of these agents includes a number of subagents, namely inventory, sales, production, purchasing and transportation. Moreover,

the system has agents other than emulation agents, such as the central agent, which does not have any correspondence with a real entity in the chain. The messages are objects that are exchanged between the agents (internal messages) and also with other entities, such as the real entities of the chain, the user and/or the external customers (external messages). All of these messages represent material, information or cash flows.

Fig. 3. The multi-agent system.

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The agent-based simulator provides an environment in which all business processes can be emulated, such as sales, purchases, negotiation with customers and suppliers, production and logistics planning at different levels, investment analysis, transportation and production scheduling, inventory management, demand forecasting, etc. Agents model all the SC entities, which include manufacturers, third-party logistics, the internal departments of a company, etc. Each agent may have one or more subagents. These internal departments have generic functions in all companies, which can be customized according to the practices of a company. One of the main shortcomings of this initial version of the multi-agent system was the lack of optimization skills, that is, although system managers could play what-if scenarios with input data and simulation models to evaluate alternative solutions, there was still a need to systematize the optimization procedure and avoid a random trial-and-error search. Moreover, the scope of the original multi-agent system was limited, as it focused on process operations and neglected other important business aspects. In the sections that follow, we describe the research carried out to overcome these initial drawbacks. 3. Novels business aspects in SCM This section deals with efforts to extend the scope of the SC analysis with the aim of obtaining a holistic representation of the system. Specifically, it focuses on two major areas: environmental impact and finances. To achieve integration between diverse areas of a company, a set of software modules was developed and incorporated into the overall multi-agent system. Our reasons for including these business aspects in our SC analysis and a detailed explanation of the associated software modules are given below. 3.1. Environmental impact Traditionally, the optimization models devised by the PSE community to assist operation and design in the CPI industry have concentrated on finding the solution that maximizes a given economic performance indicator while satisfying a set of mass balances, assignment and capacity constraints imposed by the topology of the plant. In recent years, however, there has been a growing awareness of the importance of including environmental aspects, as well as traditional economic criteria, in the optimization procedure. The first attempts to incorporate environmental aspects applied fairly myopic strategies that focused on minimizing the emissions from a plant (Ciric & Jia, 1994; El-Halwagi & Manousiouthakis, 1990; Linninger, Stephanopoulos, Ali, Han, & Stephanopoulos, 1995; Wang & Smith, 1994). Due to their limited scope, they sometimes led to solutions that reduced these emissions at the expense of increasing burdens elsewhere in the life cycle, in such a manner that overall environmental impacts increased (Azapagic & Clift, 1999). Life-cycle assessment (LCA) arose in response to this situation. LCA is an objective process for evaluating the environmental loads associated with a product, process or activity.

It identifies and quantifies the energy and materials used and the waste released to the environment, and evaluates and implements opportunities for effecting environmental improvements. The assessment covers the entire life cycle of the product, process or activity, including extracting and processing raw materials; manufacturing, transportation and distribution; reuse and maintenance; recycling and final disposal (Guin´ee et al., 2002). The essence of LCA is that it considers all material and energy flows from the “cradle” of primary resources (such as oil or ore deposits) to the “grave” of final disposal (such as stable inert material in a landfill). Today, LCA can be said to be the main instrument in environmental supply chain management (ESCM) as it can be effectively used to restructure SCs in order to improve their environmental performance (Azapagic & Clift, 1999; Chen & Shonnard, 2004; Hoffmann, Hungerbuhler, & McRae, 2001; Hugo & Pistikopoulos, 2004; Petrie & Romagnoli, 2000; Puigjaner & Espu˜na, 2006). 3.1.1. Implementation of the environmental module An environmental module was developed to include environmental considerations into the multi-agent system. This module was constructed for computing several environmental impact indexes according to the principles of the LCA. These environmental impact indexes were based on the second and third phase of the LCA methodology, as defined in the ISO 14041 (1998) and ISO 14042 (2000) standards. The module uses the information associated with the SC simulation, that is, raw material selection and resources consumed by the labor tasks, to perform the inventory analysis phase and then to evaluate a global environmental impact index according to the life-cycle inventory assessment phase. Thus, the LCA-based module constitutes a novel approach to considering environmental aspects in the SCM field. It is able to perform a study that is fully adapted to the SC network, taking into account features that include the material and energy links between facilities and the processes the product undergoes once it leaves the company. Let us note that there are several software programs, apart from the environmental module of the multi-agent system itself, that implement the LCA methodology following the ISO 14040. Some of them are: PEMS 4 Database (1998),1 TEAM and DEAM (1998)2 and SimaPro 6 LCA software (2004).3 All of these programs are able to compute material and energy balances and quantify the burdens and impacts along the life cycle. The material and energy balances for the process itself can also be performed by means of specific software programs originally devised to assist in the design and operation of chemical processes. Nevertheless, these general-purpose software programs are not capable of properly assessing the environmental impact of a SC. This has motivated the development of a specific environmental module for the multi-agent system. 1 PIRA International PIRA, Leatherhead, UK, October 31, 2005 (www.pira. co.uk/pack/lcasoftware.htm). 2 Ecobalance UK, The Ecobilan Group, Arundel, UK, October 31, 2005 (www.ecobalance.com/uk team.php). 3 PR´ e Consultants bv., The Netherlands, October 31, 2005 (www.pre.nl/simapro/default.htm).

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•

• •

•

Fig. 4. Framework for the Life-Cycle Assessment.

The application of LCA in the multi-agent system only considers the first three phases of the LCA methodological framework (ISO 14040 series). Fig. 4 shows these phases schematically, as well as the inputs and outputs required by each phase and the relationships between them. • Goal and scope definition. In this phase, the system boundaries and the object of study are set to ensure that the relevant parts of the system are included. • Inventory analysis, in which mass and energy balances are performed to quantify all the material and energy inputs, waste and emissions from the system, that is, the environmental burdens. • Impact assessment. Here, the environmental burdens quantified in the inventory analysis are added to a limited set of recognized environmental impact categories. • Interpretation. This is the final step, in which the results suggest policies aiming to reduce the environmental impacts associated with the product or process. Selecting the environmental categories that are to be considered in the impact assessment phase is a particularly important point. The following list gives the definitions of the environmental impacts that are applied in the multi-agent framework. • The resource depletion potential (RDP) describes the depletion of nonrenewable resources, for example, fossil fuels, metals and minerals, in relation to the world’s estimated reserves. • The global warming potential (GWP) is attributed to the emissions of greenhouse gases, for example, CO2 , N2 O, CH4 and

•

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other volatile organic compounds (VOC). GWP factors for different greenhouse gases are expressed relative to the GWP factor of CO2 , which is therefore defined to be unity. The ozone depletion potential (ODP) indicates the potential of chlorofluorocarbons and chlorinated hydrocarbons for depleting the ozone layer. The ODP factors of each of the ozone-depleting substance are expressed relative to the ozone depletion potential of CFC-11. The acidification potential (AP) is based on the contributions of SO2 , NOx , HCl, NH3 , and HF to potential acid deposition, that is, on their potential to form H+ ions. The eutrophication (or nutrification) potential (EP) is defined as the potential to cause over-fertilization of water and soil, which can result in increased growth of biomass. Emissions of species such as NOx , NH4 + , PO4 3− , P4 , together with the chemical oxygen demand (COD), are considered to be responsible for eutrophication. EP is expressed relative to PO4 3− . The photochemical oxidants creation potential (POCP) is also known as photochemical smog. It is thought to be caused primarily by VOCs, including alkanes, halogenated hydrocarbons, alcohols, ketones, esters, ethers, olefins, alkynes, aromatics and aldehydes. POCPs of these species are expressed relative to the POCP of ethylene. The human toxicity potential (HTP) is related to releases to air, water and soil that are toxic to humans. The toxicological factors are calculated using the acceptable daily intake or the tolerable daily intake of toxic substances. Human toxicological factors are still at an early stage of development, so the HTP can only be taken as an indication and not as an absolute measure of the toxicity potential.

