Novel Continuous Time MILP Formulation for Multipurpose Batch Plants. 2. Integrated Planning and Scheduling

During the last two decades, the problem of short-term scheduling of multiproduct and multipurpose batch plants has gained increasing attention in the academic, research, and manufacturing communities, predominantly because of the challenges and the high economic incentives. In the last 10 years, numerous formulations have been proposed in the literature based on continuous representations of time. The continuous-time formulations have proliferated because of their established advantages over discrete-time representations and in the quest to reduce the integrality gap and the resulting computational complexities. The various continuous-time models can be broadly classified into three distinct categories: slot-based, global event-based, and unit-specific event-based formulations. In this paper, we compare and evaluate the performance of six such models, based on our implementations using several benchmark example problems from the literature. Two different objective functions, maximization of profit and minimization of makespan, are considered, and the models are assessed with respect to different metrics such as the problem size (in terms of the number of binary variables, continuous variables, and constraints), computational times (on the same computer), and number of nodes needed to reach zero integrality gap. Two additional computational studies with resource constraints such as utility requirements are also considered.

Modeling and Optimization for Short-term Scheduling of Multipurpose Batch Plants

The increasing interest in multipurpose batch plants is evident, because of their inherent flexibility to cope with an ever changing market environment. These plants are easily reconfigured for product modifications, to cover a wide range of operating conditions. They are also suitable for producing different products within the same facility. In spite of this advantage, the design, synthesis, and scheduling of multipurpose batch plants can be a challenging task. This paper addresses design, synthesis, and scheduling simultaneously. It is known that the scheduling platform employed has a significant impact on the computational performance of the overall model in the design and synthesis of batch plants. The recent scheduling model that results in better computational efficiencies is extended to incorporate design and synthesis. Computational studies are presented to illustrate the effectiveness of the proposed model. A comparison with earlier formulations showed that better computational times and objective functions were obtained by this work.

Design, synthesis and scheduling of multipurpose batch plants via an effective continuous-time formulation

