Rigorous approach to scheduling of sterile drug product manufacturing

Optimizing the scheduling of liquid drug product manufacturing is paramount for pharmaceutical companies in their increasingly competitive environment and requires the modelling of industry-specific constraints. Such constraints include: (i) changing sequence-dependent setup times; (ii) maintaining a sterile production environment (e.g., through sterile holding times); (iii) periods with limited or no plant activity (e.g., no workforce during weekends); and (iv) demand timing (i.e., delivery deadline and release date constraints). In this work, an immediate precedence model is formulated to optimize the scheduling of liquid drug product manufacturing, considering the industry-specific constraints. The primary objective is to minimize the production makespan.Four case studies comprising up to 38 batches from a real multi-product facility illustrate the performance of the rigorous optimization approach. The makespan could be reduced by up to 7.9% compared to expert schedules.     

The integration of production plan and operating schedule in a pharmaceutical pilot plant

In reality, planning and scheduling activities are loosely integrated. In the case of a complex supply chain, it might be too difficult to maintain both long-term and short-term information within one large model. However, in the case of a single facility and relative short time horizon this task becomes feasible. This is the case in a pharmaceutical pilot plant, where a 2- or 3-year planning horizon is the most one would expect due to frequent changes in the products and their demands. In earlier work, we decomposed the pilot plant planning and scheduling problem into long-term planning of resources and short-term scheduling of operations [Computer Aided Process Eng. 8 (2000) 1057]. The long-term plan is mainly concerned with allocation of human resource, such as operators, engineers, chemists, and analysts to projects that have uncertain timelines. The short-term schedule fixes the human resources and considers the scheduling of activities in the pilot plant itself. The algorithm resolves uncertainty in future projects by over-allocating resources so that, on average, resource constraints are met. In this paper, we continue this exploration. In particular, we explore techniques for combining the long- and short-term into one plan without creating undue burden on the solver and the planning group. The uncertainty is a daily life of a pharmaceutical pilot plant. We present a methodology to deal with it without compromising the accuracy of the operating schedule.     

A CP formulation for scheduling multiproduct multistage batch plants

The short-term scheduling of multiproduct multistage batch plants is tackled in this paper by means of a constraint programming (CP) methodology. This approach, consisting of both a model and a search strategy, easily handles different features found in industrial environments: finite unit ready times, dissimilar parallel equipment at each stage, sequence-dependent changeovers, topology constraints, forbidden job-equipment assignments, order release times, as well as renewable resources limitations. It can also address various interstage storage and operational policies: UIS, NIS/ZW, NIS/UW, and mixed ones. Besides, it introduces two simple and efficient search methodologies based on domain knowledge, whose great impact on the computational performance is shown. The approach was extensively tested by means of several examples having various difficulty degrees. It rendered good computational results for a variety of interstage storage policies and objective functions. Moreover, this work shows that the default depth-first search strategy does not perform well for scheduling problems.     

Multisite supply planning for drug products under uncertainty

In the pharmaceutical industry, the goal of a supply planner is to make efficient capacity allocation decisions that ensure an uninterrupted supply of drug products to patients and to maintain product inventory levels close to the target stock. This task can be challenging due to the limited availability of manufacturing assets, uncertainties in product demand, fluctuations in production yields, and unplanned site downtimes. It is not uncommon to observe uneven distribution of product inventories with some products carrying excess inventories, while other products may be close to a stockout. Maintaining high stock levels can have economic repercussions due to the risk of expiration of unused products (whereas products facing a stockout can adversely affect the treatment regimen of patients). The network complexity of pharmaceutical supply-chains coupled with regulatory constraints and siloed planning systems force supply planners to rely on manual (error-prone) decision-making processes. Such an approach results in suboptimal capacity allocation and inventory management decisions. In this work, we propose a stochastic optimization methodology for the production scheduling of multiple drug products in lyophilization units across multiple sites. The framework leverages information obtained from historical and forecast data to generate scenarios of uncertain parameters (e.g., yield, demand, and downtimes) that can realize in the future. The optimization model determines a product filling schedule that maintains product stock levels close to targets under diverse scenarios. We show that this approach helps in avoiding reactive scheduling and in maintaining a more robust production plan than deterministic procedures (which ignore uncertainty). Specifically, planning under a stochastic optimization approach reduces the number of scenarios under which backlogs are observed and also reduces the magnitude of the backlogs.     