The main features and advantages of the environmental module are next highlighted through a small case study, the structure of which is given in Fig. 5. This simple network, which contains all the basic elements of a generic SC, will be used to provide insights into the model contained in the environmental module. For the sake of simplicity, a high degree of aggregation has been assumed in this example. Thus, our case study only considers a reduced number of energy and material streams. In fact, this SC representation can be considered to be the result of a detailed modeling of a manufacturer agent representing a physical plant embedded in the SC. Our study aims to obtain an ecolabel for product Pm1 . This can be done by applying the LCA methodology guidelines to the SC system under study. This procedure provides the environmental burden emissions associated with the manufacturing process of the product. We next describe in detail the way in which the LCA framework can be applied to this specific example. In the first phase of the LCA, the functional unit (product or process) must be identified. This “functionality” can always be expressed as an equivalent product amount (in kg or MJ, according to the nature of the product), which aims to facilitate later calculations. The system boundaries for this example are depicted in Fig. 5. In some cases it will be necessary to go deeper inside these boundaries to find environmental values for the global streams across the boundaries.

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Fig. 5. Elementary supply chain representation utilized in the environmental module base case study.

The second phase of the LCA, the inventory analysis phase, is next applied to the manufacturing process, which is represented by the source block of product Pm1 . This stage requires input data concerning the input streams Ps12 and Ps2 , the emissions of the process (Wm ), and the products Pm1 and Pm2 . The downstream inputs and emissions of the manufacturing process (Wo , Wu and Ww ) are also required in this second stage. A key issue in the inventory calculation is that of determining the proper allocation policy to be applied for allocating the environmental loads associated with each product. An allocation procedure is required only if the causal relationship between inputs, outputs and emissions is not known with certainty. If this is not the case, the following general expression can be applied to allocate the environmental loads:   Pk · vk = fk · (−W · vw + Fs · v s ) − Fop · Pp · vp (1) s

p=k

In this expression, Pk represents the stream of product k and vk is the corresponding eco-vector associated with product k. W · vw is the waste stream weighted by its eco-vector, Fs · vs is an input stream multiplied by its eco-vector and Pp · vp is the corresponding output stream weighted by its eco-vector p. Finally, fk and fop are allocation factors that depend on the allocation policy selected in each case (e.g., mass allocation, energy allocation).

The allocation to the chain placed on the left side of the Manufacturer, which comprises the nodes labeled as Super Supplier, Supplier 1 and Supplier 2, is next analyzed in the same manner done in the Manufacturing case. This procedure is called forward allocation (Fig. 6) because the environmental load is carried from the left to the right, that is to say, in the same direction as the material flow in the SC. Following the LCA philosophy, the environmental module also considers a backward allocation (see Fig. 7), which is carried out in the direction opposite to the SC material flow. Thus, this procedure reflects the fact that the manufacturer is also responsible for the environmental impact generated by their products after leaving the manufacturing stage. That is to say, the analysis must include the environmental impact associated with all the processes in which the products are involved, including their use, and finally, during the waste management and treatment of the generated residues. Finally, the environmental load associated with the recycle processes and streams is assumed to be included in the LCA assessment carried out by the supplier. Thus, our model (Fig. 5) cuts stream Pw to generate streams wr and Pr . These new streams include the inputs and the emissions for the recycling process and the inputs and emissions for the Supplier 1, respectively. In this case, the environmental load associated with stream Pw is considered to be zero.

Fig. 6. Forward allocation.

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Fig. 7. Backward allocation.

In the third phase of the analysis, the environmental loads are translated into environmental impact indexes. This part of the analysis will be further discussed in the case study section. 3.2. Financial considerations in SCM This section of the paper will deal with the incorporation of financial aspects in the SC analysis. As stated in the previous section, the strategies devised to date to assist in the operation and design of chemical SCs usually focus on optimizing myopic key performance indicators (KPIs) such as cost or profit and neglect the financial variables and constraints associated with cash flows. The effective control of cash is, however, one of the most important requirements of financial management and its steady and healthy circulation throughout the entire business operation has repeatedly been shown to be the basis of business solvency (Howard & Upton, 1953). In fact, the availability of cash governs the production decisions taken in a company. A production plan cannot be implemented if it violates the minimum cash flow imposed by the firm (i.e., if the amount of raw materials and/or utilities required cannot be purchased due to a temporary lack of cash). Moreover, assessing the feasibility of the scheduling/ planning decisions from a financial viewpoint may not be enough for companies that want to achieve a competitive advantage in the marketplace. Fierce competition in today’s global markets is forcing companies to perform further analyses in order to find the best production–distribution decisions to be carried out in their SCs. If they wish to remain competitive, it is essential that they properly assess the different process operations alternatives in terms of their ability to markedly improve the value of the company. In fact, maximum-profit or minimum-cost decisions may lead to poor financial results if their financial impact is not properly assessed prior to their being implemented. Thus, managers should extend their analysis to include the more general objective of maximizing the shareholder value (SHV) of the firm as opposed to the common optimization of traditional myopic KPIs such as cost or profit. We believe that companies can create more value and achieve better performance by devising integrated approaches to SCM.

Such strategies should be capable of holistically optimizing the combined effects of process operations and finances, thus exploiting the synergy between different management disciplines. The approaches that currently exist, however, still address the overall problem in a sequential fashion through the optimization of partial KPIs. The use of these traditional sequential procedures applied in the operation and design of chemical processes is mainly motivated by the functional organizational structures of the firms. Today, most companies have separate departments for production, supply, logistics, service to customers, etc. In an environment of this type, each functional area’s plan is sequentially considered as input to the others according to a hierarchy. Thus, the models supporting the decision-making in batch chemical processes operate in an isolated way. They optimize partial sets of decision variables but they do not lead to real integration relationships despite promoting the sharing of information between different business entities (Romero, Badell, Bagajewicz, & Puigjaner, 2003). This partitioning of decision-making in companies has been reflected in the goals of the studies and the optimization models developed to support them. Nevertheless, there is an increasing awareness of the impact that chemical process production systems have on firms’ finances, which has led to enterprise-wide management strategies that aim to provide a holistic view of the system. In fact, the need to extend the studies and analysis of process operations to incorporate financial considerations has been widely recognized in the literature (Applequist, Pekny, & Reklaitis, 2000; Shah, 2005; Shapiro, 2001, 2004). Specifically, Grossmann (2004) highlights that major challenges in enterprise and SC optimization include the development of models for strategic and tactical planning for process networks that must be eventually integrated with scheduling models. Thus, with the recent advances in optimization theory and software applications there is no apparent reason why we cannot construct models for SCM that merge concepts from diverse areas. Unfortunately, although optimization models seem to offer an appealing framework for analyzing corporate financial decisions and constraints, as well as for integrating them with process operation decisions and constraints (Shapiro, 2001), relatively few integrated corporate financial models have been implemented so