This report with recommendations is the result of an expert panel meeting on PAT applications in food industry that was organized by the M3C Section of the European Society of Biochemical Engineering Science (ESBES) at the 10th ESBES Symposium. The aim of the panel was to provide an update on the present status of the subject and to identify critical needs and issues for wider applications of PAT in food industry. A brief description of the current state-of-the-art and industrial uptake of the methodology is provided in this report. It concludes with a number of recommendations to facilitate further developments and a wider application of PAT in food industry. Process Analytical Technologies (PAT) [1] (European Medicines Agency EMA-FDA pilot program for parallel assessment of Quality by Design applications; Document EMA/172347/2011) have been extensively discussed in literature, particularly with respect to (bio)pharmaceutical process modelling, monitoring and control [2]. Table 1 provides an historic overview of the PAT development in the context of food applications. Although successful applications within food industry are increasingly being reported [3, 4], the session on PAT in food industries at the ESBES-IFIBiop 2014 in Lille highlighted significant challenges and opportunities for further development in this area. This position paper briefly reviews the current state-of-the-art, industrial needs and opportunities as well as scientific challenges to be addressed in order to extend the use of PAT methodology in the food industries. Currently, quality and safety control are still based mainly on discontinuous analysis with traditional analytical methods in the lab or, at best, at-line measurements. This is no longer sufficient to fulfill the needs of the food industry. Due to higher safety and quality standards and demands and high throughput of production facilities, the number of samples to be analyzed is increasing. Rapid analysis methods and PAT are required to address these needs along the complete production chain leading to a better understanding and control of raw materials, intermediate products in the production process as well as the final products to be packaged and delivered. The goal is to achieve real time analysis in order: • to avoid usage of any out-of-specification raw material and to detect adulteration, substitution, tampering and counterfeiting leading to non-authentic products; • to be able to intervene and stop/change processes in order to secure the target quality; • to assess the final quality to avoid out-of-specification products being packaged and shipped, thus leading to undesirable customer dissatisfaction and costs associated with the resolution of complaints. Over a hundred years ago (on May 22nd, 1913) the first patent on a PAT device ("Pfeiffenanalysator" for measuring the ratio of H2 and N2 gas for ammonia synthesis) was granted to Paul Gmelin from Badische Anilin- und Soda-Fabrik, BASF (Patentschrift Nr. 281157, Klasse 42/. Gruppe 4). Since then, PAT found broad application in chemical industry, which is dominated by highly automated, continuous processes. Today in chemical processes, such as the synthesis of isocyanates, e.g. hexamethylendiisocyanate (HDI), typically 60-130 PAT measurements are collected. In contrast, in sectors like (bio)pharmaceutical or food industry, the application of PAT is significantly less frequent today, especially, in terms of on-line analytics, where the measurement takes place in or close to the production step (or unit operation). One reason for this is the reduced degree of automation of the processes in these industries, which are dominated by unit operations, single production steps consecutively executed after each other, resulting in production batches. Analytics of a production batch takes place mostly off-line in analytical laboratories during hold-up times of the process intermediate between the different unit operations. Regulatory requirements represent an equally important driver for extensive online analytics. With the 2004 FDA's Quality by Design initiative, regulatory agencies demand systematic risk based process development and understanding of the processing space. This also allows for flexible process adjustments within the explored space for producing the desired product quality. In order to achieve the required understanding, more extensive analytical data is required, ideally obtained in-time on raw materials, process intermediates and ideally also on product quality attributes. In food industry, where typically high product titers are obtained, product analytics is sometimes possible by in-line measurements, such as spectroscopy (section 4). In biopharmaceutical processes, product titers are usually very low, the products are proteins with high molecular weight, and quality attributes are challenging to analyse. In these situations, online sampling with automated sample preparation and analytics may open up a solution [5]. But, identifying and implementing analytical methods, which are fast enough for delivering results on product quality attributes (e.g. protein glycosylation) in time, during the unit operation for allowing process modulation, remains a challenge. The overall typical goals in industry are high safety, high and stable product quality, high yield, low consumption of resources (materials, energy, room, time, and people), reduced influence of variability in raw materials as well as an increased shelf life of products which holds also in food processes. However, compared to the chemical and biopharmaceutical industries, food industry has to deal with certain characteristics, which renders PAT a formidable challenge in this context. The characteristic features in food industry are: • Raw materials are not pure substances: they are complex combinations of pure substances with varying compositions • Raw materials are soft, variable size, fragile and slippery • Physical properties of raw materials depend heavily on temperature, pressure, moisture and harvesting, and storage conditions • Raw materials undergo usually a phase transformation during processing and hence change their physical properties during processing • Micro processes (physical, (bio)-chemical, microbiological) are frequently not known • Highly perishable products. Here the challenge is to produce good quality, which maintains for a long time (shelf life) • High demand for hygiene These characteristics lead to a challenge for the application of sensors in the food industry. For important quality and process variables, such as sensory assessment, micro flora or spoilage, reliable and robust sensors are not yet available. Moreover, the sensors which are available are typically used only in isolated applications and frequently provide insufficient reliability. They are often not integrated in a common data management infrastructure. The materials of construction do not always consider suitability of contact with food and the solutions developed within advanced research projects frequently demand high care and maintenance. One reason why PAT is not as common as in other areas is that in food industry knowledge from various subject areas is necessary (such as physics, chemistry, biology, mathematics, informatics, engineering, nutritional science). For unit operations mathematical models are available in principle, but