Metaheuristic multiobjective optimisation approach for the scheduling of multiproduct batch chemical...

Journal of Cleaner Production 16 (2008) 233e244www.elsevier.com/locate/jclepro

Metaheuristic multiobjective optimisation approach for thescheduling of multiproduct batch chemical plants

Marıa Jose Arbiza, Anna Bonfill, Gonzalo Guillen, Fernando D. Mele,Antonio Espuna, Luis Puigjaner*

Universitat Politecnica de Catalunya, Chemical Engineering Department, E.T.S.E.I.B. Diagonal 647, E-08028 Barcelona, Spain

Received 1 January 2004; received in revised form 1 January 2006; accepted 18 August 2006

Available online 23 October 2006

Abstract

This article introduces a novel framework to deal with the scheduling problem concerning batch chemical plants. The main contribution ofthis work in comparison with previous approaches relies on the fact that it includes the environmental impact as an objective to be optimised,integrated with other more commonly used as makespan and/or financial performance. To address this problem, an advanced planning andscheduling tool (APS), which includes an environmental evaluation module based on the Life Cycle Assessment (LCA) criteria, a temporisationalgorithm and a financial module, coupled with a set of multiobjective genetic algorithms allows the computation of a set of non-dominatedsolutions in terms of the predefined criteria. This set of solutions can be used by the decision-maker in order to select the one that representsthe right compromise among the different objectives.� 2006 Elsevier Ltd. All rights reserved.

Keywords: Environmental impact; Scheduling; Multiobjective optimisation

1. Introduction

Production planning and scheduling refer to the routine ofallocating resources and equipment over time in order to exe-cute the process tasks required to manufacture products. Suchallocation tries to satisfy a specific product demand and qual-ity while fulfilling optimisation criteria defined beforehand.Production planning implies allocation decisions over longtime scales (months for example), which involve a lot of un-certainty and need of little detail, while scheduling focuseson the shorter time scale allocation and the sequencing deci-sions required to satisfy the product demand. Typically, inthe case of scheduling, a specific product is assigned to spe-cific equipment at a given time, while in the case of planning,production and equipment allocation is decided in a given

* Corresponding author. Tel.: þ34 934016678; fax: þ34 934010979.

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

0959-6526/$ - see front matter � 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jclepro.2006.08.028

period of time without being specifically sequenced duringsuch period.

The flexibility in utilizing available resources such asequipment units, utilities, production time and raw materialsis a key characteristic of the scheduling problem associatedto batch chemical plants. Such flexibility poses an interestingdecision-making process related to the optimisation of plantoperation. Additionally, the decision-making process mayoften involve several and usually conflicting objectives con-cerning economy, client satisfaction, environmental impact,etc., which should be satisfied simultaneously. Unfortunately,most of the batch plants operation optimisation tools considerexplicitly only one of such objectives, while the remainingones are merely incorporated just as constraints or more com-monly as performance indicators without taking part in theoptimisation procedure. In order to enhance the capabilitiesof such tools, thus enabling the incorporation of different cri-teria, a more comprehensive view of optimisation procedureand tools is of the utmost importance.

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234 M.J. Arbiza et al. / Journal of Cleaner Production 16 (2008) 233e244

The scheduling problem in the chemical industry has beenextensively studied and different methodologies for model-ling, simulation and optimisation of batch processes havebeen proposed in the literature (e.g. see [1e3]). Furthermore,research works considering environmental aspects in thescheduling problem are assorted. Grau et al. [4] consideredthe effect of waste considerations on batch plant scheduling;Ahmad and Barton [5,6] addressed solvent recovery targetingissues for pollution prevention in batch distillation. Linningeret al. [7] introduced a methodology for the systematic synthe-sis and assessment of batch processes featuring MinimumAvoidable Pollution, which is automated in their Batch De-sign-Kit software system. Pistikopoulos et al. [8] introduceda methodology for Minimum Environmental Impact of contin-uous processes which embeds Life Cycle Assessment princi-ples within a process optimisation framework. To this work,Stefanis et al. [9] incorporated ecological considerations inthe optimal design and scheduling of batch/semicontinuousprocesses.

Moreover, in all these works and despite the different indi-cated criteria involved in a decision process, only one objec-tive (makespan, cost, profit, environmental impact or duedates fulfilment) is considered to the optimisation of theproblem.

In this sense, this work introduces a framework able to dealwith the scheduling problem explicitly and simultaneouslyconsidering several objectives: the makespan, the environmen-tal and financial impact of the resulting schedule, amongothers not mentioned here. In such strategy, a set of multiob-jective (MO) optimisation algorithms is combined with ascheduling tool that includes a temporisation module, anenvironmental assessment module and a financial modulethat allow the evaluation of the different objectives of theexplored solutions.

2. Problem statement

Let us consider a multiproduct batch chemical plant whichcan be described through the ISA SP88 representation. The fol-lowing data are assumed to be known in advance: the structureof the plant, the recipes of each product and the orders to befulfilled. The problem is then to obtain a set of non-dominatedschedules that minimise the makespan and the environmentalimpact and maximise the availability of cash. Therefore, thefollowing decisions must be made:

� number and size of batches to be performed,� raw material selection,� sequence of batches,� temporisation of the activities for every batch,� resource consumption assignment.