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far. However, in the PSE literature, the works of Yi and Reklaitis (2003, 2004) are highly regarded contributions to the field. One of our main research concerns over the last decade has been to develop these kinds of integrated models in order to holistically optimize the combined effects of different decision variables. Specifically, given their high potential for improvement and the fact that there are few contributions to the field, we have focused on devising holistic modeling approaches for SCM that incorporate concepts from process operations and finances. Until today, process operations and finances have been treated as separate problems and the modeling approaches supporting them have been traditionally implemented in independent environments. On the process operations side, a high number of models, especially in the last 25 years, have been developed to perform short-term scheduling and longer-term planning of single batch chemical plants (for a short review see M´endez et al., 2006). The SCM problem has also been the focus of much interest and, as a result, many strategic, tactical and operational approaches have been devised (Beamon, 1998; Vidal & Goetschalckx, 1997). Similarly, a number of budgeting models started to appear in the late 1950s, when linear programming computation methods also emerged, with the aim of facilitating the decision-making process as regards financial matters (Baumol, 1952; Lerner & Stone, 1968; Miller & Orr, 1966; Orgler, 1969, 1970; Robichek, Teichroew, & Jones, 1965). Srinivasan (1986) presents a review of these kinds of cash management models based on mathematical programming tools. During the last years, part of our research has focused on merging the underlying ideas and concepts described in the aforementioned approaches in order to construct holistic tools for SCM that cover process operations as well as financial variables and constraints. In a pioneering piece of research, Badell, Nougues, and Puigjaner (1998) presented a hybrid strategy for incorporating financial considerations into an advanced planning and scheduling (APS) application that implemented metaheuristic optimization algorithms. The final purpose was to guarantee the liquidity of the schedule that satisfied a set of due-dates previously negotiated with the customers. The initial goal of checking the feasibility of the planning decisions from a financial viewpoint was later extended to include the more ambitious objective of optimizing operations and finances in unison. Thus, Badell, Romero, and Puigjaner (2004) and Badell, Romero, and Puigjaner (2005) addressed the integration of financial aspects with short-term planning in the batch process industry, including retrofitting activities at the plant level. To achieve this integration, a short-term cash management model (Orgler, 1969) was modified, extended and connected to a standard scheduling model that acted as an APS tool. The objective function was to maximize the sum of payments, whether or not prompt payment discounts were taken into account, plus the marketable securities revenues minus the costs of the short-term credit line. In Romero et al. (2003), the cash management formulation was widened to include further financial variables and constraints. Specifically, the possibility of pledging receivables as a way of obtaining further funding was introduced into the model. Moreover, the new objective function pursued in this formulation was the cash flow of dividends, that

is, the amount of cash that can be withdrawn from the company at a given instant of time. The selection of this objective aimed to increase the shareholder value (SHV) of the firm, which today seems to be a priority. The aforementioned approaches dealt with the integration of operations and finances in the batch process industry, and usually worked at the plant level. The extension of the methods presented in these works to the whole SC was addressed by Guill´en, Badell, Espu˜na, and Puigjaner (2006). The financial model here introduced was based on the one presented by Romero et al. (2003). However, in this case, the change in equity was pursued as an objective, as an alternative to the cash flow of dividends. The recent development of a multi-agent system for SCM offered a unique opportunity to integrate finances and operations in a single analysis platform. This is the most recent step taken towards integrating the two areas. The main features of the resulting integrated framework are described next. 3.2.1. Implementation: financial module A financial module was constructed to optimize the financial variables associated with the SC operation and also to ensure the firm’s liquidity. The module implemented linear programming tools to address the short-term management of cash and accounted for the maximization of the change in equity of the company. The connection with the multi-agent simulator was made through the payments of raw materials, production and transport utilities (i.e., dates and sizes of purchases of raw materials and utilities) and the sale of products carried out by the agents in the system. The mathematical formulation embedded in the financial module was taken from the work of Guill´en et al. (2006), and can be seen as an extension of the model developed by Orgler (1969). As such, this formulation optimizes the cash flows associated with SC operation and also provides a financial KPI to assist the central manager in finding the best planning decisions in terms of their ability to increase the SHV of the firm. Thus, the cash management formulation allows payments to providers, short-term borrowing, pledging decisions and the buying/selling of securities to be scheduled in line with production tasks. A set of constraints representing balances of cash, debt, securities, and so on are applied to accommodate the aforementioned issues. Such constraints are described in detail in the subsequent section. 3.2.1.1. Mathematical formulation. The budgeting model considers t planning periods in which the financial decisions are taken. The cash balance for each planning period is the following: Casht = Casht−1 + ECasht + NetCLine + NetMS t t  − Payet  t + Otherst ∀t e

(2)

t

Eq. (2) describes the cash for each period t (Casht ). Here, Casht is a function of the previous cash (Casht−1 ), the exogenous cash from the sale of products or any other inflow of

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

cash (ECasht ), the amount borrowed or repaid to the credit line (NetCLine ), the sales and purchases of securities transactions t (NetMS t ), raw materials, production and transport payments on accounts payable incurred in any previous or actual period t (Payett ), and other expected outflows or inflows of cash (Otherst ). A certain proportion of the accounts receivable may be pledged at the beginning of a period. Pledging is the transfer of a receivable from the previous creditor (assignor) to a new creditor (assignee). Therefore, when a firm pledges its future receivables, it receives only a part (generally 80 percent) of their face value in the same period. Thus, it can be assumed that a certain proportion of the outstanding receivables at the beginning of a period are received through pledges during that period, as stated in Eq. (19). In the equation, the variable Pledtt represents the amount pledged within period t on accounts receivable incurred in period t and maturing within period t + tdel . Our formulation also assumes that all the accounts receivable have the same maturing period (tdel ). This consideration can be easily modified in order to reflect more complex situations. Pledging is a very expensive way of getting cash that should only be used when no more credit can be obtained from the bank: t+t del −1

Pledtt  ≤ ARect

∀t

(3)

t  =t t−1 

ECasht = ARect−tdel −

+

t 

Pledt  t · φ

∀t

(4)

Finally, the exogenous cash should be computed by means of Eq. (4) as the difference between the accounts receivable incurred in period t − tdel minus the amount of receivables pledged in previous periods plus the amount pledged in the current period. In this expression, φ represents the face value of the receivables being pledged, which is generally 0.8: CLinet = CLinet−1 + NetCLine + ir · CLinet−1 t

CLinet ≤ MaxCLine ∀t

= StMS − NetMS t −

∀t

∀t

(5) (6) (7)

A short-term financing source is represented by an open line of credit constrained by MaxCredit. Under an agreement with the bank, loans can be obtained at the beginning of any period and are due after 1 year at a weekly interest rate (ir) that depends on the agreement with the bank. The bank requires a compensating balance, generally of no less than 20 percent of the amount borrowed. Therefore, the minimum cash (MinCash) has to be more than the compensating balance imposed by the bank. Eqs. (5)–(7) make a balance on borrowing by considering the debt (CLinet−1 ) for each period updated from the previous periods, ) and the balance between borrowing and repayments (NetCLine t

t−1  t  =1

t−1  t  =1

ZtMS t

T  t  =t+1

YtMS t +

T  t  =t+1

ZtMS t +

MS ZttMS  · (1 + Ett  )

· (1 + EttMS  )

≤

StMS

+

t−1  t  =1

MS YttMS  · (1 + Dtt  )

∀t

t−1  t  =1

MS YttMS  · (1 + Dtt  )

(8) ∀t

(9)

Eq. (8) makes a balance for marketable securities. The portfolio of marketable securities held by the firm at the beginning of the first period includes several sets of securities with known face values maturing within the time horizon (StMS ). All marketable securities can be sold prior to maturity at a discount or loss to the firm, as stated in Eq. (8). The revenues and costs associated with the transactions in marketable securities are given by techniMS cal coefficients (DttMS  and Ett  ). The cash invested at period t on securities maturing in period t is YtMS  t . The cash income obtained from the security sold in period t maturing in period t is ZtMS t . Eq. (9) is applied to ensure that the total amount of marketable securities sold prior to maturity in each period is lower than the amount of marketable securities that are available (those belonging to the initial portfolio plus the ones purchased in previous periods minus those sold before):

t  =1

t  =t−tdel +1

NetCLine = Borrowt − Repayt t

the interest of the credit line (ir·CLinet−1 ):

t−1 

Pledt−tdel t 

t  =t−tdel

659

Payett  · Coefett  ≤ EPurchet

∀e, ∀t

(10)

With regard to the accounts payable (raw materials, production and transport utilities purchases), it is assumed that the financial officer may stretch or delay payments on such accounts at his or her discretion. Discounts for prompt payment can be obtained if purchases are paid promptly but will not be granted if the payments are stretched. Since it is not reasonable to demand that the total accounts payable be zero at the end of the planning period, the payment constraints are formulated as inequalities, as stated in Eq. (10). Technical coefficients (Coefett ), which multiply the payments executed in periods t on accounts payable incurred in t, are introduced into Eq. (10) to enable the terms of the raw materials, production and transport credits (e.g., 2 percent-1 week, net-28 days) to be taken into account: Casht ≥ MinCash

∀t

(11)

Eq. (11) stipulates that the cash in each period (Casht ) must be more than a minimum value (MinCash). Ideally, the approach proposed should provide a minimum steady level of cash without upper or lower bounds. In practice, positive peaks of cash may appear due to the short span between cash inflows and outflows provoked by transactions such as purchases or sales of marketable securities, sales of final products, the payment of liabilities, and so on. If such delays do not occur, then the profile is flat. A minimum amount of cash is therefore required to handle uncertain events, such as delays in customer payments, to ensure enterprise liquidity, and also because banks require compensating balances during financing operations.