frequently they are too complicated to adapt. One of the biggest challenges in food industries is the dynamic nature of the processes. Changes in geometry, porosity, microstructure, solubility as well as mass and energy transfer coefficients must be addressed. Mostly gradients of temperature and moisture have to be considered as well as changes in kinetic parameters during process run. End product qualities like color, smell and 'brokens' also strongly influence the process. Therefore, food processes can be considered to be significantly more complex then chemical and bio-pharmaceutical processes. To achieve more stable processes PAT applications are necessary to check the quality of the raw and processed materials and their relationship to each other. If the quality is changing, then control actions resulting in online parameter changes are required in order to maintain constant product quality. Measurement systems are required, which guarantee that the process is in accordance with recipe and formulation. Furthermore, disturbances must be compensated for using control actions to reduce process variability and to conform to food regulations. As Glassey [6] argues, PAT methodology can aid in product design and testing as well as in ensuring full compliance with the HACCP and ISO 22000:2005 requirements during processing. As demonstrated below, PAT methodologies have the potential to aid the identification of critical control points and their critical limits, their effective monitoring and control, but also effective communication with suppliers and customers. Documentation which requires measurements of important variables is especially important so that traceability can be guaranteed. Here PAT has to deliver the corresponding measurement systems. Clearly a high demand for PAT in food industry is evident as is the need for further developments in the science and technology that help address the specific challenges posed by the characteristics of the food industry highlighted above. The complexity of raw materials that are typically soft and easily damageable is arguably one of the major scientific and technological challenges in food industry. During storage and processing the quality of such raw materials can decline due to oxidation processes, pressure and temperature effects. In addition, the visual impression of the final product (i.e. its appearance) is much more important than in other industries due to the fact that this will influence the purchase decision of the consumer. During the whole processing from raw material to the storage of the final product, hygiene is of utmost importance. Therefore non-invasive sensor systems are required in these applications. Measurement systems based on optical principles are particularly suitable from this perspective. Such measurement systems, including near infrared (NIR), Raman and fluorescence spectroscopy as well as computer-assisted image-based systems, potentially have a number of advantages in food process supervision and automation. Spectroscopic methods and imaging devices are well suited for PAT purposes because they are fast, non-destructive, provide multiple chemical information, allowing remote in-process analysis via fiber optics or instruments mounted directly on-line. Fluorescence spectroscopy is the most sensitive spectroscopic technique. Recently, many applications have been developed using fluorescence techniques [3, 7, 8]. Raw materials, the supervision of processing as well as product quality and the contamination of the equipment can be monitored by fluorescence. For example, Everard et al. [3] presented a method for detection of fecal contamination on spinach leaves. They coupled three hyperspectral imaging (HSI) configurations with two multivariate image analysis techniques and compared fluorescence imaging in the visible region with ultra violet and violet excitation sources, and reflectance imaging in the visible to near-infrared regions. They showed, that both fluorescence configurations had 100% detection rates for fecal contamination up to 1:10 dilution level and violet HSI had 99% and 87% detection rates for 1:20 and 1:30 levels, respectively. Everard et al. emphasized that on-line detection of fecal contamination on leaves has the potential to reduce the cases of food borne illnesses and their associated costs. A similar approach is presented by Lee et al. [7] where bovine faeces on Romaine lettuce and baby spinach leaves were investigated. They pointed out that two-band ratios using bands at 665.6 nm and 680.0 nm for lettuce and at 660.8 nm and 680.0 nm for spinach effectively differentiated all contamination spots applied. Grote et al. [8] described a fluorescence measurement technique to monitor a sourdough fermentation process. For the prediction of pH value and acidity during rye sourdough fermentations they applied partial least squares regression and principal component regression models for prediction and compared them with an evaluation where principal component analysis was combined with artificial neural networks. Depending on process operation and evaluation technique the average percentage root mean square errors of prediction for pH values were between 2.5 and 5.1%. For the prediction of the acidity level, the best results were between 6.0 and 8.1%. Liu et al. [9] used the Hoffman reaction to convert acrylamide to a compound which shows strong fluorescence emission at 480 nm. They showed good correlation of acrylamide in the range of 0.015 μg/mL to 20 μg/mL. Using this technique the food security will be increased. A fluorescence imaging device to detect deli residues on deli slicers were used by Beck et al. [10] processing four cheeses and four processed meats. The authors suggested that a fluorescence imaging device can be applied for routine use even in delicatessens. Fig. 1 clearly shows that the application of fluorescence for the monitoring of food processes increased from less than 10 before 2003 to more than 60 a year since 2013. This figure includes all papers from a search containing the key words "Food" and "Fluorescence". Although most of these papers describe laboratory applications rather than industrial PAT applications, they indicate potential future applications in this technology in food industry. Number of published papers obtained from the Scopus database searching for the words "Food" and "Image analysis" or "Raman" or "Near infrared spectroscopy" or "Fluorescence spectroscopy". Raman spectroscopy can only be applied if no fluorescence occurs in the corresponding excitation range. He et al. [11] applied the surface enhanced Raman scattering spectroscopy to detect banned food additives, such as Sudan I dye and Rhodamine B in food, Malachite green residues in aquaculture fish. They concluded, that Raman spectroscopy and chemometric evaluation techniques can be used to identify banned food additives to ensure food safety. Ilaslan et al. [12] presented a method based on Raman spectroscopy to provide a rapid method for evaluating the quantitative analysis of glucose, fructose, and sucrose in soft drinks. Wang et al. [13] applied a Raman spectrometer as a process analyzer to monitor the wine fermentation. They demonstrated that sugar, ethanol and glycerol can be measured on-line with high correlation (higher than 0.98) to the HPLC reference measurements. Nache et al. [14] investigated