A zero wait transfer policy has been considered, i.e. an inter-mediate product must be immediately transferred to the nextprocessing step just after its production. Neither intermediatestorage nor waiting times in the processing unit is available.

3. Solving strategy

The APS software used in this work has been developed byUPC [10]. This software has been designed with a modularstructure that allows the use of different packages which incor-porate additional functionalities to the main software. In orderto address the problem described before, the following mod-ules have been developed and used:

� A temporisation module, which computes the initial andfinal times of all the operations involved in a schedule.� A financial module, which evaluates the financial impact

associated to a given schedule.� An LCA module, which determines the environmental im-

pact of the solutions based on the LCA methodology.� An optimisation tool, with several single and MO algorithms

that seek the non-dominated solutions of the problem.

4. Implementation

The APS software is developed in Builder Cþþ, each mod-ule described before is a plug-in of it. An object-oriented datastructure was used, allowing customizations by switching oneobject by another. For more details see Canton [10].

4.1. Temporisation module

This module is based in the Event Operation Network tim-ing model (EON, see Ref. [11]) and it describes complex timeconstraints within the recipes. The EON is based on a series ofelements: events, operations and links. An event is the instantof time in which some change occurs; it is represented bymeans of nodes. It can be linked to operations (solid arrows)or to other events (dashed arrows), as seen in Fig. 1a.

Fig. 1. EON model.

235M.J. Arbiza et al. / Journal of Cleaner Production 16 (2008) 233e244

Fig. 2. EON representation example: the same EON can represent different recipes.

Each event n is associated to a time value, tn, and a lowerbound tmin

n (Eq. (2)). The lower bound can be used to forcedelays on a given solution in order to find a new solutionthat reaches special constraints (i.e. calendar constraints).The time values tn for each event will be the variables of thetiming problem we want to solve.

Operations designate those time intervals to be observedbetween the starting event (initial node, in) and the terminationevent (final node, fn). Each operation m is represented bya box linked with solid arrows to its associated nodes (inm

and fnm, Fig. 1b). Operations are the equality links betweennodes given by Eq. (3) in terms of the characteristic propertiesof each operation: the operation time TOP and the waitingtime. The operation time is a pre-determined value (as

a function of the amount being processed, unit assigned, prod-uct changeover, or a value referenced to another operation orto auxiliary equipment unit) which origin does not affect theEON description. The waiting time is the time slack foreach operation bounded as expressed by Eq. (4).

Finally, links designate those explicit internodal (event-event)precedence constraints. Each link k is represented by a dashedarrow from its origin node (onk) to its destiny node (dnk) andits associated increment of time (Dtk, Fig. 1a). The inequalityconstraint given by internodal links is expressed by Eq. (5).

Up to this point, the EON representation allows to describeall the timing constraints to determine a feasible timing for thestructure of activities of a given process. However, an objec-tive is needed to discriminate a good solution among the

Fig. 3. EON representation example.


infinite feasible ones. A simple and practical one is makespanwhich allows compressing the resulting schedules. However,makespan may still be a much degenerated objective. Amore flexible and general objective may be defined by theweighted contributions of makespan, waiting times and start-ing times (Eq. (1)).

So the whole LP-Problem formulation may be defined bythe following set of equations:minimise:

Z ¼ C1MSþXM

m¼1

C2mtwm þ

XN

n¼1

C3ntn ð1Þ

subject to:

tminn � tn �MS c n; n¼ 1.N ð2Þ

tfnm� tinm

�TOPm ¼ twm c m; m¼ 1.M ð3Þ

0� twm � twmaxm c m; m¼ 1.M ð4Þ

tdnk� tonk

þDtk c k; k ¼ 1.K ð5ÞThe main advantage of the EON model is that it is com-

posed of very simple pieces which results in a very simplemodel, however, it allows to describe very complex productionrecipes with complex time constraints. Solving the LP a goodstarting point is found.

Fig. 2 shows different EON networks that define the recipespresented in the same figure in the Gantt chart. As it is shown,the same EON representation can also be used to represent dif-ferent stages with a zero wait policy.

Therefore, the basic methodology to build the EON net-work for one recipe can be summarised in two main steps:

1. Create one operation for each one described in the pro-cess-stage-operation description.

2. Convert the links declared in the process-stage-operationdescription to an EON representation.

Some predefined links have been established to allow aneasier description of the recipe by the user. Each of themhas a specific way of being transferred to an EON structure.These links can be categorized in two groups:

1. Equality links: simultaneous, consecutive, relationship be-tween initial times, relationship between ending times

2. Inequality links: initial time precedence, ending time pre-cedence, consecutive precedence, time inclusion.

These links establish different constraints between the ini-tial time (It) and the ending time (Et) of the first operationand the initial and ending times (It0 and Et0) of the second op-eration (see Ref. [10]).