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The formulation seeks to enhance the shareholder’s value (SHV) in the firm, which seems to be today’s priority. One possible way of achieving this goal is to maximize the increment in equity of enterprise (Equity). Using Eq. (12), this value can be computed as the net difference between the increment in assets, which includes both the increment in current (CA) and fixed assets (FA) and the increment in liabilities, which in turn includes the increment in current liabilities (CL) and the change in the long-term debt (L) (Shapiro, 2001): E = CA + FA − CL − L

(12)

Finally, the accounts receivable incurred in periods t and their maturing period are determined from the sales of products carried out by the agents, as stated in Eq. (16). Here, the maturing period of the accounts receivable (tdel ) represents the probable or estimated delay between the purchase incidence and the corresponding payment. This equation allows the budgeting model to be integrated into the multi-agent system. The linear programming problem solved by the financial modules can thus be stated as follows: Financial Model:

maximise E Liquid assets are represented by CA. In our model, this subject to Eqs. (2)–(16) term is computed from the accounts receivable, the available cash and the inventories at the end of the time horizon (T ) and 4. Multi-agent system: integrated framework at time zero (t0 ), as expressed in Eq. (13). In this equation, the prices of the materials kept as inventories (SPricest ) represent In this section, we present our overall solution strategy for the market prices that these products would reach in the market SCM, which is based on the multi-agent system previously if they were sold at the end of the time horizon. Illiquid assets, described. The focus was on incorporating the SC dynamics such as plants or equipment, are represented by FA. ⎫ ⎧ T T T ⎬ ⎨    ARect  − Pledtt  CA = Casht=T + ⎭ ⎩  t =T −tdel +1

+



Sst=T · SPricest=T −



t=T −tdel +1t =T −tdel +1

Casht=1 + ARect=1 +

s



t

(14)

Here CA* represents the increment in current assets before taxes, trate represents the tax rate and dep the depreciation term for the given time horizon. Short-term liabilities are represented by CL. This term includes the accounts payable, which are due to the remaining debt or the consumption of raw materials, labor and transport utilities, as stated in Eq. (15). Finally, L refers to long-term bank loans or bonds.  CL = CLineT + EPurchet e

 e

t

t

t

Payet,t  · Coefet,t  − CLinet0

(15)

To integrate the financial module and the multi-agent system, the production liabilities and exogenous cash at every week period (EPurchet ) are calculated as a function of production planning variables. Production liabilities are given by the production and distribution tasks carried out by the agents of the system:  Salesst · Pricest ∀t (16) ARect = s ∈ FP

Sst=1 · SPricest=1 + Taxes

(13)

s

With regard to taxes, these should be determined according to the applicable legislation, which may lead to different formulations. In this paper, the following equation, which aims to reflect a general case, was applied:  Taxes ≥ (CA∗ + FA + Divt − CL − dep) · trate

−



and also on enlarging the scope of the analysis. Our main aim was to achieve a realistic system for holistically optimizing the SC operation. Thus, this framework must be able to reproduce in a realistic manner the SC operation while also considering a variety of objectives given by the firm’s interests. To achieve this goal, the multi-agent system was taken as a basis for further developments. The first step was to enlarge the scope of the analysis so as to include objectives other than profit or cost. Thus, the environmental and financial modules previously described were added to the multi-agent framework. Inserting these novel modules into the multi-agent system provided a way to further explore the necessary trade-offs upon which the decision-making procedure should be based. However, the lack of optimization skills, which is the main disadvantage of this sort of approach, still represented a major shortcoming. Thus, to go beyond the mere modeling of a generic SC, a hybrid simulation-based optimization solving strategy was incorporated. In PSE literature, simulation-based optimization approaches to SCM have received scant attention and require further study. However, Subramanian, Pekny, and Reklaitis (2000), Subramanian, Pekny, and Reklaitis (2001), Subramanian, Pekny, Reklaitis, and Blau (2003), Jung, Blau, Pekny, Reklaitis, and Eversdyk (2004) and Wan, Pekny, and Reklaitis (2005) have made highly regarded contributions to the field. Thus, the logical rules implemented in the agents to drive their operation and response against the arriving events were parameterized and an optimization algorithm was then invoked to act over these parameters to improve an objective function defined beforehand. Fig. 8 shows the way in which the simulation model is coupled with the optimization algorithm. Within this

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

Fig. 8. Framework for stochastic simulation-based optimization.

framework, the optimization algorithm works iteratively in a loop, taking the values of the objective function, the variables and the constraints at each iteration and then computing new values for the decision variables, which are further evaluated using the simulator. Let us note that this approach involves different simulation runs over the planning horizon. Each of these simulations considers a different Monte Carlo sample of the probability distributions that characterize the uncertain parameters ω. Each

661

performance measure fp (η,ω) is a function of the set of decision variables η and also of the specific realization of the uncertain parameters ω. A set of decisions are made periodically in each of these simulations to replenish the inventories at the different SC entities. The simulator has the outstanding advantage of being capable of representing the real-world SC operation as fitted as desirable. The expected value of each performance measure p can then be computed by repeating the procedure mentioned above for a sufficient number n of Monte Carlo samples and making then the average of the performance results obtained in each scenario (Fp (η) = E[fp (η, ω)]). The accuracy of this expected value is indeed given by the number of simulation runs carried out. A schematic representation of the specific implementation of the multi-objective multi-agent framework is depicted in Fig. 9. As shown, the agent-based simulator module still acts as the core of the methodology by responding to uncertainties through local dispatching rules, invoking local optimization modules when necessary, and solving conflicts through the exchange of messages. The simulator has a number of agents that map each entity of a real-world SC network and mimic its behavior. This simulator receives a set of input values (decision variables), η, and then, by emulating the system dynamics, provides valuable information for calculating p performance measures, which have been previously defined by the analyst. A multi-objective optimization algorithm is coupled with the multi-agent system in order to look for the non-dominated solutions of the SCM problem being analyzed, that is, those solutions that properly assess the trade-off between the different objectives. As a result, an approximation of the Pareto set of solutions is obtained. Therefore, the decision-makers get not only one solution, but a set of alternatives from which they can then further explore interesting trade-offs.

Fig. 9. Multi-objective approach.

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L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

5. Case study

Fig. 10. Implementation of the proposed framework.

A software prototype was built as part of our research and was tested on a variety of SC problems, including real-world case studies. In addition, the software design was carried out using best practices in object-oriented design, such as UML (Unified Modeling Language) modeling and design patterns (see Fig. 10). This will make the tool’s design suitable for future extensions, such as the incorporation of new decision-making algorithms and the inclusion of new objects. The software was implemented in C# using Microsoft® ’s .NET framework. The real agents are .NET web servers that communicate among themselves by means of XML (Extended Markup Language) messages, under the SOAP protocol. Specifically, in the case of the simulated agents, all the data required to define an SC case are contained in an XML file whose extension is .scm. A detailed description of the agent-based framework and the simulation-based optimization strategy developed to improve SC performance, which constitute the core of our research in SCM, can be found in Mele et al. (2004, 2006).

