Batch scheduling in process industries: an application of resource–constrained project scheduling

The paper deals with batch scheduling problems in process industries where final products arise from several successive chemical or physical transformations of raw materials using multi–purpose equipment. In batch production mode, the total requirements of intermediate and final products are partitioned into batches. The production start of a batch at a given level requires the availability of all input products. We consider the problem of scheduling the production of given batches such that the makespan is minimized. Constraints like minimum and maximum time lags between successive production levels, sequence–dependent facility setup times, finite intermediate storages, production breaks, and time–varying manpower contribute to the complexity of this problem. We propose a new solution approach using models and methods of resource–constrained project scheduling, which (approximately) solves problems of industrial size within a reasonable amount of time. Received: October 15, 1999 / Accepted: March 21, 2000     

Plant co-ordination in pharmaceutics supply networks

The production of active ingredients in the chemical-pharmaceutical industry involves numerous production stages with cumulative lead times of up to two years. Mainly because of rigorous purity requirements and the need of extensive cleaning of the equipment units, production is carried out in campaigns, i.e. multiple batches of the same product type are produced successively before changing to another product type. Each campaign requires a specific configuration of equipment units according to the recipes of the particular chemical process. In the chemical-pharmaceutical industry, production stages are often assigned to different locations, even different countries. Hence the co-ordination of plant operations within the resulting multi-national supply network is of major importance. A key issue is the co-ordination of campaign schedules at different production stages in the various plants. In practice, it is almost impossible to determine exact optimal solutions to the corresponding complex supply network problem with respect to overall logistics costs. In order to reduce the required computational effort, we introduce several aggregation schemes and a novel MILP model formulation which is based on a continuous representation of time. Moreover, we propose an iterative near-optimal solution procedure which can be successfully applied to even exceptionally large real life problem instances. The applicability of the approach suggested is shown using a case study from industry. Correspondence to: H.-O. Günther     

Campaign planning for multi-stage batch processes in the chemical industry

Inspired by a case study from industry, the production of special chemical products is considered. In this industrial environment, multi-purpose equipment is operated in batch mode to carry out the diverse processing tasks. Often, extensive set-up and cleaning of the equipment are required when production switches between different types of products. Hence, processes are scheduled in campaign mode, i.e. a number of batches of the same type are processed in sequence. The production of chem ical products usually involves various stages with significant cumulative lead times. Typically, these production stages are assigned to different plants. A hierarchical modelling approach is presented which co-ordinates the various plant operations within the entire supply network. In the first stage, the length of the campaigns, their timing, the corresponding material flows, and equipment requirements have to be determined. At this stage, an aggregation scheme based on feasibility constraints is employed in order to reflect the limited availability of the various types of production equipment. The second stage consists of an assignment model, which allocates the available equipment units between the production campaigns determined in the first stage of the solution procedure. In the third stage, resource conflicts are resolved, which may occur if clean-out operations and minimal campaign lengths have to be considered. The proposed hierarchical approach allows a more compact model formulation compared to ot her approaches known from the literature. As a result, a very efficient and flexible solution approach is obtained. In particular, commercially available standard solvers can be used to solve a wide range of campaign planning problems arising in the chemical industry.     

Integrated planning of acquisition,disassembly and bulk recycling: a case study on electronic scrap recovery

Abstract. Due to national and supranational legislation activities, the recovery of discarded products will attain an increasing momentum. Electronic equipment consists of many different parts and materials. Therefore, the related recovery process is often divided into disassembly to remove harmful substances or reusable parts and into bulk recycling to recover ferrous and non-ferrous metals. In order to consider the interactions between choice of scrap to be recovered (acquisition problem), disassembly and bulk recycling, a mixed-integer linear programming model for integrated planning of these stages is presented in this case study. It is applied to determine the daily allocation of products to processes for a major electronic scrap recovery centre that faces limited processing capacities and market restrictions. The optimization calculations covering typical discarded electronic products to be recycled in the related centre lead to a relevant improvement of the economic success. RID="*" ID="*" The authors would like to thank the German “Bundesministerium für Bildung und Forschung” (Federal Ministry of Education and Research) for supporting the research project “Substance Flow Oriented Closed Loop Supply Chain Management in the Electrical and Electronic Equipment Industry (STREAM)rdquo;. Correspondence to: T. Spengler     