Raman spectra from pork meat to monitor the early postmortem lactate accumulation and pH decline. They suggested that the locally weighted regression applied to the standard normal variate (SNV) normalized Raman spectra provide one of the most accurate and robust models with a cross-validated coefficient of determination (r2cv) of 0.97 for pH and lactate, a cross-validated root mean square error (RMSECV) of 4.5 mmol/kg for the lactate prediction and 0.06 pH-units for the pH prediction. These results demonstrate significant potential of combining chemometrics and Raman spectroscopy for on-line meat quality control applications. Fig. 1 shows the number of papers recorded in Scopus (search words "Food" and "Raman"). Compared to fluorescence, the number of papers describing Raman spectroscopy is twice as high in recent years with a significant rate of increase, demonstrating the increasing interest in this method for food process monitoring. Computer vision systems enable one of the main aspects of consumer preference – the appearance of a product – to be inherently considered. Therefore, computer vision systems for the supervision of food processing also gained importance over the years. An overview of several examples is given by Sun [15]. Especially the supervision of food drying processes is discussed by Aghbashlo at al. [16]. They pointed out that there is a large unexploited potential in the image data captured during various food processing operations. More informative feature extraction algorithms or novel pattern recognition procedures have to be developed. Paquet-Durand et al. [4] described a system for the supervision of the baking process. They demonstrated, by using the Viola–Jones-algorithm as well as neural networks, that the pastry can be identified and the volume increase as well as color development can be monitored. To detect defective apples Zhang et al. [17] used a computer vision system, which was combined with an automatic lightness correction system. For 160 samples they showed a 95% overall detection accuracy. For the evaluation they used a weighted relevance vector machine classifier. Fig. 1 shows the number of papers over time from Scopus searching for "Food" and "Image analysis". Here the applications start earlier compared to the spectroscopic methods, the number of applications per year is higher than in the case of spectroscopic applications; except in the year 2014, where more reports of Raman applications were published. Moreover imaging systems using visible and NIR region are available to perform quality checks based on the spectroscopic information derived from each point in the image. One example is the on-line analysis of the widely varying fat distribution in salmon for sorting purposes [18]. Near infrared (NIR) is a well-established method for rapid analysis of food raw materials and products [18], either on-/in-line, at-line or off-line. In the lab or at-line multiple components such as fat, protein, moisture and many more, can be analyzed without any sample preparation in all kinds of liquid, solid and semi-solid samples. Raw materials can be verified for identity and further characterized regarding composition already in the goods reception. The composition, freshness and adulteration of edible oils [19], e.g. olive oil [20], can be analyzed rapidly before a truck is unloaded. Many other sample types like meat, grains, flour, dairy products [21] and others can be analyzed. Even mixtures like vitamin premixes can be analyzed to make sure that the correct material was delivered and can be used in production. There are several approaches and technologies for PAT available, ranging from simple filter based devices over dispersive diode array spectrometers to Fourier-Transform (FT)-NIR instruments. Samples can be analyzed in-line by fiber optic probes or by contactless systems (Fig. 2). Smaller instruments can be directly attached to pipes, chutes or in other installations. A) NIR reflection probe in a fluid bed dryer. (B) Probe head for contactless measurement of grain and other solids. Applications cover a broad range from a simple monitoring of moisture content of a product on a conveyor belt to more complex control situations. In dairy industry there are demands to control milk powder production by monitoring the feed of the spray tower and the powder after fluid bed drying. Other important production steps to control are the standardization of milk, cream, whey and concentrates [22]. In frying processes with big volumes of oil an in-line monitoring of the oil quality with regards to acid value, anisidine value and the content of polar and polymerized components [23] are of particular interest. Another example of high volume processes where monitoring of protein, moisture and ash is important is the milling of grain to flour and the production of cereals of any kind. Finally there are more and more fermentation processes controlled by in-line NIR to optimize the conditions and follow the feeding and consumption cycles during biomass buildup [24]. In 2013 roughly 120 papers were published, however the recent increase is not as steep as in the case of Raman spectroscopy (Fig. 1). The economic benefits due to PAT can be attributed to higher product quality and yield as well as decreased product variation. This will reduce the overall production costs significantly and increase competitiveness. Furthermore, the knowledge and understanding of the process will increase. However, the level of automation in industrial food processes is significantly lower compared to the chemical and pharmaceutical processes. This is partly due to the complexity of food processes. On the other hand, the lack of reliable sensor systems to determine important process parameters and variables contributed to this in the past. Sensors represent a fundamentalpart of all automation systems, although they only represent a part of the requirements for wider application of PAT in food industry. The areas of further development and recommendations enabling more extensive use of the PAT within this industry also include: • Further industrial case studies and wider dissemination of the positive impact of reliable sensor technology in raw material and product quality as well as process monitoring. • Operational and maintenance requirements of sensor technologies will remain a significant aspect of future sensor technology uptake in this industry. • Data management and analysis software will play a significant role in extending the PAT application within the food industry. Platform solutions, preferably supporting wireless data transfer, at competitive pricing levels are required. • Cost benefit analysis studies are particularly important given the business drivers of this industry. • The impact of PAT is likely to be more pronounced in the new processes, although it is important to continue to encourage the application of PAT approaches within established food processes to enhance the process economics and compliance with the standards ensuring safe food supply chains. • PAT can significantly contribute to the stringent traceability and documentation requirements, although issues of compatibility and data standardization will impact upon data management systems employed by the companies within the supply chain. The authors declare no financial or commercial conflict of interest.