In this section, the main advantages of our integrated framework for SCM in the CPI will be highlighted through a case study. A SC network consisting of 12 interconnected entities i, the structure of which is depicted in Fig. 11, is used in this section to illustrate the capabilities of the multi-agent system. The SC under study comprises three plants (F1, F2 and F3), three distribution centers (D1, D2 and D3), five retailers (R1–R5) and one supplier S. The SC network operates as a pull system (make-to-order system) with a centralized view and a complete degree of information sharing. A set of inventory control policies are implemented at the nodes of the network. Specifically, a periodic revision strategy is applied at the distribution centers whereas a continuous one is used at the retailers. The former strategy implies that every τ ij time units, the inventory position Iij for product j at node i is checked. If Iij is below the reorder point sij , a replenishment quantity uij = Sij − Iij is ordered to raise the stock level to Sij . If the position is above sij , nothing is done until the next review. In the latter strategy, the revision is made continuously (i.e., τ ij = 0). In both strategies, sij is known as the reorder point and Sij is the storage capacity of each node i for each product j. The demand is assumed to be uncertain and it is modeled as a set of scenarios with given probability of occurrence. Each scenario comprises a set of events distributed over the time horizon of the study. Each of these events has an associated amount of material and time of occurrence. Moreover, the amount of materials are assumed to be normally distributed around a mean value whereas the inter-arrival time intervals are considered to be uniformly distributed. Table 1 shows the values for the customer demand. Table 2 shows for each product the initial values of the different inventory parameters applied at each SC node. τ ij the review period for the distribution centers, sij is the reorder point, Inv0ij

Fig. 11. SC network.

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

663

Table 1 Demand data at each sales region R1

Mean (u) Variance (u2 ) λij

R2

R3

R4

R5

A

B

C

A

B

C

A

B

C

A

B

C

A

B

C

20 5 111

80 20 111

45 5 123

12 3 123

89 32 111

47 12 124

80 4 105

24 5 150

120 50 140

35 15 140

80 15 140

84 15 150

90 20 111

110 23 150

80 25 140

Table 2 Inventory parameters before the optimization process ([τij ] = h, [sij ] = u, [Sij ] = 103 u, [Inv0ij ] = 103 u) Sa

P

τ ij

sij

Sij

7

800

8.0

F1b

P A B C

F2b

a b c d

F3b

sij

Sij

Inv0ij

τ ij

sij

Sij

Inv0ij

τ ij

sij

Sij

Inv0ij

7 7 7 7

800 800 700 850

8.0 8.0 8.0 8.0

6.0 6.0 7.0 3.5

7 7 7 7

750 750 850 800

8.0 8.0 8.0 8.0

6.0 6.0 7.0 6.5

7 7 7 7

750 750 750 750

8.0 8.0 8.0 8.0

6.0 6.0 6.0 6.0

D2c

D3c

τ ij

sij

Sij

Inv0ij

τ ij

sij

Sij

Inv0ij

τ ij

sij

Sij

Inv0ij

7 7 7

800 700 850

7.0 7.0 7.0

6.0 7.0 3.5

7 7 7

750 850 800

7.0 7.0 7.0

6.0 7.0 6.5

7 7 7

750 750 750

7.0 7.0 7.0

6.0 6.0 6.0

R1d

A B C

R2d

R3d

R4d

R5d

sij

Sij

Inv0ij

sij

Sij

Inv0ij

sij

Sij

Inv0ij

sij

Sij

Inv0ij

sij

Sij

Inv0ij

15 15 20

0.50 0.50 0.50

0.20 0.30 0.25

50 36 40

0.50 0.50 0.50

0.23 0.25 0.28

40 50 35

0.50 0.50 0.50

0.26 0.29 0.20

50 35

0.50 0.50

0.24 0.25

40 50

0.50 0.50

0.20 0.30

Supplier. Manufacturing plants. Distribution centers. Retailers.

is the inventory level at the starting point of the simulation, and Sij is the storage capacity at each node. The upper and lower bounds of the decision variables has been set taking as reference the initial values with which the SC operates. For the review period, we assume that 0 ≤ τij ≤ 1.2 · τij0 . In this expression, τij0 represents the initial value of each parameter, which are shown in Table 2. For the rest of the parameters, a similar procedure has been applied: 0 ≤ sij ≤ 1.2 · sij0 and 0 ≤ Sij ≤ 1.2 · Sij0 . The unit production and inventory costs (vpcij and vicijt ) are given in Tables 3 and 4. The production time is equal to

Table 4 Variable inventory costs at each node, per product and simulation step, vicijt (×103 m.u./u/t)

P A B C

Table 3 Unit production costs at each plant, vpcij (m.u./u)

A B C

6.0

τ ij

D1c

A B C

Inv0ij

F1

F2

F3

1.0 2.0 3.0

3.0 2.0 1.0

2.0 3.0 3.0

A B C

Supplier

Manufacturing plants

S

F1

F2

F3

0.10 – – –

0.15 0.15 0.20 1.00

0.15 0.15 0.20 0.40

1.00 1.00 1.00 1.00

Distribution centers

Retailers

D1

D2

D3

R1

R2

R3

R4

R5

0.10 0.20 0.30

0.15 0.20 1.00

0.15 0.20 0.40

1.00 1.00 1.00

1.50 0.50 0.50

1.00 1.00 1.00

0.15 0.15 0.15

0.15 0.20 0.20

664

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Table 5 Product prices, priceij (m.u./u)

A B C

R1

R2

R3

R4

R5

800 900 1,500

110 210 305

95 200 290

100 202 309

120 220 300

The data required to compute the environmental indexes associated with the SC operation are the consumption of utilities and raw materials and the emissions of each process. This analysis covers all the main production/distribution tasks carried out in the SC, including the extraction of raw materials and the manufacturing process itself. Nevertheless, for the sake of simplicity, the use and disposal phases have not been considered in this example although the environmental module is indeed able to deal with them. This specific study can thus be seen as a “cradle to gate” analysis instead of a “cradle to grave” study. The data corresponding to the functional unit, inputs of materials and energy, and outputs of products, sub-products and wastes from the system under study can be found in Table 6. The first column of this table indicates whether the inputs are elemental (“yes”) or not (“not”). There are two flows that are not elemental and must then be computed: NiCl2 and electricity. Thus, additional data for these two inputs are required (Tables 7 and 8). Let us note that in Table 6, the data are referred to the functional unit, 50 u of product B, whereas in Tables 7 and 8, the data are expressed according to an arbitrary calculation basis. The calculation basis for data concerning NiCl2 production is 120 kg whereas for the electricity production is 4,500 MJ. The aforementioned data must be loaded in the system database. This information will then be retrieved by the LCA module, which will start with the inventory calculations. The module performs material and energy balances taking into account the structure of the network. An allocation method is applied to allocate the environmental loads of the two output streams (NiCl2 and NiSO4 ) that are generated in the production of NiCl2 . In this case the mass allocation method (Jensen et al., 1998) has been applied. This method distributes the burdens (inputs and emissions) of the manufacturing process between

1 min per unit of product j for all the products. Furthermore, for the sake of simplicity, we have assumed that the transportation costs and times are the same for all the products and nodes. The variable transportation cost per unit, vtcij , is equal to 0.10 m.u./u. The transportation time is considered to be uncertain and it is sampled from a normal distribution with a mean of 1h and variance of 2h2 . Table 5 shows the product prices (priceij ). The main activity of this SC is the electroplating of three different metallic objects (A, B and C). These electroplating plants have the following relevant inputs: electricity, water, the raw objects to be treated, and chromium and nickel salts for the electrochemical treatment. The SC has also another plant that produces nickel(II) chloride (NiCl2 ). This plant provides also nickel(II) sulphate (NiSO4 ), which is a by-product that contributes to increase the SC earnings. Moreover, the plant producing NiCl2 consumes coal, fuel and nickel ore. In the phase of Goal and Scope of the LCA study, the boundaries of the system are set, as it is depicted in Fig. 11. This work assumes that chromium salts, tubes and water are elemental flows (i.e., they come directly from the environment and do not exhibit any associated burden other than the resource depletion itself). On the other hand, electricity comes from a generation process that uses mainly coal and fuel as raw materials. The functional unit has been referred to product B.