In Fig. 3, as an example, are represented in EON model thetwo first batches of the case study presented in this work(Fig. 8).

4.2. Financial module

A topical review of historical guidelines and approaches inintegration of operative scheduling and cash managementmodelling must take into account that budgeting models for fi-nancial control emerged earlier than operation schedules. Theinitial sequential approach focused on individual financing de-cisions was later developed towards the simultaneous consid-eration of financial decisions (e.g. see Refs. [12e15]).

Particularly, Charnes et al. [12] went beyond studying thesuccess of optimisation advances in production schedulingmodels. In their opinion, for a number of reasons the optimi-sation applications were concentrated in the production area,but there was no reason for not applying the same techniquesin financial planning, including purchases and product sales, oreven more, in joint management of operations and financialplanning. In the same line Robichek et al. [13] recognizedthat in order to reach the overall optimum in short and longterm capital budgeting the solution should be determined si-multaneously and not by sequential actions; they also empha-sized that the new developments in linear programming andfinancial management were still not mature to let them capturethe whole financial problem within a single straightforwardtreatment. In their opinion, the reason for considering isolatedsubproblems in financial management was that the overall fi-nancing problem was too complex to be analyzed all at once.

On the operative side, a huge number of models, especiallyin the last 25 years, have been developed to perform short termscheduling and longer term planning of batch chemical plantsaccounting for the maximisation of profit or minimization ofmakespan (for a short review see Shah [1]). However, verylimited number of works was reported on the joint financialand operative modelling. The work of Badell et al. [16]addresses the implementation of financial cross-functionallinks with scheduling, planning and budgeting in short termplanning, while Romero et al. [17] address scheduling andplanning with financial management in the batch chemicalprocess. Yi and Reklaitis [18] presented an integrated analysisof production and financing decisions regarding the optimaldesign of batch-storage networks. Shapiro [19] recognizesthat optimisation models offer an appealing framework for an-alyzing corporate financial decisions and constraints as well asfor integrating them with supply chain decisions and con-straints. He also admits that unfortunately relatively few inte-grated corporate financial models have been implemented. Inhis opinion [19], linkages among the three classes of decisions(supply chain, demand, and corporate finances) should beevaluated.

If in practice the financial matters are not still integrated ontheir own to support financial decision-making, it is mainly be-cause until today scheduling/planning and budgeting model-ling have been treated as separate problems and have beenimplemented in independent environments. This paper de-scribes an integrated approach for operations managementbased on the simultaneous consideration of operative andfinancial decisions regarding the management of batch chem-ical plants. Therefore, the cash profile associated to a given


schedule, from which the cash availability and thus the finan-cial performance of the plan can be computed, is determinedby a financial module which uses the information providedby the temporisation module. The computation of the cashprofile is therefore carried out once the schedule has beencomputed and taking also into account the delays betweenthe execution of the production tasks and the flows of mate-rials, and the times when the associated cash movementstake place. Specifically, it is necessary to know the durationof the delays associated to payments of raw materials and util-ities, and to the collection of the accounts receivables.

From the financial point of view, it is convenient to havea high amount of cash available. Firstly, because it avoids hav-ing to ask for financing sources that increase the total cost ofthe production plan such as opening lines of credit or pledgingof accounts receivables. In the second place, because the idlecash can be invested in marketable securities or other financialproducts thus providing extra benefits to the company. There-fore, in this work the maximisation of the cash availability rep-resented by the integral of the cash profile is pursued as anadditional objective to be optimised together with the environ-mental impact and the makespan.

4.2.1. Mathematical formulationThe cash balance for each planning period is the following:

Casht ¼ Casht�1þECasht � Paymentst ð6Þ

The equation describes the cash for each period t (Casht).Here, Casht is a function of the previous cash (Casht�1), theexogenous cash from the sales of products (ECasht), the pay-ments of raw materials, production and transport utilities(Paymentst).

With regard to the accounts payable (raw materials, produc-tion and transport utilities purchases), it is assumed that the fi-nancial officer cannot stretch or delay payments on suchaccounts, and therefore, discounts for prompt payment cannotbe taken. Nevertheless, the model could be extended in orderto take into account the terms of the raw materials, productionand transport credits (i.e. 2% per week, net: 28 days). It is alsoassumed in the model that there is a fixed delay between thepurchase incidence and the corresponding payment. Therefore,the delays associated with the payments of utilities, and withthe collection of the accounts receivables must be providedas input data into the model.

4.2.2. Objective functionWhile the more common objectives used by the process

systems engineering community are minimum makespan,due date fulfilment, maximum profit, net present value(NPV), internal rate of return (IRR), and payback time, thefinance community has been for years making financial busi-ness decisions taking into account other indicators: marketto book value, liquidity ratios, leverage, capital structureratios, return on equity, sales margin, turnover ratios, stocksecurity ratios, etc.