A scheduling method for Berth and Quay cranes

This paper discusses a method for scheduling Berth and Quay cranes, which are critical resources in port container terminals. An integer programming model is formulated by considering various practical constraints. A two-phase solution procedure is suggested for solving the mathematical model. The first phase determines the Berthing position and time of each vessel as well as the number of cranes assigned to each vessel at each time segment. The subgradient optimization technique is applied to obtain a near-optimal solution of the first phase. In the second phase, a detailed schedule for each Quay crane is constructed based on the solution found from the first phase. The dynamic programming technique is applied to solve the problem of the second phase. A numerical experiment was conducted to test the performance of the suggested algorithms. RID="*" ID="*" This research has been supported in part by Brain Korea 21 Program (1999–2002). Correspondence to: Y.-M. Park     

An integrated system solution for supply chain optimization in the chemical process industry

This paper considers a complex scheduling problem in the chemical process industry involving batch production. The application described comprises a network of production plants with interdependent production schedules, multi-stage production at multi-purpose facilities, and chain production. The paper addresses three distinct aspects: (i) a scheduling solution obtained from a genetic algorithm based optimizer, (ii) a mechanism for collaborative planning among the involved plants, and (iii) a tool for manual updates and schedule changes. The tailor made optimization algorithm simultaneously considers alternative production paths and facility selection as well as product and resource specific parameters such as batch sizes, and setup and cleanup times. The collaborative planning concept allows all the plants to work simultaneously as partners in a supply chain resulting in higher transparency, greater flexibility, and reduced response time as a whole. The user interface supports monitoring production schedules graphically and provides custom-built utilities for manual changes to the production schedule, investigation of various what-if scenarios, and marketing queries. RID="*" ID="*" The authors would like to thank Hans-Otto Günther and Roland Heilmann for helpful comments on draft versions of this paper.     

Advanced production scheduling for batch plants in process industries

An Advanced Planning System (APS) offers support at all planning levels along the supply chain while observing limited resources. We consider an APS for process industries (e.g. chemical and pharmaceutical industries) consisting of the modules network design (for long–term decisions), supply network planning (for medium–term decisions), and detailed production scheduling (for short–term decisions). For each module, we outline the decision problem, discuss the specifi cs of process industries, and review state–of–the–art solution approaches. For the module detailed production scheduling, a new solution approach is proposed in the case of batch production, which can solve much larger practical problems than the methods known thus far. The new approach decomposes detailed production scheduling for batch production into batching and batch scheduling. The batching problem converts the primary requirements for products into individual batches, where the work load is to be minimized. We formulate the batching problem as a nonlinear mixed–integer program and transform it into a linear mixed–binary program of moderate size, which can be solved by standard software. The batch scheduling problem allocates the batches to scarce resources such as processing units, workers, and intermediate storage facilities, where some regular objective function like the makespan is to be minimized. The batch scheduling problem is modelled as a resource–constrained project scheduling problem, which can be solved by an efficient truncated branch–and–bound algorithm developed recently. The performance of the new solution procedures for batching and batch scheduling is demonstrated by solving several instances of a case study from process industries.     

Strategic technology planning in hospital management

Abstract. Hospital managers regularly are confronted with their patients' demand for increased service performance on the one hand and tight budgets on the other. As medical technologies influence both the costs and the service spectrum, strategic technology planning is among the critical tasks in hospital management. This paper addresses the corresponding problem of selecting the “best” portfolio of medical devices and proposes an appropriate decision support system. It starts with a multiobjective mathematical programming model that determines the solution space of all efficient portfolios of medical technology investments. The members of the planning committee with their diverging interests then are supported by their interactive exploration of that space until they jointly reach a satisfying portfolio and are not willing to make any further compromises between its objective levels. As one of its salient features the system does not require a priori preference information. RID="*" ID="*" A previous version of this paper has been presented at the Wiesbaden 2000 Meeting of the GOR-Working Group “Operations Research in Health Care”. The authors thank Andrea Lührs and Thomas Rollins, both from Siemens AG, for their valuable support. Moreover, thanks are due to the anonymous referees for their comments on a previous version of this paper. Correspondence to: C. Stummer     