Table 6 Aggregated data for all the electroplating plants, the distribution centers and the retailers Inputs Elemental flow? No Yes Yes Yes No a b

Emissions Name NiCl2 Cr salts Brass Water Electricity

Value 125 200 125 2,000 230

Products

Unit

Name

Value

Unit

Name

Value

Unit

kg kg kg kg MJ

COa

0.0025 0.0025 0.0025 0.0025 0.0250

kg kg kg kg kg

A B C

100 50 25

u u u

CO2 a SOx a Crb Nib

To the air. To the water.

Table 7 Data for the NiCl2 production process Inputs Elemental flow? Yes Yes Yes a b

Emissions Name Coal Fuel Ni ore

To the air. To the water.

Value 20 40 50

Products

Unit

Name

Value

Unit

Name

Value

Unit

kg kg kg

COa

0.0250 0.0025 0.0200 0.0250

kg kg kg kg

NiCl2 NiSO4

120 100

kg kg

CO2 a NOx a Nib

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

665

Table 8 Data for the process supplying electricity Inputs

Emissions

Elemental flow? Yes Yes a

Name Coal Fuel

Value 45 50

Unit

Name

kg kg

COa

Products Value 0.0250

Unit

Name

Value

Unit

kg

Electricity

4, 500

MJ

To the air.

Table 9 Allocation to the NiCl2 Products Name NiCl2

a b

Inputs Value

Unit

120

kg

Emissions

Elemental flow?

Name

Yes Yes Yes

Value

Coal Fuel Ni ore

10.9091 21.8182 27.2727

Unit

Name

Value

Unit

kg kg kg

COa

0.013636 0.001364 0.010909 0.013636

kg kg kg kg

CO2 a NOx a Nib

To the air. To the water.

Table 10 Material balance over 50 u of product B Inputs

Emissions

Products

Name

Value

Unit

Name

Value

Unit

Name

Value

Unit

Brass items Coal Cr salts Fuel Ni ore Water

125 13.66364 200 25.28283 28.40909 2,000

kg kg kg kg kg kg

COa CO2 a NOx a SOx a Crb Nib

0.017982 0.003920 0.062475 0.002500 0.002500 0.039205

kg kg kg kg kg kg

A B C

100 50 25

u u u

a b

To the air. To the water.

the two products. To do so, the loads are multiplied by a factor that, in this case, is equal to 60/(60 + 50) = 0.545 for the NiCl2 and 50/(50 + 60) = 0.455 for the NiSO4 (see Table 7). The results of this allocation procedure can be seen in Table 9. Let us note that the production of electricity does not require any allocation method as the electricity is the only product generated by the process. The results of the mass balance associated with the main product are shown in Table 10. The avoided burden method is next applied to allocate the environmental burdens to the functional unit (product B). This

method requires data concerning the standard manufacturing processes of products A and C. The results of this phase are shown in Table 11. This table, which is known as the inventory table, provides the environmental burdens expressed as the amount of resources consumed and wastes released per functional unit. In the Impact Assessment phase, which is next applied, the environmental impact indexes are computed from the inventory table using the potential factors provided by Guin´ee et al. (2002). In the multi-agent framework, the environmental burdens are not

Table 11 Inventory table Inputs Elemental flow? Yes Yes Yes Yes Yes a b

Emissions Name Brass Coal Cr salts Fuel Ni ore

To the air. To the water.

Value 125 125 200 125 125

Products

Unit

Name

Value

Unit

Name

Value

Unit

kg kg kg kg kg

COa

0.002982 0.002420 0.042475 0.000500 0.002300 0.037205

kg kg kg kg kg kg

B

50

u

CO2 a NOx a SOx a Crb Nib

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static, instead, they change dynamically according to the operation of the SC. To compute the inputs and emissions dynamically, the following equation can be applied: me = ϕeP · t P + ϕeI · t I + ϕeT · t T

The problem then is to find the values of the parameters associated with the inventory control policies implemented at the nodes of the SC that maximize the economic performance and minimize the environmental impact.

(17)

where me is the mass in kg of environmental issue e (e.g., resource, emission). Superscripts P, I and T stand for the three main activities in a SC, that is, production, storing and transportation, respectively. ϕeP is the contribution to the environmental burden e by the activity P expressed in kg per time unit of activity P. Finally, tP accounts for the total time during the simulation in which activity P is active, expressed in time units. This equation allow to compute the environmental loads associated with the SC as a function of the production/distribution tasks carried out in its nodes. With regard to the financial matters, we assume that the firm has an initial portfolio of marketable securities given by Table 12 at the beginning of the time horizon. Twelve financial periods with a length of 1 week are considered. The initial cash is equal to the minimum cash (5,000,000 m.u.). Under an agreement with a bank, the firm has an open line of credit at a 8 percent annual interest with a maximum debt allowed of 2,500,000 m.u., being the initial debt equal to 1,000,000 m.u. The change in assets is computed considering that the raw materials and final products kept as final inventories at the end of the time horizon can be sold at a 50 percent of their market value. On the other hand, the value of the final inventories of intermediate products is equal to zero. Three external suppliers are considered: the first one provides raw materials, the second one production utilities and the last one transport services. Liabilities incurred with the raw materials supplier and the supplier of production utilities have to be repaid within 4 weeks according to the terms of the credit (2 percent-7 days, net-28 days for the raw materials supplier and net-28 days for the second one). The payments associated with the transport services cannot be stretched and must be fulfilled within the same period of time in which the purchase incidence takes place. The technical coefficients for the marketable securities purchased and sold by the firm are computed assuming an annual interest rate of 2.8 percent for purchases and 3.5 percent for sales. At the end of the time horizon (week 12) 500,000 m.u. are withdrawn from the company as dividends. There are also outflows of cash equal to 2.25, 1, 0.75 and 1.25 millions of m.u. in periods 4, 6, 8 and 12 due to wages, rents, changes in fixed assets and the repayment of the long-term debt, which remains constant during the whole time horizon. Finally, the receivables on sales executed in any period are paid with a 28-day delay and may be pledged at a 80 percent of their face value. Table 12 MS (m.u.)) Initial portfolio of marketable securities × 10−3 (St∗ t* 1

2

3

4

5

6

7

8

9

10

11

12

150

150

70

50

40

75

60

100

100

25

60

80

5.1. Objectives As stated before, two objectives are considered in this study: economic performance and environmental impact. Then, the multi-objective (MO) problem can be stated as follows:

−E[E(η, ω)] −F1 (η) = min U = (18) η F2 (η) = E[EnvIndex(η, ω)] where U is the set of objective functions. In Eq. (18), Fp (η) is a function of the inventory parameters η that is evaluated by using the results of multiple Monte Carlo samplings with embedded discrete event simulations. The economic performance (i.e., change in equity) achieved by the SC in each simulation run is computed by the financial module whereas the environmental impact index is determined by the environmental module. These values are then used to compute the expected values of the objectives by making the average of the performances achieved in each scenario. The environmental impact indexes to be minimized – EnvIndex(η,ω)-, can be based on either the second or third phase of the LCA methodology. In this case study, the environmental impact calculation is based on the “problem-oriented” approach to impact assessment proposed by Guin´ee et al. (2002). This work applies a set of coefficients associated with material or energy flows (continuous variables) that represent the relative contribution of each burden to an impact factor. Specifically, in our case, the global warming potential (GWP) has been chosen as the environmental objective function to be minimized. To compute the GWP factors associated with different greenhouse gases, the GWP of CO2 is taken as reference. The GWP of CO2 is thus defined to be unity. Our model assumes that the environmental burdens and impacts functions are linear (i.e., they are directly proportional to the functional unit(s) and there is not any synergistic or antagonistic effect between them). The necessary steps to calculate the environmental impact index are: • Step I. Perform the material and energy balances associated with all the SC entities, following the principles of the ISO 14040 series. This step provides the inventory table with all the environmental loads: inputs flows coming from the environment and outputs flows. The outputs, in turn, can be classified as outputs economically valuable (products and by-products) and emissions to the environment. • Step II. Use the following equation to translate the SC emissions into an indicator of the Greenhouse Effect (GHE) enhancement: GHE =

 e

GWPe · me

(19)