Nevertheless, the direct enhancement of shareholder’s value(SHV) in the firm seems to be today’s priority. SHV can beimproved by maximising the availability of cash as from thefinancial point of view; it is convenient to have a high amountof cash available. Firstly, because it avoids having to ask forfinancing sources that increase the total cost of the productionplan such as opening lines of credit or pledging of accountsreceivables. In the second place, because the idle cash canbe invested in marketable securities or other financial productsthus providing extra benefits to the company.

Therefore, in this work the financial module allows thecomputation of the cash availability, which is pursued as anadditional objective to be optimised together with the environ-mental impact and the makespan. The availability of cash(ACash) is measured as the integral of the cash profile, whichis computed taking into account the information provided bythe temporisation module, mainly the starting times of thebatches and the due dates of the orders. With the starting timesof the batches and the delays between the purchase incidencesand the corresponding payments one can compute the inputsof cash. The outputs of cash are determined with the delays as-sociated with the payments of utilities and with the due datesof the orders.

ACash¼Zt

0

Casht dt ð7Þ

4.3. Environmental impact module

4.3.1. LCA definitionAccording to the Society of Environmental Toxicology and

Chemistry (SETAC): ‘‘the LCA is an objective process to eval-uate the environmental loads associated with a product, pro-cess or activity by identifying and quantifying energy andmaterials used and waste released to environment, and to eval-uate and implement opportunities to affect environmentalimprovements. The assessment includes the entire life cycleof the product, process or activity, encompassing extractingand processing raw materials; manufacturing, transportationand distribution; re-use, maintenance; recycling andfinal disposal’’.

Based on the work carried out by the SETAC, the ISO hasfurther developed and managed to reach agreement among itsglobal membership on a series of standards: the ISO 14040series on LCA (ISO 14040, 1997 [20]; ISO 14041, 1998[21]; ISO 14042, 2000 [22] and ISO 14043, 2000 [23]).

4.3.2. The LCA-based moduleThis module determines the environmental impact of the

solutions and is based on the LCA methodology. It uses the in-formation associated to the schedule, i.e. raw material selec-tion and resources consumed by the labour tasks, to performthe Life Cycle Inventory Analysis phase and then to evaluatea global environmental impact index according to the Life Cy-cle Impact Assessment phase. In the specific implementation


presented in this work, these indexes are calculated as theweighted sum of three particular environmental indexes:greenhouse effect (in kg of CO2 eq), acidification potential(in kg of SO2 eq) and biochemical oxygen demand (in kg ofO2 eq).

4.3.3. Impact indexesAs it has been mentioned before, three impact categories

have been selected to perform the Life Cycle Impact Assess-ment to obtain some environmental impact indexes: enhance-ment of the greenhouse effect (GHE), acidification (AC) andbiochemical oxygen demand (BOD).

4.3.3.1. Enhancement of the greenhouse effect. For some sub-stances that contributed to this effect, parameters have beendeveloped in the form of a global warming potential(GWPi). These parameters are used to express the direct con-tribution to the greenhouse effect in a relative measure thatuses CO2 as a reference: the extent to which a mass unit ofa given substance can absorb infrared radiation comparedwith a mass unit of CO2. In this way, atmospheric emissions(in kg) can be converted to CO2 emissions (in kg) with anequivalent greenhouse effect:

greenhouse effect ðkgÞ ¼X

i

GWPi$emissioni ðair; kgÞ ð8Þ

4.3.3.2. Acidification. The contribution to acidification in theenvironment can be determined by weighting with acidifica-tion potentials (APi), which are a measure of the propensityto release Hþ compared with SO2. Atmospheric emissionsare converted, using the APi , to SO2 emissions (in kg) result-ing in equivalent acidification:

acidification ðkgÞ ¼X

i

APi$emissioni ðair; kgÞ ð9Þ

4.3.3.3. BOD. This category accounts for the amount of oxy-gen used for biochemical oxidation by a unit volume of waterat a given temperature and for a given time. BOD is an indexof the degree of organic oxidizable matter in the water.

The model described before corresponds to that proposedby Guinee et al. [24]. Values for GWPi and APi have beenpicked up from the literature [25]. Finally, the environmentalobjective function is:

Objective¼ uGHEGHEþuACACþuBODBOD ð10Þ

where u stands for the weight of each category in the objectivefunction. The values have been set in: uCHE ¼ 10�4, uAC ¼10�1, and uBOD ¼ 1.

4.4. Optimisation module

The scheduling problem addressed in this work is a Multi-objective Optimisation Problem (MOOP) that involves threeconflicting criteria to be simultaneously satisfied (makespaneenvironmental impactecash availability). To balance thetrade-off between these criteria and to ensure a satisfactoryperformance, a set of standard MO algorithms have beenimplemented within the APS framework. The library ofCþþ classes MOMHLibþþ (Multiple Objective Meta-Heuristics Library in Cþþ, by Jaszkiewicz [26]) has beenused with customized genome classes. The library incorpo-rates MO meta-heuristics (GNU Lesser General Public) onthe basis of Pareto simulated annealing and MO genetic localsearch. For an extended review on MOOP refer to, for exam-ple, Coello [27] and Deb [28].