An improvement-based MILP optimization approach to complex AWS scheduling

The automated wet-etch station (AWS) is one of the most critical stages of a modern semiconductor manufacturing system (SMS), which has to simultaneously deal with many complex constraints and limited resources. Due to its inherent complexity, industrial-sized automated wet-etch station scheduling problems are rarely solved through full rigorous mathematical formulations. Decomposition techniques based on heuristic, meta-heuristics and simulation-based methods have been traditionally reported in literature to provide feasible solutions with reasonable CPU times.This work introduces an improvement MILP-based decomposition strategy that combines the benefits of a rigorous continuous-time MILP (mixed integer linear programming) formulation with the flexibility of heuristic procedures. The schedule generated provides enhanced solutions over time to challenging real-world automated wet etch station scheduling problems with moderate computational cost. This methodology was able to provide more than a 7% of improvement in comparison with the best results reported in literature for the most complex problem instances analyzed.     

制药工程专业药物化学的教学体会

制药工程专业是以工程学、化学、药学和生物技术为基础,探索制造药物的基本原理及实现工业化生产的工程技术。制药工程专业的目标是培养具有现代制药工程基本理论和基本技术、能在医药、农药、精细化工、生物制药等部门从事产品生产、科技开发、应用研究和管理方面的高级工程技术人才。本文针对制药工程专业的特点及培养目标,阐述了药物化学课堂教学的体会。从教学内容的优化、教师自身素质的提高、教学方法的改进等方面做了较为详细的研究和探索。     

Real‐time dynamic hoist scheduling for multistage material handling process under uncertainties

Multistage material handling processes are broadly used for manufacturing various products/jobs, where hoists are commonly used to transport inline products according to their processing recipes. When multiple types of jobs with different recipes are simultaneously and continuously handled in a production line, the hoist movement scheduling should be thoroughly investigated to ensure the operational feasibility of every job inline and in the meantime to maximize the productivity if possible. The hoist scheduling will be more complicated, if uncertainties of new coming jobs are considered, that is, the arrival time, type, recipe, and number of new jobs are totally unknown and unpredictable before they join the production line. To process the multiple jobs already inline and the newly added jobs, the hoist movements must be swiftly rescheduled and precisely implemented whenever new job(s) come. Because a reschedule has to be obtained online without violating processing time constraints for each job, the solution identification time for rescheduling must be taken into account by the new schedule itself. All these stringent requisites motivate the development of real‐time dynamic hoist scheduling (RDHS) targeting online generation of reschedules for productivity maximization under uncertainties. Hitherto, no systematic and rigorous methodologies have been reported for this study. In this article, a novel RDHS methodology has been developed, which takes into account uncertainties of new coming jobs and targets real‐time scheduling optimality and applicability. It generally includes a reinitialization algorithm to accomplish the seamless connection between the previous scheduling and rescheduling operations, and a mixed‐integer linear programming model to obtain the optimal hoist reschedule. The RDHS methodology addresses all the major scheduling issues of multistage material handling processes, such as multiple recipes, multiple jobs, multicapacity processing units, diverse processing time requirements, and even optimal processing queue for new coming jobs. The efficacy of the developed methodology is demonstrated through various case studies. © 2012 American Institute of Chemical Engineers AIChE J, 59: 465–482, 2013     