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

667

where GHE is the GHE enhancement indicator expressed in kg of CO2 , and GWPe is the GWP corresponding to emission e according to the model of R. Heijungs (Guin´ee et al., 2002). Finally, me is the mass in kg of emission e released to the air. The choice of the environmental objectives to be optimized depends on the Goal and Scope of the study. In this work, an environmental impact has been selected as the objective to be minimized. Nevertheless, as was mentioned before, the optimization strategy could be applied either at the inventory or impact assessment levels. The environmental objectives would be therefore defined accordingly, as either burdens or impacts. 5.2. Results The multi-agent system is applied to solve the problem previously outlined. The financial and environmental modules are used to assess the economic and environmental performances of the SC respectively. A multi-objective GA (MOGA) is utilized to seek the best values of the decision variables taking into account the objectives computed by the aforementioned modules. Moreover, the performance of the MOGA can be improved by applying a tuning strategy for determining the optimal parameters of the GA, namely population size, and probabilities of crossover and mutation. Each simulation run entails a planning horizon of 3 months. The GA handles 96 decision variables that are associated with the inventory replenishment strategies applied in the SC entities: the inventory parameters sij , Sij and τ ij at the factories and distribution centers (66 variables), and the parameters sij and Sij at the retailers (30 variables). Real-valued encoding for the variables and maximum number of generations as termination criterion have been used. Figs. 12–14 show some snapshots of the graphical user interface (GUI) of the modules developed to perform MO optimization and LCA calculations. Table 13 shows the settings used for the MOGA. In Fig. 15, two approximations of the Pareto front showing the trade-off between the economic performance index (change in equity) and the GHE index are depicted. The curve on the left is the initial approximation of the Pareto front, before starting the optimization process. The curve on the right is the

Fig. 13. GUI for the MO optimization: graphical results.

Fig. 14. GUI for the LCA module.

approximation of the Pareto front obtained at the end of the optimization process when the maximum number of generations is reached. Figs. 16 and 17 show the evolution of the inventory level during the simulation run at the distribution center D1 for the two extreme points of the Pareto front, as it appears in the GUI of the multi-agent system. The points located in the right-hand side of the Pareto front correspond to solutions that represent a very responsive SC. The operation of such SCs is characterized by low inventory levels. This operation policy yields bigger profits, since in this example high inventory costs have been assumed. On the other hand, it Table 13 Settings for the GA-based strategy

Fig. 12. GUI for the MO optimization: settings and numerical results.

Algorithm used

NSGAII

Number of decision variables of the outer loop Number of timelines, n Population size, N Maximum number of generations, MaxGen Crossover probability, Px Mutation probability, Pm

96 90 20 200 1.0 .1

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Fig. 15. Pareto front approximation between the expected change in equity and the greenhouse effect index.

leads to high environmental impacts, which are mainly due to the very busy transportation tasks required by these solutions, for which very high contributions to the environmental index have been defined. In other words, these solutions achieve a superior economic performance at the expense of higher GHE levels. The points in the left-hand side of the front, on the contrary, have lower values of the profit but also lower values of the GHE index. The CPU time required for the algorithm execution ranges from 20 min to several hours in the cases tested. The simulation runs were carried out on an AMDK6 computer, 2.16 GHz, 512 MB. Let us note that although it is possible to improve the quality of the solutions by increasing the number of iterations, our strategy is able to provide feasible and acceptable solutions in reasonable CPU times. This CPU time depends on the number of simulation runs to be made (i.e., number of Monte Carlo samples to be explored) during each algorithm execution, and also on the tuning parameters of the GA-based strategy. 6. Concluding remarks and future work

Fig. 16. Inventory profiles of product B at distribution center D1: on the left-hand side of the Pareto front.

Fig. 17. Inventory profiles of product B at distribution center D1: on the righthand side of the Pareto front.

This paper describes the research carried out by our group in the last few years, which has mainly been devoted to developing a new modeling technique for SCM based on a simulation model that uses software agents as building blocks. The resulting agentbased system is a discrete event simulator that is able to use a number of different tools such as if–then rules and mathematical programming algorithms. An appropriate approximate strategy for tackling SCM problems has been developed from the viewpoints of analysis, improvement and optimization. This strategy relies on the use of metaheuristics over the multi-agent simulator. The resulting tool is flexible and extensible and allows new properties in the objects defined and new objects to be defined. Moreover, this framework includes environmental and financial considerations that enlarge the scope of the SC analysis and assist in assessing the trade-off between diverse environmental and economic concerns. The application of dynamic simulation and optimization to the SCM problem constitutes a wide-ranging, appealing field, in which there is much work to be done. Integration between levels continues to be an unresolved matter, and there are many areas in which there are opportunities for improvement, such as data management and connecting different tools. The research carried out so far can thus be taken as a basis for future enhancements. We propose that future research be undertaken on the following topics: • Simulation-based optimization methodologies: further improvements are required in the form of better methods, metamodels and filters to accelerate the algorithm’s convergence. • Optimization under uncertainty: further work is needed to develop new strategies to deal with the curse of dimensionality featuring the stochastic approaches. • MO optimization: the general framework developed by our group could be extended to incorporate others KPIs (social

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

impacts, safety impacts, etc.) as objectives to be optimized within the decision-making process. • Interaction with upper and lower decision levels: there is still much work to be done to effectively integrate the present approach with the higher business level and the lower production scheduling and process control levels. • Incorporation of negotiation abilities: incorporation of negotiation abilities: this topic concerns the consideration of the negotiation process between customers and suppliers that takes place in SCs. Acknowledgements The authors wish to acknowledge support of this research work from the European Commission (Contract Nos. GIRD-CT2001-00466 and MRTN-CT-2004-512233), the CICyT-MEC (Project No. DPI2002-00856), and the CIRIT-Generalitat de Catalunya (Project No. I-898). Contribution from Fernando Mele, PhD Thesis work at the research group CEPIMA is also much appreciated. References Applequist, G. E., Pekny, J. F., & Reklaitis, G. V. (2000). Risk and uncertainty in managing manufacturing supply chains. Computers and Chemical Engineering, 24, 47–50. Azapagic, A., & Clift, R. (1999). The application of life cycle assessment to process optimisation. Computers and Chemical Engineering, 10, 1509–1526. Badell, M., Nougu´es, J. M., & Puigjaner, L. (1998). Integrated on line production and financial scheduling with intelligent autonomous agent based information system. Computers and Chemical Engineering, 22, s271–s278. Badell, M., Romero, J., & Puigjaner, L. (2004). Planning, scheduling and budgeting value-added chains. Computers and Chemical Engineering, 28, 45–61. Badell, M., Romero, J., & Puigjaner, L. (2005). Optimal budget and cashflows during retrofitting periods in batch chemical process industries. International Journal of Production Economics, 95, 359–372. Banks, J. (1998). Handbook of simulation: Principles, methodology, advances, applications and practice. John Wiley & Sons, Inc. Baumol, W. J. (1952). The transactions demand for cash: An inventory theoretic approach. Quantitative Journal of Economy, 66(4), 545. Beamon, B. M. (1998). Supply chain design and analysis: Models and methods. International Journal of Production Economics, 55, 281–294. Chen, H., & Shonnard, D. R. (2004). Systematic framework for environmentally conscious chemical process design: Early and detailed design stages. Industrial and Engineering Chemistry Research, 43(2), 535–552. Chen, Y., Peng, Y., Finin, T., Labrou, Y., Cost, S., Chu, B., Yao, J., Sun, R., & Wilhelm, B. (1999). A negotiation based multi-agent system for supply chain management. Working notes of the agents ’99 workshop on agents for electronic commerce and managing the Internet-enabled supply chain. Ciric, A. R., & Jia, T. (1994). Economic sensitivity analysis of waste treatment costs in source reduction projects: Continuous optimisation problems. Computers and Chemical Engineering, 18, 481–495. El-Halwagi, M. M., & Manousiouthakis, V. (1990). Automatic synthesis of massexchange networks with single-components targets. Chemical Engineering Science, 45, 2813–2831. Goodwin, R., Keskinocak, P., Murthy, S., Wu, F., & Akkiraju, R. (1999). Intelligent decision support for the e-supply chain. In Artificial intelligence for electronic commerce, AAAI workshop 99 (p. 770). Grossmann, I. E. (2004). Challenges in the new millennium: Product discovery and design, enterprise and supply chain optimization, global life cycle assessment. Computers and Chemical Engineering, 29(1), 29–39. Guill´en, G., Badell, B., Espu˜na, A., & Puigjaner, L. (2006). Simultaneous optimization of process operations and financial decisions to enhance the