A standard MO genetic algorithm (NSGA-II [29]) has beenimplemented within the APS framework to compute non-dom-inated solutions for the scheduling problem. The encodingused to represent the decision variables as well as the operatorsimplemented within the algorithms are presented in the fol-lowing sections.

4.4.1. EncodingEach individual of the population of solutions identifies

a production schedule and consists of two types of discrete de-cision variables: the sequence in which the operations are to beexecuted, and the selection of raw materials. The representa-tion used is a vector of integer values matching the sequenceof batches and denoting, for each batch, the correspondingproduct according to the raw material selected. Based on theraw material selected, different production recipes would berequired to produce the same type of product; therefore, prod-ucts of the same type are distinguished. An example is given inFig. 4, where N is the number of batches to be scheduled overthe time horizon under consideration, and Pi is the productidentifier; the bordered cells constitute the ‘‘chromosome’’for every potential solution.

4.4.2. InitializationThe initialization procedure implemented generates the first

population of solutions in a random way assigning to every po-sition of the sequence an integer number between 0 and P� 1as batch identifier. It should be noted that since the orders to befulfilled are given, the maximum number of batches to be pro-duced for each product is fixed in advance. To avoid the gen-eration of unfeasible solutions, an additional method to restorefeasibility is defined according the following procedure.

Feasibility procedureWhile solution is not feasibleSelect randomly two positions in the sequence (S1 and S2)

Position in the sequence 1 2 3 N Identifier (chromosome) P1 P3 P2 PN

Fig. 4. Chromosome.


If Product in S1 (or S2) identifier is in excess and Productof S2 (or S1) is in deficitMake both product identifiers equal to which is in deficit

Do

4.4.3. Mutation operatorFor the mutation procedure, two positions of the vector are

randomly selected. If the product identifiers are different, bothpositions are exchanged; otherwise, the procedure is repeateduntil there is an exchange.

4.4.4. Crossover operatorA multiple point reproduction procedure has been imple-

mented as crossover operator. This procedure, illustrated inFig. 5, is based on the generation of the new offspring solu-tions from blocks of k genes of the parents (with the exceptionof the last block, the length of which will vary according to thechromosome length, N ). The parent who gives the initial kgenes is randomly selected. The parameter k should be chosenin order to transmit as much as possible the good features ofthe parents to the children. Again, to avoid unfeasible solu-tions the feasibility procedure exposed in Section 1.1.2 aboveis applied.

Parent 1 New Solution Parent 2

k

2k

3k

4k

Fig. 5. Crossover operator.

4.4.5. EvaluationThe optimisation module guides the search for alternative

schedules with balanced makespaneenvironmental impactecash availability values. Each of the solutions (schedules)generated is evaluated in terms of these three criteria. Thedecision variables (production sequence and raw materialselected) are used as inputs in the temporisation, LCA andfinancial modules introduced before to evaluate the makespan,environmental impact and cash measures, respectively.

Fig. 6. Solution procedure of low chart.


Fig. 7. Case study: Robinson and Loonkar [30].

5. Solution procedure

The functional modules of the APS framework presentedabove have been integrated and coordinated to obtain thePareto set of schedules that balance the trade-off betweenminimum makespan, minimum environmental impact, andmaximum cash availability.

The solution method proceeds as stated in Fig. 6. First, a fea-sible initial solution is obtained using the heuristic rules imple-mented in the APS. This solution is then used to initialize themultiobjective optimisation algorithm, which directs the searchto the non-dominated set of solutions. Each alternative sched-ule generated from the reproduction processes is evaluated interms of each of the criteria considered. For this purpose, thesequence and raw material selection decisions provided bythe optimisation algorithm are used in the temporisation mod-ule to calculate the detailed timing and the makespan of the

Table 1

Product recipes

Recipe Stage Operation TOP (h) Unit

A (RM1)

A (RM2)

C

Pumping 1 Pumping 1 1.33 Pump 1

Reaction Reactor charge 1.33 Reactor

Reaction 3

Reactor discharge 2

Pumping 2 Pumping 2 2 Pump 2

Heat exchange Cooling 2 Heat exchanger

Tank Tank charge 2 Tank

Tank 4

Tank discharge 2


Centrifuge Centrifuge 2 Centrifuge

Drying Drier charge 2 Drier

Drying 5

B Pumping 1 Pumping 1 1.33 Pump 1

Reaction Reactor charge 1.33 Reactor

Reaction 3

Reactor discharge 2


Heat exchange Cooling 2 Heat exchanger

Centrifuge Centrifuge 2 Centrifuge

Drying Drier charge 2 Drier

Drying 5

schedule. Besides, using the information related to raw mate-rials selection and resources consumption provided by the tem-porisation module, the LCA and financial modules evaluate theassociated environmental and financial impact indexes, respec-tively. The termination criteria defined in the optimisation algo-rithm (either by convergence or by number of generations)determine the end of the solution process.

6. Case study

As case study, a well known academic problem from Rob-inson and Loonkar [30] is proposed (see Fig. 7). Despite beinga simple example, it facilitates the study of the proposed strat-egy and helps to understand the solutions obtained.