Effective scheduling of a large-scale paint production system

A novel mathematical formulation for short-term scheduling of multipurpose batch plants in chemical manufacturing

In this chapter, the concept of the state sequence network (SSN) representation, which is the cornerstone of the material entailed in this textbook, is presented. This representation is based on states only, eliminating the use of tasks and units. Using this new representation as a basis, a novel continuous time MILP formulation for short-term scheduling of multipurpose batch plants is developed (Majozi and Zhu, 2001, Ind. Eng. Chem. Res., 40(25): 5935–5949). The presented formulation can readily be extended to intermediate due date scenarios. Time points are used to denote the use or production of a particular state. This formulation leads to a small number of binary variables and much better results when compared to other continuous time formulations published in literature. The reduced number of binary variables is a result of considering states only, thereby eliminating binary variables corresponding to tasks and units. This method has been applied to literature examples and industrial problems which show significant improvement in reducing the number of binary variables, hence CPU times. The last section of this chapter introduces the concept of units aggregation in reducing the binary dimension of large-scale problems. This makes it possible for the method to solve large-scale industrial problems. In the forthcoming chapters of this textbook it will be demonstrated how this formulation is applied in the context of batch process integration with the ultimate aim of freshwater and energy optimization.

ADVERTISEMENT RETURN TO ISSUEPREVCorrespondenceComments on “New General Continuous-Time State−Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants” by Christos T. Maravelias and Ignacio E. Grossmann and on “Enhanced Continuous-Time Unit-Specific Event-Based Formulation for Short-Term Scheduling of Multipurpose Batch Processes: Resource Constraints and Mixed Storage Policies” by Stacy L. Janak, Xiaoxia Lin, and Christodoulos A. FloudasChristodoulos A. Floudas and Stacy L. JanakView Author Information Department of Chemical Engineering, Princeton University, Princeton, New Jersey 08544-5263 Cite this: Ind. Eng. Chem. Res. 2005, 44, 6, 1985–1986Publication Date (Web):February 19, 2005Publication History Published online19 February 2005Published inissue 1 March 2005https://doi.org/10.1021/ie050135jCopyright © 2005 American Chemical SocietyRequest reuse permissions This publication is free to access through this site. Learn MoreArticle Views290Altmetric-Citations1LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (37 KB) Get e-AlertscloseSUBJECTS:Mathematical methods,Theoretical models Get e-Alerts

