[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-392825-105":53,"doc-detail-392825-en":127},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","124-design-of-single-product-processing-sequences","12.4 DESIGN OF SINGLE PRODUCT PROCESSING SEQUENCES","","Section 12.4 focuses on designing batch processing sequences for single-product manufacturing. It explains that scheduling and batch cycle-time optimization can be computationally demanding when recipes include many tasks and units, so batch times are often specified per equipment task while optimizing cycle time for a given recipe. The section describes how recipes map tasks to equipment, how task integration and equipment sizing determine feasible batch sizes and times, and how scheduling is visualized using equipment occupation diagrams such as Gantt charts to identify bottlenecks and bottleneck-driven cycle times.",{"@graph":63,"@context":119},[64,80,102],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/124-design-of-single-product-processing-sequences/392825/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/124-design-of-single-product-processing-sequences/392825.png","ImageObject",442,249,{"name":88,"@type":89},"Ben ","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-19","2026-09-25",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",6,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"Why is it often impractical to optimize batch times for individual processing units in practice?","Question",{"text":109,"@type":110},"Because real processes typically have recipes with many tasks and processing units, making unit-by-unit batch-time optimization computationally demanding when preparing schedules.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How are batch cycle times determined and visualized in the scheduling framework?",{"text":114,"@type":110},"Cycle time is measured between completions of batches, and equipment occupation is visualized with a Gantt chart showing when each equipment item is utilized, revealing bottlenecks.",{"name":116,"@type":107,"acceptedAnswer":117},"What does the bottleneck unit mean in the context of batch scheduling?",{"text":118,"@type":110},"The bottleneck is the unit with the longest batch time, so it remains in operation continuously; the cycle time is effectively its batch time.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},392825,1791480183,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":136,"language":137,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":138,"faqs":139,"seo_title":140,"seo_description":61,"update_tm":141,"read_time":76},2336478951081,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","nn,and  \nduring  \nities are  \nluring a  \nfor the  \nme):  \nProfiles28hr-1  \nwhere T,is the batch time for the reactor and t.is the column operating time.In addition,as the opti-mization proceeds,it is necessary to satisfy the following inequality constraints:  \nT1o≤Thor  \nT,一(t,+te)≥0  \nTe一(tc+tcc)≥0  \nFor the specifications in Table 12.1,the following solution was obtained using successive quadraticprogramming(SQP)in GAMS(see Section 18.6).The reactor operates for t,=4.44 hr to produce aproduct containing 0.062,0.373,and 0.565 mole fractions of A,B,and C.For periodic cycling,its batchtime,T,=18.74 hr,which exceeds the total of the reactions and cleaning times.The distillation columnoperates for tc=3.69hr,which together with its cleaning time,tcc=0.5 hr,gives a batch time for thecolumn,T。=4.19 hr.The total time,or cycle time,is Tou=22.93 hr,which falls within the horizontime specified,Thor=24 hr.These times correspond to the minimum cost,φ=$10,240.By varyingt,it can be shown that this is the minimum cost.■  \n# 12.4 DESIGN OF SINGLE PRODUCT PROCESSING SEQUENCES\n\nHaving examined small optimal control problems for batch process units in Section 12.2 andfor reactor-separator sequences in Section 12.3,it should be clear that the determination ofoptimal batch times,given batch sizes expressed as batch volumes per unit mass of product,can be demanding computationally.Since most processes,in practice,have recipes with nu-merous tasks and a comparable number of processing units(e.g.,the tPA process in Chapters3 and 4),it is normally not practical to optimize the batch times for the individual processingunits when preparing a schedule of tasks and equipment items for the manufacture of a prod-uct.Consequently,when preparing a schedule of tasks and equipment items,it is common tospecify batch times for tasks to be performed in specific units,usually with batch sizes,andto optimize cycle times for a specific recipe.In some cases,using the rates of production andyields,the vessels are designed as well;that is,vessel sizes are determined to minimize thecost of the plant while determining the cycle times for a specific recipe.In this section,schedules are determined for the batch processes that involve only single products.In thenext section,the methodology is extended for multi-product batch processes.  \nBatch process design begins with the specification of a recipe of tasks to produce a prod-uct.In continuous processing,each task is carried out in a specific equipment item,with one-to-one correspondence between them,shown on a flowsheet that remains fixed in time.Similarly,in batch processes,the tasks are assigned to equipment items,but over specific in-tervals of time,which vary with batch size,which is often determined by the available equip-ment sizes.For example,in the tPA process in Sections 3.4 and 4.5,given the rate of tPAproduction [50 pg tPA/(cell-day),where pg are picograms =10-¹²]and the cell concentra-tion(between 0.225×10⁶and 3×10⁶cell/mL),the availability of a 5,000-L cultivator de-termines the 14-day batch time and the batch size(2.24kg of tPA,produced in 4,000 L ofmedium,yielding 1.6 kg of final product)for the cultivator.As discussed in Section 3.4,process synthesis involves the creation of a sequence or flowsheet of operations,which canbe referred to as a recipe of operations or tasks.During the task integration step,tasks areoften combined to be carried out in a single equipment item;for example,heating and reac-tion in a pyrolysis furnace.Also,during this step,the decision to use continuous or batchprocessing is made.At this point,the available equipment sizes often determine the batchsizes and times.  \nBatch Cycle Times  \nWhen scheduling and designing batch processes,several formalisms are widely used,as re-viewed by Reklaitis(1995).In this section,and those that follow,portions of the presentationare derived from his article.  \n396 Chapter 12 Optimal Design and Scheduling of Batch Processes  \nIn batch processes,it is c","cbCainuveNSKsAWd","https://ap.wps.com/l/cbCainuveNSKsAWd","pdf",2145613,7,"English","# 12.4 DESIGN OF SINGLE PRODUCT PROCESSING SEQUENCES\n## Batch process design and recipe formulation\n## Batch cycle times and scheduling concepts","[{\"question\":\"Why is it often impractical to optimize batch times for individual processing units in practice?\",\"answer\":\"Because real processes typically have recipes with many tasks and processing units, making unit-by-unit batch-time optimization computationally demanding when preparing schedules.\"},{\"question\":\"How are batch cycle times determined and visualized in the scheduling framework?\",\"answer\":\"Cycle time is measured between completions of batches, and equipment occupation is visualized with a Gantt chart showing when each equipment item is utilized, revealing bottlenecks.\"},{\"question\":\"What does the bottleneck unit mean in the context of batch scheduling?\",\"answer\":\"The bottleneck is the unit with the longest batch time, so it remains in operation continuously; the cycle time is effectively its batch time.\"}]","12.4 DESIGN OF SINGLE PRODUCT PROCESSING SEQUENCES | PDF",1790374749]