The system comprises eight semicontinuous and discontin-uous production units belonging to six types. A processing rateof 1500 product units per unit of time has been considered forthe semicontinuous equipment and a batch size of 2000 unitsfor the discontinuous ones. Two different raw materials havebeen considered to produce A, thus resulting in different pro-cessing times at the reaction stage. Therefore, two recipes A1and A2 are distinguished to produce A, being the selection ofraw material a subset of the decision variables. Product recipesare presented in Table 1.

Table 2

Environmental loads associated to raw materials

Environmental burdens RM1 (g/kg) RM2 (g/kg)

To the air

Particles 0.02 0.017

SO2 4.00 3.00

Hydrocarbons 0.50 0.40

NOx 4.20 4.00

CO 0.70 0.72

CO2 4000.00 3750.00

To the water

Biological demand of oxygen (BDO) 0.075 0.073

Heavy metals 7� 10�6 5� 10�6

Total dissolved solids (TDS) 0.002 0.001

To the soil

Solids 0.02 0.02


Three objectives have been considered to evaluate theschedules: cash, environmental impact and makespan. The so-lution of the problem is formed by a set of schedules (non-dominated solutions) that minimise the environmental impactand the makespan, while maximising the available cash asso-ciated to the plant.

6.1. LCA module

For the LCA evaluation, the considered inputs are electric-ity, fuel and raw materials. The electricity and raw materialshave their own environmental burden. As a result of the Inven-tory Analysis, in the following expressions the electrical en-ergy consumption and the fuel consumption as a function ofthe number of batches of product A made using raw materialRM1 or RM2 (NA1 and NA2, respectively), for a total produc-tion of N batches are shown:

Electricity ½kJ=N� ¼ 290 601:6þ 644:544NA1 þ 958:392NA2

ð11Þ

Table 3

Environmental loads associated with electricity consumption (Swiss Federal

Office of Environment [31])

Environmental burdens g/kJ

Air

Particles 5.46� 10�5

SO2 6.95� 10�4

Hydrocarbons 5.86� 10�4

NOx 3.43� 10�4

CO 9.69� 10�5

CO2 0.12268

Water

Biological demand of oxygen (BDO) 4.1� 10�8

Heavy metals 8.3� 10�10

Total dissolved solids (TDS) 8.79� 10�5

Soil

Solids 0.01364

Fuel ½kJ=N� ¼ 3:444þ 0:4592NA1þ 0:2296NA2 ð12Þ

Table 2 shows the environmental burdens of raw materialsRM1 and RM2, whereas Table 3 shows the environmental bur-dens corresponding to electricity (production, mining of en-ergy carriers and transportation), both expressed in g/kg.Finally, Table 4 shows the emissions due to the process itself.

7. Results

An initial schedule for the considered case study is obtainedwithout optimising, just sequencing the operations. Fig. 8 de-picts the Gantt chart of the identified initial schedule alongwith the cash requirements and the accumulated carbon diox-ide emission profiles. This schedule has a makespan of 71.66 hwith an environmental impact of 9967 units and a financialmeasure of 16 462 monetary units.

Table 4

Environmental loads associated with the production process

Environmental burdens g/kg Product

Air

Particles 0.017Xþ 0.002

SO2 3.6Xþ 0.001

Hydrocarbons 0.42X

NOx 3.98X

CO 0.63X

CO2 3163.5X

Water

Biological demand of oxygen (BDO) 0.025þ 0.025Y

Heavy metals 10�6þ 10�6YTotal dissolved solids (TDS) 0.002þ 0.004Y

Soil

Solids 0.02þ 0.02Y

Here, X represents kg of consumed fuel per kg of product, and Y is the number

of changes between raw materials and the number of changes between

RM1�RM2.

Fig. 8. Initial schedule.


Fig. 9. Pareto optimal solution.

From the optimisation of this initial schedule, a set of Par-eto optimal solutions is obtained. In Figs. 9 and 10 the Paretopoints by pairs of criteria are shown.

Each Pareto point identifies a non-dominated and feasibleschedule. According to the decision-maker preferences, oneof these schedules will be finally selected and implemented.Fig. 11 shows one of these schedules which have an improvedfinancial value (18 147 monetary units) with regard to the ini-tial solution. Moreover, this schedule has a makespan of71.99 h and an environmental impact of 10 167 units, soa slight increase in the makespan and the environmental im-pact may be appreciated.

In this particular case, it can be seen from Fig. 10 that somepoints show that a better cash management can be obtainedwithout losing too much in the makespan and the environmen-tal impact criteria.
Fig. 10. Three-dimensional Pareto optimal solution.


Fig. 11. Schedule corresponding to the chosen solution.

It is important to mention again that a set of approximatedPareto optimal solutions is obtained in reasonable computa-tional time and the final decision is up to the decision-maker’scriterion.