Combined strategic and operational planning – an MILP success story in chemical industry

We describe and solve a real world problem in chemical industry which combines operational planning with strategic aspects. In our simultaneous strategic & operational planning (SSDOP) approach we develop a model based on mixed-integer linear (MILP) optimization and apply it to a real-world problem; the approach seems to be applicable in many other situations provided that people in production planning, process development, strategic and financial planning departments cooperate. The problem is related to the supply chain management of a multi-site production network in which production units are subject to purchase, opening or shut-down decisions leading to an MILP model based on a time-indexed formulation. Besides the framework of the SSDOP approach and consistent net present value calculations, this model includes two additional special and original features: a detailed nonlinear price structure for the raw material purchase model, and a detailed discussion of transport times with respect to the time discretization scheme involving a probability concept. In a maximizing net profit scenario the client reports cost saving of several millions US$. The strategic feature present in the model is analyzed in a consistent framework based on the operational planning model, and vice versa. The demand driven operational planning part links consistently to and influences the strategic. Since the results (strategic desicions or designs) have consequences for many years, and depend on demand forecast, raw material availability, and expected costs or sales prices, resp., a careful sensitivity analysis is necessary showing how stable the decisions might be wit h respect to these input data.     

Analysis of a single stage production system with heterogeneous machines

The performance of a single stage production system with two heterogeneous machines and two classes of jobs is investigated. The machines have a common buffer with jobs of both classes waiting for service. The arrivals are assumed to follow a Poisson process and the service times to be distributed exponentially. The evaluated production system differs from a classical homogeneous multiple server queueing system with regard to inhomogeneities of the two machines. Time inhomogeneity – the service times of the two machines being unequal – and functional inhomogeneity – one of the machines can handle only one class (A) of jobs – are to be distinguished. In the case of time inhomogeneity the calculation of system performance parameters may be carried out using an explicit formula, whereas for the analysis of functional inhomogeneity a numerical solution has to be derived. The impact of time inhomogeneity is very small and decreases with the system workload. On the contrary, functional inhomogeneity leads to elevated cycle times of up to 40% depending on the degree of inhomogeneity (measured by the fraction of A jobs) and the workload. Therefore, in contrast to the time-inhomogeneous case, single stage production systems with functional inhomogeneity can only be approximated tolerably by a homogeneous multiple server queueing system if the fraction of one-machine jobs is less than 30%. The increased throughput times above 30% are supplied by the diagram developed from the numerical solutions. RID="*" ID="*" While this research was constructed the author was affiliated to Institute of Conveying Technology and Logistics. Correspondence to: C. R. Lippolt     

MILP-based campaign scheduling in a specialty chemicals plant: a case study

Supply chain management in chemical process industry focuses on production planning and scheduling to reduce production cost and inventories and simultaneously increase the utilization of production capacities and the service level. These objectives and the specific characteristics of chemical production processes result in complex planning problems. To handle this complexity, advanced planning systems (APS) are implemented and often enhanced by tailor-made optimization algorithms. In this article, we focus on a real-world problem of production planning arising from a specialty chemicals plant. Formulations for finished products comprise several production and refinement processes which result in all types of material flows. Most processes cannot be operated on only one multi-purpose facility, but on a choice of different facilities. Due to sequence dependencies, several batches of identical processes are grouped together to form production campaigns. We describe a method for multicriteria optimization of short- and mid-term production campaign scheduling which is based on a time-continuous MILP formulation. In a preparatory step, deterministic algorithms calculate the structures of the formulations and solve the bills of material for each primary demand. The facility selection for each production campaign is done in a first MILP step. Optimized campaign scheduling is performed in a second step, which again is based on MILP. We show how this method can be successfully adapted to compute optimized schedules even for problem examples of real-world size, and we furthermore outline implementation issues including integration with an APS.     