Summary of the Basic StepsThe basic steps in the suggested procedure for the optimal design of multi-purposebatch plants can be summarized as follows:1. List the candidate product groups.2. Obtain the super-structure that contains the candidate groups.3. Derive the horizon constraints..4. Examine the horizon constraints. If at least one horizon constraintimplicitly contains all the time periods, complete the merged formulationand solve the MINLP given in Equations (38) to (44) with the correspondinghorizon constraints. Otherwise, go to step 5.5. Select a product(s) that breaks the loop(s) in the super-structure. Treat thechosen product(s) as two or more artificial products.6. Revise the super-structure to include the additional products. Verify thatthe loop is broken. If this condition is met, go to step 7. Otherwise,return to step 5 and modify the products chosen for splitting.7. Derive the multi-period form of the constraints for the product(s) that aresplit into its (their) values for the time periods in which it (they) appear.Formulate the merged representation of the model for the rest of theproducts, including the horizon constraints. At least one horizonconstraint will contain implicitly all the time periods.Example 2The seven product, ten stage example problem of Suhami and Mah (1982) has beensolved to illustrate the design of a large multi-purpose batch plant. From the super-structure of this problem (Figure 4), the horizon constraints shown in Table II arederived.Using these constraints, the example has been solved with the merged formulation.Data for this problem appears in Table III. In addition, the following specificationshave been used: H = 6200 hr, a = 250 SFr, fi = 0.6, 1 < N <, 3, and 250 < V£ 10,000. As seen in Table IV, the MINLP formulation involves 48 variables and 67constraints. MINOS/Augmented (Murtagh and Saunders, 1980) required 16.09 secondsof CPU-time on a DEC-20 computer to solve the relaxed nonlinear program.

A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty

A new robust optimization approach for scheduling under uncertainty:: I. Bounded uncertainty

PurposeThis paper aims to develop a bi-objective mixed integer non-linear programing model to optimize the supply chain networks consisting of raw material providers, final product manufacturers and distribution centers. Raw material substitution caused by varying raw material supply amounts, prices and carbon emissions and final product substitution due to different product prices and carbon emissions are considered.Design/methodology/approachThe proposed model aims to achieve total profit maximization and total carbon emission minimization. The objective function of carbon emissions is converted into a maximization problem by changing minimum to maximum. The composite objective function is the weighted sum of the bias value of each objective function. The model is then solved using software Lingo12.FindingsNumerical analysis results show that an increase in the number of alternate raw materials for original raw material helps improve supply chain network performance, and variation in that number causes detectable but not significant changes in downstream final product substitution results.Originality/valueThe major differences between this work and existing research are as follows: first, although previous research considered carbon emissions in supply chain network optimization, it has not considered the substitution effects of products or raw materials. This paper considers the substitution of both raw material and productions. Second, the item substitution considered by previous research is derived from inventory shortage or price difference of original items. However, the substitution considered in the present paper is a response to differences in purchase price, production cost and carbon emissions for items.

The application of Nerin Recycling Technologies (NRT) in electronic waste (E-waste) smelting was introduced in this study, and the material and energy balance was calculated based on the practical data with the METSIM software (METSIM International, USA). The main results are as follows: (1) the optimized processing parameters in the NRT smelting practice were the E-waste feeding rate of 5.95 t/h, oxidation smelting duration of 3.5 h, reduction smelting duration of 0.5 h, oxygen enrichment of 21–40 vol.%, oxygen consumption of 68.06 Nm3/ton raw material, slag temperature of 1280 °C, slag composition: Fe/SiO2 mass ratio of 0.8–1.4, CaO, 15–20 wt.%, Cu in crude copper ≥ 95 wt.%, Cu in slag, 0.5 wt.%, recovery of Cu, Au, and Ag ≥ 98%; (2) 98.49% Au, 98.04% Ag, 94.11% Ni, and 79.13% Sn entered the crude copper phase in the smelting process, 76.73% Pb and 67.22% Zn volatilized to the dust phase, and all halogen elements terminated in the dust and off-gas; (3) total heat input of the process was 79,480 MJ/h, the energy released by chemical reactions accounted for 69.94% of the total, and heat from fuels burning accounted for 33.04%. The energy brought away by the off-gas was 38,440 MJ/h, which was the largest part in heat output. The heat loss with the smelting slag accounted for 28.47% of the total.

Priority-rule based scheduling of chemical batch processes