In-silico product formulation design through latent variable model inversion

Two of the first important decisions to take in the development of a solid oral drug product are the selection of excipients that are to be mixed with the active pharmaceutical ingredient (API) in a commercial formulation, and the manufacturing route. This work proposes to use a latent variable model methodology presented in a previous work (Polizzi and García-Muñoz, Int. J. Pharm., 2011, 418, 235–242) to enable the in-silico design of new product formulations. A constrained optimization framework is used to invert the underlying model in order to select the best excipients and concentrations for a given API to ensure the achievement of a pharmaceutical blend with a desired profile of particle, powder and compact mechanical properties. The approach is verified by designing a new pharmaceutical formulation for direct compression, using an API that was previously formulated via a wet granulated process. The experimental results confirm the effectiveness of the method. The proposed methodology can act as an important tool to guide and accelerate the decision making process in pharmaceutical product development, while minimizing the required experimentation as well as the raw materials consumption. The approach can be extended to consider other constraints (or targets) such as stability, as long as there is a mathematical way to relate the targets (e.g., degradation extent) to the incoming formulation.     

Preprocessing and tightening methods for time-indexed MIP chemical production scheduling models

We propose a series of preprocessing algorithms for the generation of strong valid inequalities for time-indexed, discrete and continuous, mixed-integer programming scheduling models for problems in network production environments. Specifically, starting from time- and inventory-related instance data, the proposed algorithms use constraint propagation techniques to calculate parameters that are used to bound the number of times subsets of tasks can be executed in a feasible solution. We also extend some of the propagation ideas to generate three classes of new tightening constraints. The proposed methods result in tightening constraints expressed in terms of assignment binary variables (X_ijt = 1 if task i is assigned to start on unit j at time point t) which are present in all time-indexed MIP models, therefore they are applicable to all time-indexed models accounting for a wide range of processing features. Finally, the methods are shown to lead to up to two orders of magnitude reduction in computational time when optimal solutions are found and significantly improve optimality gap when a time limit is enforced.     

Steady-state optimization of chemical processes with guaranteed robust stability and controllability under parametric uncertainty and disturbances

A new methodology is proposed for the steady-state optimal design of chemical processes under parametric uncertainty and disturbances. The methodology allows the integration of uniform constraints for robust controllability and stability in an optimization problem by using the Routh–Hurwitz test and zero dynamics based method. The underlying mathematical problem is difficult to solve because it involves infinite stability and controllability constraints. We developed an algorithm where an infinite number of constraints can be implemented as several relaxation problems that are solved iteratively. Additionally, the dynamic simulation results under parametric uncertainty and disturbances are also used to estimate the bound of the state perturbations rather than assumptions based on experience, which may lead to overly conservative or non-implementable design. To illustrate the methodology, three different examples are presented and robustly stable and controllable designs are obtained.     

Continuous-time scheduling formulation for multipurpose batch plants

Short-term scheduling of batch processes is a complex combinatorial problem with remarkable impact on the total revenue of chemical plants. It consists of the optimal allocation of limited resources to tasks over time in order to manufacture final products following given batch recipes. This article addresses the short-term scheduling of multipurpose batch plants, using a mixed integer linear programming formulation based on the state-task network representation. It employs both single-grid and multi-grid continuous-time representations, derived from generalized disjunctive programming. In comparison to other multigrid scheduling models in the literature, the proposed multi-grid model uses no big-M constraints and leads to more compact mathematical models with strong linear relaxations, which often results in shorter computational times. The single-grid counterpart of the formulation is not as favorable, as it leads to weaker linear relaxations than the multi-grid approach and is not capable of handling changeover time constraints.     

A pattern matching method for large‐scale multipurpose process scheduling

This article proposes a novel pattern matching method for the large‐scale multipurpose process scheduling with variable or constant processing times. For the commonly used mathematical programming models, large‐scale scheduling with long‐time horizons implies a large number of binary variables and time sequence constraints, which makes the models intractable. Hence, decomposition and cyclic scheduling are often applied to such scheduling. In this work, a long‐time horizon of scheduling is divided into two phases. Phase one is duplicated from a pattern schedule constructed according to the principle that crucial units work continuously, in parallel and/or with full load as possible, exclusive of time‐consuming optimization. Phase two involves a small‐size subproblem that can be optimized easily by a heuristic method. The computational effort of the proposed method does not increase with the problem size. The pattern schedule can be not only used for production/profit maximization but also for makespan estimation and minimization. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Production scheduling in a steelmaking-continuous casting plant