8. Conclusions

An important issue is that environmental considerationshave been addressed as an integral part of the conceptual batchprocess problem. While most of the environmental develop-ments tend to reduce waste generation, they do not explicitlyaccount for wastes associated with inputs to the process andemissions that occur during the use or final disposal of theproduct. In this work an application of the LCA approach asa way of introducing environmental considerations in an in-dustrial problem is proposed. On the other hand, it showsthe possibility of integrating another objective functions intothe traditional scheduling formulation.

Acknowledgements

Financial support received from the Spanish ‘‘Ministerio deEducacion, Cultura y Deporte’’ (FPU programs) is fullyappreciated. Besides, financial support from ECOPHOS(INCO-CT-2005-013359) and PRISM (MRTN-CT-2004-512233) projects is gratefully acknowledged.

References

[1] Shah N. Single and multisite planning and scheduling: current status and

future challenges. Foundations of computer-aided process operations.

AIChE Symp Ser 1998;75e90.

[2] Pekny JF, Reklaitis GV. Towards the convergence of theory and practice:

a technology guide for scheduling/planning methodology. Foundations of

Computer-Aided Process Operations. AIChE Symp Ser 1998;91e111.

[3] Floudas CA, Xiaoxia L. Continuous-time versus discrete-time ap-

proaches for scheduling of chemical processes: a review. Comp Chem

Eng 2004;28(11):2109e29.

[4] Grau R, Espuna A, Puigjaner L. Focusing in by-product recovery and

waste minimization in batch production scheduling. Comp Chem Eng

1994;18:271e5.

[5] Ahmad BS, Barton EI. Solvent recovery targeting for pollution preven-

tion in pharmaceutical and specialty chemical manufacturing. Volume

on pollution prevention via process and product modifications. AIChE

Symp Ser 1994;90(303):59e73.

[6] Ahmad BS, Barton PI. Synthesis of Batch Processes with Integrated

Solvent Recovery and Recycling. Presented at the AIChE Annual Meet-

ing, Miami Beach, FL, 1995.

[7] Linninger AA, Shalim AA, Stephanopoulos E, Han C,

Stephanopoulos G. Synthesis and assessment of batch processes for

pollution prevention. Volume on pollution prevention via process and

product modifications. AIChE Symp Ser 1994;90(303):46e58.

[8] Pistikopoulos EN, Stefanis SK, Livingston AG. A methodology for

minimum environmental impact analysis. Volume on pollution preven-

tion via process and product modifications. AlChE Symp Ser 1994;

90(303):139e50.

[9] Stefanis SK, Livingston AG, Pistikopoulos EN. Environmental impact

considerations in the optimal design and scheduling of batch processes.

Comp Chem Eng 1997;21(10):1073e94.

[10] Canton J. Integrated support system for planning and scheduling of batch

chemical plants. PhD Thesis, Universitat Politecnica de Catalunya,

Espana, 2003.

[11] Graells M, Canton J, Peschaud B, Puigjaner L. General approach and tool

for the scheduling of complex production systems. Comp Chem Eng

1998;22(Suppl):S395e402.

[12] Charnes A, Cooper WW, Ijiri Y. Breakeven budgeting and programming

to goals. J Acc Res 1963;1(1):16e43.

[13] Robichek AA, Teichroew D, Jones JM. Optimal short-term financing de-

cision. Manage Sci 1965;12(1).

[14] Orgler YE. Cash management. California: Wadsworth; 1970.

[15] Srinivasan V. Deterministic cash flow management. Omega 1986;14(2):

145e66.


[16] Badell M, Romero J, Puigjaner L. Planning, scheduling and budgeting

value-added chains. Comp Chem Eng 2004;28:45e61.

[17] Romero J, Badell M, Bagajewicz M, Puigjaner L. Integrating budgeting

models into scheduling and planning models for the chemical batch

industry. Ind Eng Chem Res 2003;42:6125e34.

[18] Yi G, Reklaitis GV. Optimal design of batch-storage network with finan-

cial transactions and cash flows. AIChE J 2004;50(11):2849e65.

[19] Shapiro JF. Challenges of strategic supply chain planning and modelling.

Comput Chem Eng 2004;28:855e61.

[20] ISO 14040. Environmental managementelife cycle assessment e princi-

ples and framework. ISO; 1997.

[21] ISO 14041. Environmental managementelife cycle assessment e scope

and goal definition and life cycle inventory analysis. ISO; 1998.

[22] ISO 14042. Environmental managementelife cycle assessment e life

cycle impact assessment. ISO; 2000.

[23] ISO 14043. Environmental managementelife cycle assessment e life

cycle interpretation. ISO; 2000.

[24] Guinee JB, Gorree M, Heijungs R, Huppes G, Kleijn R, Koning A, et al.

Handbook on life cycle assessment. Operational guide to the ISO stan-

dards. Dordrecht: Kluwer Academic Publishers; 2002.

[25] Jensen AA, Hoffman L, Møller BT, Schmidt A, Christiansen K,

Elkington J, et al. Life Cycle Assessment (LCA). A guide to approaches,

experiences and information sources. European Environmental Agency;

1998.

[26] Jaszkiewicz A. Multiple-objective metaheuristics algorithms for combi-

natorial optimisation. Habilitation Thesis, 360, Poznan University of

Technology, Poznan, 2001.