Portfolio management in the binomial model: conditions for outperforming benchmarks

The performance of a portfolio manager is in practice usually measured by the result of his trading strategy compared to a benchmark. Therefore the information whether there exists a strategy that allows to outperform the benchmark is of high value for an active investor. The article shows how this information can be generated in the binomial model. In this context the connection between trading strategies and the investor's expectations concerning future asset prices is analyzed. Based on these findings several conditions are derived that allow the portfolio manager to judge whether the benchmark can be outperformed by an active trading strategy. RID="*" ID="*" Thomas Balzer now works in the Risk Measurement & Management Department of Credit Suisse First Boston in London. The views expressed in this article are those of the author, and do not necessarily represent those of Credit Suisse Group or Credit Suisse First Boston. The author thanks Dr. Michael Olbrich for careful reading and several useful comments.     

Long term planning of inter-company energy supply concepts

In order to assess the economic and ecological effects of inter-company energy supply concepts, an optimising model integrating investment and long-term production planning has been developed. The model represents the energy production of companies on a very disaggregated level taking into account different resources, energy carriers and production processes. This model has been applied to five industrial companies to analyse the economic and ecological implications resulting from investments in inter-company energy supply concepts. Existing technologies as well as possible investment options have been assessed by a techno-economic analysis taking into account company specific circumstances. In addition, the new German combined heat and power law has been modelled in detail, because the supplementary payments legally established in this law may effect energy go supply concepts in a considerable way. Computational results show the installation of a combined cycle power plant adapted to the specific conditions of the case at hand would be the most promising option to fulfil the future energy demand of the companies involved. Correspondence to: W. Fichtner     

An application of mixed-integer linear programming models on the redesign of the supply network of Nutricia Dairy &; Drinks Group in Hungary

Between 1995 and 1998 Nutricia acquired a number of dairy companies in Hungary. Each of these companies produced a wide variety of products for its regional market. Although alterations had been made to the production system in the last few years, production and transportation costs were still substantial. This paper presents a research study with regard to the optimisation of the supply network of Nutricia Hungary using a mixed-integer linear programming model. Focussing on consolidation and product specialisation of plants the objective was to find the optimal number of plants, their locations and the allocation of the product portfolio to these plants, when minimizing the sum of production and transportation costs. The model is in line with traditional location/allocation models, with a modification concerning inter-transportation of semi-finished products between plants. The production costs used in this model are based on a Green field situation, taking into account new and more advanced technologies available today. The model is used by the Nutricia Dairy and Drinks Group as a decision supporting tool. Correspondence to: F. H. E. Wouda     

A Mixed-Integer Optimization Strategy for Oil Supply in Distribution Complexes

As a result of an increasingly competitive market, companies must find ways to organize their activities regarding their economic outcome. An important feature in this context involves transportation operations, usually considered one of the major bottlenecks in the production chain. While delays imply loss of time and lack of resources, deliveries ahead of the deadlines may cause excess of inventories. Therefore, every company must pursue efficient transportation schedules within their operational planning. This work addresses short-term crude oil scheduling problems in a distribution complex that contains ports, refineries and a pipeline infrastructure capable of transferring oil from the former to the latter. The ports comprise piers, which receive vessels for discharging, storage tanks and a network that connects each other. The refineries have their own storage infrastructure, modeled as a large storage unit, along with crude distillation units, considered as constant level consumers. The problem involves a number of other issues, including intermediate storage, settling tasks and allocation of crude oil by its qualitative characteristics. A decomposition strategy based on large-scale mixed-integer linear programming (MILP) continuous-time models is developed. First, an MILP model that considers an aggregate representation for the pipeline and intermediate storage infrastructure is proposed. Decision variables involve the assignment of oil tankers to piers as well as tanker unloading and pipeline loading operations. The solution of this model provides the initial conditions for MILP models that represent the pipeline and intermediate storage infrastructure at a detailed level. Algorithms based on the LP-based branch-and-bound method are employed. Results from a port scenario of 13 tankers, 4 piers, 14 crude types, 18 storage tanks and 2 pipelines were obtained in approximately 90 minutes from an MILP problem containing 1996 continuous variables, 1039 binary variables and 7203 constraints.     