In this paper we describe an optimization procedure for planning the production of steel ingots in a steelmaking-continuous casting plant. The strict requirements of the production process defeated most of the earlier approaches to steelmaking-continuous casting production scheduling, mainly due to the lack of information in the optimization models. Our formulation of the problem is based on the alternative graph, which is a generalization of the disjunctive graph of Roy and Sussman. The alternative graph formulation allow us to describe in detail all the constraints that are relevant for the scheduling problem. We then solve the problem by using a beam search procedure, and compare our results with a lower bound of the optimal solutions and with the actual performance obtained in the plant. Computational experience shows the effectiveness of this approach.     

Planning production on a single processor with sequence-dependent setups part 1: determination of campaigns

Production planning of processors located within in a facility or distributed across facilities is a routine and crucial industrial activity. So far, most attempts at this have treated planning horizon as a decision variable, and have limited their scope to sequence-independent setups. In this two-part paper, we present a new and improved methodology for solving the single machine economic lot scheduling problem (ELSP) with sequence-dependent setups and a given planning horizon. We decompose the entire complex problem into two subproblems; one involving lot sizing and the other involving lot sequencing and scheduling. In this part, we present a novel mixed integer nonlinear programming (MINLP) formulation for the lot-sizing problem. Using a multi-segment separable programming approach, we transform this MINLP into a MILP and propose one rigorous and two heuristic algorithms for the latter. Based on a thorough numerical evaluation using randomly simulated large problems, we find that our best heuristic gives solutions within 0.01% of the optimal on an average and in much less time than the optimal algorithm. Furthermore, it works equally well on problems with sequence-independent setups. Overall, our methodology is well suited for real-life large-scale industrial problems.     

An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities

This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.     

Dynamic predictive scheduling of operational strategies for continuous processes using mixed-logic dynamic optimization

Industrial processes are usually operated in a highly dynamic environment, e.g. with time-varying market prizes, customer demand, technological development or up- and downstream processes. Due to these disturbances, the operational strategies comprising objectives and constraints are regularly adjusted to reflect a change in the environment in order to achieve or maintain optimal process performance. The related operational objectives need not only be of an economical nature, but can also include flexibility, risk or ecological objectives. In this paper, a novel methodology is presented for the modeling and dynamic predictive scheduling of operational strategies for continuous processes. Optimal control actions are computed on a moving horizon employing discrete-continuous modeling and mixed-logic dynamic optimization as introduced by Oldenburg et al. (2003). The approach is successfully demonstrated considering the operation of a wastewater treatment plant.     

高校课程调度系统的研究与实现

课程调度是高校教务管理的重要工作,是学校日常教学、资源合理使用的关键一环。当学校规模较小时,排课的数据量和约束条件较少,人工排课的方法尚可适用,但是随着学校规模的不断扩大,人工排课的效率和资源协调能力已经难以满足要求。文中借鉴一种需求资源矩阵的算法,对其进行了改进,并以此算法为核心,设计并实现了一个适合多校区、资源冗余较少、约束条件较多的课程调度系统,较好地解决了高校的课程调度问题。     

最佳间歇水循环网络的合成和时序安排

This work develops an optimization-based methodology for the design and scheduling of batch water recycle networks. This task requires the identification of network configuration, fresh-water usage, recycle assignments from sources to sinks, wastewater discharge, and a scheduling scheme. A new source-tank-sink representation is developed to allow for storage and dispatch tanks. The problem is solved in stages by first eliminating scheduling constraints and determining minimum usage of fresh water and wastewater discharge. An iterative procedure is formulated to minimize the total annual cost of the system by trading off capital versus operating costs. The work overcomes limitations in previous literature work including restricted recycle within the same cycle, lumped balances that may not lead to feasible solutions, and unrealistic objective functions. A case study is solved to illustrate the usefulness of the devised procedure.