[27] Coello CA. A comprehensive survey of evolutionary-based multiobjec-

tive optimisation techniques. Knowledge and Information Systems. An

International Journal 1999;1(3):269e308.

[28] Deb K. Multi-objective optimization using evolutionary algorithms. John

Wiley & Sons, Inc.; 2001.

[29] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjec-

tive genetic algorithm: NSGA-II. IEEE Trans Evol Comput 2002;6(2).

[30] Robinson JD, Loonkar YR. Minimising capital investment for multipur-

pose batch plants. Process Technol Int 1972;17:861e3.

[31] Swiss Federal Office of Environment, Forests and Landscape (FOEFL).

Ecobalance of packaging materials state of 1990. Berne: FOEFL; 1991.

Marıa Jose Arbiza is a PhD student in the Chemical Engineering Depart-

ment of UPC. She obtained her degree in Chemical Engineering at the Uni-

versidad Nacional de Mar del Plata, Buenos Aires (Argentina), in 1998.

During her stay at UPC, she has worked in several research projects and

has participated in conference and congresses. Her research interests are

in the area of scheduling and rescheduling in batch, continuous and semi-

continuous plants.

Anna Bonfill is a PhD student at the Chemical Engineering Department of

UPC. She obtained her degrees in Chemical Engineering from the Univer-

sitat de Barcelona. Her research interests focus on the development of sto-

chastic techniques, either rigorous or heuristic-based, for planning and

scheduling under uncertainty. She has developed decision-support frame-

works to proactively address the problem of uncertainty in product de-

mands, operation times and equipment availability, incorporating some

risk management considerations. She has also extended the production

scheduling architecture to incorporate transport scheduling within a multi-

site system.

Gonzalo Guillen is a PhD student in the Chemical Engineering Department of

UPC. He obtained his degrees in Chemical Engineering at the Universidad de

Murcia, Murcia (Spain), in 2001. His research interests are in the area of pro-

cess systems engineering. Specifically, he has developed novel mathematical

tools for supply chain management (SCM), which incorporate customer satis-

faction, environmental, financial and risk management considerations. He has

also developed decomposition techniques aiming at the reduction of the com-

putational effort associated with the resolution of large-scale mixed-integer

lineal problems (MILP) arising in the area of optimisation under uncertainty.

He has published five papers, eight book chapters, and has 19 conference

presentations.

Fernando Daniel Mele received the degree in Chemical Engineering in 2000

from the Universidad Nacional de Tucuman, Argentina. His research interests

include the development of computational tools to support the decision-mak-

ing in the area of Supply Chain Management. He has worked on simulation-

based optimisation with the inclusion of important elements taken from the

areas of planning under uncertainty and multiobjective optimisation, among

others. Special consideration has been devoted to models and algorithms for

environmentally conscious supply chain optimisation.

Antonio Espuna has a PhD Excellence Award in Chemical Engineering from

UPC. He is an Associate Professor at the Chemical Engineering Department eUPC and the coordinator of the subjects on Environmental Management and

Separation Processes. His research interests are mainly process modelling,

with special emphasis in Process Integration and Intensification for a sustain-

able development. This contemplates the optimum design and operation of the

complete supply chain through the entire product life cycle under multiobjec-

tive criteria (productivity, environmental impact, safety, resources optimisa-

tion) that also accounts for the different levels of detail (strategic, tactical

and operational) and diverse optimisation techniques (mathematical program-

ming, stochastic methods, LCA, etc.). Since 1985, he has participated in more

than 20 RTD projects in these areas, both founded by private industries and

organisations and public research institutions. He has published over 60 re-

search papers and more than 140 communications at conferences.

Professor Lluis Puigjaner is Professor of Chemical Engineering at UPC and

Director of the Environmental Centre. He was Head of the Chemical Engineer-

ing Department for six years and Director for Research and Development at

the Higher Technical School of Industrial Engineering. His professional expe-

rience includes positions at several Institutions (Purdue University, Stanford

University, Max Planck Institute, and King’s College, University of Houston,

Imperial College, Cork Technical College, UNAM, UNICAMP and NASA).

He is the national delegate in the Working Party of CAPE of the EFCE and

belongs to the Executive Committee of Industry in the Official Chamber of

Commerce, Industry and Navigation of Barcelona. He has published over

350 papers and is the author of over 100 technical reports and editor/co-editor

of 10 books. He serves in the Editorial Board of Computers and Chemical En-

gineering, Computers and Chemistry, Engineering and Processing, Journal of

Process Control, Automatica e Instrumentacion (CETISA), Science and Tech-

nology of Environmental Protection (ISEP). He has been awarded by several

Honour Societies and received the Award of Technology Innovation from

Rhone-Poulenc, Narcis Monturiol Medal to distinguished Scientists, Gaspar

de Portola Award, ESPRIT-PACE Technology Innovation Award. He is in

charge of a Group on Design, Operation and Control of Chemical and Biotech-

nology Processes (TQG), which involves 35 researchers.

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