Lot-sizing for a single-stage single-product production system with rework of perishable production defectives

We consider a single-stage single-product production system. Produced units may be non-defective, reworkable defective, or non-reworkable defective. The system switches between production and rework. After producing a fixed number (N) of units, all reworkable defective units are reworked. Reworkable defectives are perishable or can become technologically obsolete. We assume that the rework time and the rework cost increase linearly with the time that a unit is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using this expression, the optimal value for N can be determined numerically. Moreover, it is easy to perform a sensitivity analysis, as we illustrate. RID="*" ID="*"The research of Dr. Ruud H. Teunter has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research presented in this paper is part of the research on re-use in the context of the EU sponsored TMR project REVersed LOGistics (ERB 4061 PL 97-5650) in which take part the Otto-von-Guericke Universitaet Magdeburg (D), the Erasmus University Rotterdam (NL), the Eindhoven University of Technology (NL), INSEAD (F), the Aristoteles University of Thessaloniki (GR), and the University of Piraeus (GR). We thank the anonymous referees for their many helpful comments. Correspondence to: R. H. Teunter     

Estimating financial risk under time-varying extremal return behavior

Potentially increasing volatility and downside risk is essential to financial risk management which is concerned with the tails, or particularly, the lower tail, of the distribution of speculative asset returns. Applying extreme value theory, the present paper outlines a simple model capturing time-varying tail behavior and studies conditional daily return quantiles for the German DAX. Our results indicate an overall increased risk of large one-day holding-period losses related to a structural break given by the 1987 crash, systematic out-of-sample underestimation of the magnitude of extreme quantiles as well as clustering in estimated quantile exceedances which cannot be fully explained by the forecasting model. RID="*" ID="*" Part of the paper was written while the author was visiting the Center for Mathematical Sciences at Munich University of Technology. He is grateful for the members' hospitality and thanks Claudia Klüppelberg for helpful discussions as well as two anonymous referees for comments improving the paper.     

Reduced outpatient waiting times with improved appointment scheduling: a simulation modelling approach

Abstract. An outpatient department represents a complex system through which many patients with varying needs pass each day. An effective appointment system is a critical component in controlling patient waiting times within clinic sessions. Current waiting times are often unacceptable and place great stress on clinic staff. This paper describes the development and use of a detailed simulation model of an Ear, Nose and Throat (ENT) outpatient department. The simulation allows various appointment schedules to be examined and their effects on the clinic evaluated. The model has been used to identify a number of critical factors that influence patient waiting times and the build up of queues in the clinic. Alternative appointment schedules have been shown to drastically reduce patient waiting times, without the need for extra resources, and enable the department to move towards meeting the UK Government's Patient's Charter. RID="*" ID="*" The authors would like to express their thanks for the valuable support provided by the anonymous participants (outpatient department staff). Thanks also to Helen Gilby, Dr Arjan Shahani and Professor Valter de Senna for their useful comments and help during the research. Correspondence to: P.R. Harper     

Intensity-modulated radiotherapy – a large scale multi-criteria programming problem

Abstract. Radiation therapy planning is often a tight rope walk between dangerous insufficient dose in the target volume and life threatening overdosing of organs at risk. Finding ideal balances between these inherently contradictory goals challenges dosimetrists and physicians in their daily practice. Todays inverse planning systems calculate treatment plans based on a single evaluation function that measures the quality of a radiation treatment plan. Unfortunately, such a one dimensional approach cannot satisfactorily map the different backgrounds of physicians and the patient dependent necessities. So, too often a time consuming iterative optimization process between evaluation of the dose distribution and redefinition of the evaluation function is needed. In this paper we propose a generic multi-criteria approach based on Pareto's solution concept. For each entity of interest – target volume or organ at risk – a structure dependent evaluation function is defined measuring deviations from ideal doses that are calculated from statistical functions. A reasonable bunch of clinically meaningful Pareto optimal solutions are stored in a data base, which can be interactively searched by physicians. The system guarantees dynamic planning as well as the discussion of tradeoffs between different entities. Mathematically, we model the inverse problem as a multi-criteria linear programming problem. Because of the large scale nature of the problem it is not possible to solve the problem in a 3D-setting without adaptive reduction by appropriate approximation schemes. Our approach is twofold: First, the discretization of the continuous problem results from an adaptive hierarchical clustering process which is used for a local refinement of constraints during the optimization procedure. Second, the set of Pareto optimal solutions is approximated by an adaptive grid of representatives that are found by a hybrid process of calculating extreme compromises and interpolation methods. Correspondence to: K.-H. Küfer