669

integrated planning/scheduling of chemical supply chains. Computers and Chemical Engineering, 30, 421–436. Guin´ee, J. B., Gorr´ee, M., Heijungs, R., Huppes, G., Kleijn, R., de Koning, A., van Oers, L., Sleeswijk, A. W., Suh, S., de Haes, H. A. U., de Bruijn, H., van Duin, R., & Huijbregts, M. A. J. (2002). Handbook on life cycle assessment. Operational guide to the ISO standards. Dordrecht: Kluwer Academic Publishers. Hoffmann, V. H., Hungerbuhler, K., & McRae, G. J. (2001). Multiobjective screening and evaluation of chemical process technologies. Industrial and Engineering Chemistry Research, 40(21), 4513–4524. Howard, B. B., & Upton, M. (1953). Introduction to business finance. McGrawHill. Hugo, A., & Pistikopoulos, E. N. (2004). Environmentally conscious planning and design of supply chain networks. In B. Chen & A. W. Westerberg (Eds.), Process systems engineering 2003 (pp. 214–219). Amsterdam: Elsevier. IRAM-ISO 14041 (1998). Gesti´on Ambiental An´alisis del Ciclo de vidaDefnici´on de la meta y el alcance y an´alisis del inventario del ciclo de vida. IRAM-ISO 14042 (2000). Gest´on Ambiental An´alisis del Ciclo de vida- Evaluati´on del impacto del ciclo de vida. Jensen, A. A., Hoffman, L., ller, B. T. M., Schmidt, A., Christiansen, K., Elkington, J., & van Dijk, F. (1998). Life Cycle Assessment (LCA). In A guide to approaches, experiences and information sources. European Environmental Agency. Julka, N., Karimi, I., & Srinivasan, R. (2002a). Agent-based supply chain management. 1. Framework. Computers and Chemical Engineering, 26, 1755–1769. Julka, N., Karimi, I., & Srinivasan, R. (2002b). Agent-based supply chain management. 2. A refinery application. Computers and Chemical Engineering, 26, 1771–1781. Jung, J. Y., Blau, G., Pekny, J. F., Reklaitis, G. V., & Eversdyk, D. (2004). A simulation based optimization approach to supply chain management under demand uncertainty. Computers and Chemical Engineering, 28, 2087–2106. Lerner, E., & Stone, J. (1968). Simulating a cash budget. California Management Review, 11(2), 78. Linninger, A. A., Stephanopoulos, E., Ali, S. A., Han, C., & Stephanopoulos, G. (1995). Generation and assessment of batch processes with ecological considerations. Computers and Chemical Engineering (S), 19, S7–S13. Mele, F. D., Espu˜na, A., & Puigjaner, L. (2002). Discrete event simulation for supply chain management. In AIChE annual meeting 2002 Mele, F. D., Guill´en, G., Espu˜na, A., & Puigjaner, L. (2006). A simulationbased optimization framework for parameter optimization of supply chain networks. Industrial Engineering and Chemistry Research, 45, 3133– 3148. Mele, F. D., Guill´en, G., Urbano, F., Espu˜na, A., & Puigjaner, L. (2004). A novel agent-based approach for supply chain retrofitting. In Agrawal & Floudas (Eds.), FOCAP-D 2004 (pp. 461–464). M´endez, C. A., Cerd´a, J., Grossmann, I. E., Harjunkoski, I., & Fahl, M. (2006). State-of-the-art review of optimization methods for short-term scheduling of batch processes. Computers and Chemical Engineering, 30(6–7), 913–946. Miller, M. H., & Orr, R. A. (1966). Model of the demand for money by firms. Quantitative Journal of Economy, 80(3), 413. Orgler, Y. E. (1969). An unequal-period model for cash management decisions. Management Science, 20(10), 1350. Orgler, Y. E. (1970). Cash management. California: Wadsworth. Petrie, B. A. G. B. J., & Romagnoli, J. (2000). Process synthesis and optimisation tools for environmental design: Methodology and structure. Computers and Chemical Engineering, 24(2–7), 1195–1200. Puigjaner, L., & Espu˜na, A. (2006). Integration in supply chain management. In L. Puigjaner & G. Heyen (Eds.), Computer Aided Process & Product Engineering-CAPE (pp. 695–730). Berlin: Springer-Verlag. Robichek, A. A., Teichroew, D., & Jones, J. M. (1965). Optimal shortterm financing decision. Management Science, 12, 1–11. Romero, J., Badell, M., Bagajewicz, M., & Puigjaner, L. (2003). Integrating budgeting models into scheduling and planning models for the chemical batch industry. Industrial and Engineering Chemistry Research, 42, 6125–6134. Sauter, J. A., Parunak, H. V. D., & Goic, J. (1999). Ants in the supply chain. In Workshop on agents for electronic commerce at agents 99 (p. 770).

670

L. Puigjaner, G. Guill´en-Gos´albez / Computers and Chemical Engineering 32 (2008) 650–670

Shah, N. (2005). Process industry supply chains: Advances and challenges. Computers and Chemical Engineering, 29, 1225–1235. Shapiro, J. F. (2001). Modeling the supply chain. Duxbury. Shapiro, J. F. (2004). Challenges of strategic supply chain planning and modeling. Computers and Chemical Engineering, 28, 855–861. Srinivasan, V. (1986). Deterministic cash flow management. Omega, 14(2), 145–166. Subramanian, D., Pekny, J. F., & Reklaitis, G. V. (2000). A simulation– optimization framework for addressing combinatorial and stochastic aspects of an R&D pipeline management problem. Computers and Chemical Engineering, 24, 1005–1011. Subramanian, D., Pekny, J. F., & Reklaitis, G. V. (2001). A simulation– optimization framework for research and development pipeline management. AIChE Journal, 47(10), 2226–2242. Subramanian, D., Pekny, J. F., Reklaitis, G. V., & Blau, G. E. (2003). Simulation–optimization framework for stochastic optimization of R&D pipeline management. AIChE Journal, 49(1), 96–112.

Vidal, C. J., & Goetschalckx, M. (1997). Strategic production–distribution models: A critical review with emphasis on global supply chain models. European Journal of Operational Research, 98, 1–18. Wan, X. T., Pekny, J. F., & Reklaitis, G. V. (2005). Simulation-based optimization with surrogate models—Application to supply chain management. Computers and Chemical Engineering, 29(6), 1317–1328. Wang, Y. P., & Smith, R. (1994). Waste water minimisation. Chemical Engineering Science, 49, 981–1006. Works, T. M. (2004). MATLAB 7.0 (R14), Simulink 6.0. Stateflow 6.0. User’s manual. The Math Works Inc. Yi, G., & Reklaitis, G. V. (2003). Optimal design of batch-storage network with recycle streams. AIChE Journal, 49(12), 3084–3094. Yi, G., & Reklaitis, G. V. (2004). Optimal design of batch-storage network with financial transactions and cash flows. AIChE Journal, 50(11), 2849– 2865.