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Discrete and continuous time representations and mathematical models for large production scheduling problems: A case study from the pharmaceutical industry

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2011年第2期215卷 383-392页

作者： Stefansson, Hlynur Sigmarsdottir, Sigrun Jensson, Pall Shah, Nilay Reykjavik Univ Sch Sci & Engn Reykjavik Iceland Univ Iceland Fac Engn Reykjavik Iceland Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

The underlying time framework used is one of the major differences in the basic structure of mathematical programming formulations used for production scheduling problems. The models are either based on continuous or discrete time representations. In the literature there is no general agreement on which is better or more suitable for different types of production or business environments. In this paper we study a large real-world scheduling problem from a pharmaceutical company. The problem is at least NP-hard and cannot be solved with standard solution methods. We therefore decompose the problem into two parts and compare discrete and continuous time representations for solving the individual parts. Our results show pros and cons of each model. The continuous formulation can be used to solve larger test cases and it is also more accurate for the problem under consideration. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Production Scheduling mixed integer linear programming Time representations

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The MIND method: A decision support for optimization of industrial energy systems - Principles and case studies

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APPLIED ENERGY 2011年第3期88卷 577-589页

作者： Karlsson, Magnus Linkoping Univ Dept Management & Engn Div Energy Syst SE-58183 Linkoping Sweden

Changes in complex industrial energy systems require adequate tools to be evaluated satisfactorily. The MIND method (Method for analysis of INDustrial energy systems) is a flexible method constructed as decision support for different types of analyses of industrial energy systems. It is based on mixed integer linear programming (MILP) and developed at Linkoping University in Sweden. Several industries, ranging from the food industry to the pulp and paper industry, have hitherto been modelled and analyzed using the MIND method. In this paper the principles regarding the use of the method and the creation of constraints of the modelled system are presented. Two case studies are also included, a dairy and a pulp and paper mill, that focus some measures that can be evaluated using the MIND method, e.g. load shaping, fuel conversion and introduction of energy efficiency measures. The case studies illustrate the use of the method and its strengths and weaknesses. The results from the case studies are related to the main issues stated by the European Commission, such as reduction of greenhouse gas emissions, improvements regarding security of supply and increased use of renewable energy, and show great potential as regards both cost reductions and possible load shifting. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Decision support systems mixed integer linear programming Energy efficiency Industrial energy systems Load shaping Optimization Modelling European Commission 20-20-20 Objectives

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Application of Fuzzy Multi-Objective linear programming Model in a Multi-Period Multi-Product Production Planning Problem

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INTERNATIONAL JOURNAL OF COMPUTATIONAL INTELLIGENCE SYSTEMS 2011年第2期4卷 228-243页

作者： Taghizadeh, Kaveh Bagherpour, Morteza Mahdavi, Iraj Mazandaran Univ Sci & Technol Dept Ind Engn Babol Sar Iran Iran Univ Sci & Technol Dept Ind Engn Tehran Iran

The Multi-Period Multi-Product (MPMP) production planning, as a well known problem in literature, attempts to match production rates of individual products with fluctuated market demand over planning horizon. This study, demonstrates how the conventional MPMP linear programming (LP) model may fail to utilize available capacity of machines, and also a novel Multi Objective linear programming (MOLP) model is developed to simultaneously minimize net present value of production costs and maximize machine utilization. The proposed model consists of production constraints such as available labor, inventory, maximum subcontracting levels and also forecasted demands. The proposed MOLP model is further converted to a Fuzzy Multi Objective linear programming (FMOLP) model utilizing piecewise linear membership functions. The model, accommodates the Decision Maker (DM) with a more systematic decision making approach enabling the DM to adjust the search direction during the solving procedure to achieve the most satisfactory result.

关键词： Multi-Period Multi-Product production planning Aggregate production planning Fuzzy Multi-Objective linear programming Piecewise linear membership functions mixed integer linear programming

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Global supply chain planning for pharmaceuticals

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2011年第11A期89卷 2396-2409页

作者： Sousa, Rui T. Liu, Songsong Papageorgiou, Lazaros G. Shah, Nilay Univ London Imperial Coll Sci Technol & Med Ctr Proc Syst Engn London SW7 2AZ England UCL Ctr Proc Syst Engn Dept Chem Engn London WC1E 7JE England

The shortening of patent life periods, generic competition and public health policies, among other factors, have changed the operating context of the pharmaceutical industry. In this work we address a dynamic allocation/planning problem that optimises the global supply chain planning of a pharmaceutical company, from production stages at primary and secondary sites to product distribution to markets. The model explores different production and distribution costs and tax rates at different locations in order to maximise the company's net profit value (NPV). Large instances of the model are not solvable in realistic time scales, so two decomposition algorithms were developed. In the first method, the supply chain is decomposed into independent primary and secondary subproblems, and each of them is optimised separately. The second algorithm is a temporal decomposition, where the main problem is separated into several independent subproblems, one per each time period. These algorithms enable the solution of large instances of the problem in reasonable time with good quality results. (C) 2011 Published by Elsevier B.V. on behalf of The Institution of Chemical Engineers.

关键词： Global supply chain Pharmaceuticals mixed integer linear programming Large-scale optimisation Decomposition algorithm

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A discrete colonial competitive algorithm for hybrid flowshop scheduling to minimize earliness and quadratic tardiness penalties

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EXPERT SYSTEMS WITH APPLICATIONS 2011年第12期38卷 14490-14498页

作者： Behnamian, J. Zandieh, M. Shahid Beheshti Univ Management & Accounting Fac Dept Ind Management GC Tehran Iran Amirkabir Univ Technol Dept Ind Engn Tehran Iran

Recently introduced colonial competitive algorithm (CCA) has shown its excellent capability on different optimization problems. The aim of this paper is to propose a discrete version of this method to determine a schedule that minimizes sum of the linear earliness and quadratic tardiness in the hybrid flowshops scheduling problem with simultaneously considering effects of sequence-dependent setup times and limited waiting time. In other word we assume that the waiting time for each job between two consecutive stages cannot be greater than a given upper bound. Also for this problem, a mixed integer program is formulated. Computational results are presented to evaluate the performance of the proposed algorithms for problems with different structures. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Hybrid flowshops scheduling Limited waiting time Colonial competitive algorithm mixed integer linear programming Earliness and tardiness penalties

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Dynamic hybrid simulation of batch processes driven by a scheduling module

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COMPUTERS & CHEMICAL ENGINEERING 2011年第10期35卷 2098-2112页

作者： Fabre, Florian Hetreux, Gilles Le Lann, Jean-Marc Zarate, Pascale INPT ENSIACET UMR CNRS 5503 Lab Genie Chim PSI GI F-31030 Toulouse 4 France INPT ENSIACET IRIT F-31062 Toulouse 9 France

Simulation is now a CAPE tool widely used by practicing engineers for process design and control. In particular, it allows various offline analyses to improve system performance such as productivity, energy efficiency, waste reduction, etc. In this framework, we have developed the dynamic hybrid simulation environment PrODHyS whose particularity is to provide general and reusable object-oriented components dedicated to the modeling of devices and operations found in chemical processes. Unlike continuous processes, the dynamic simulation of batch processes requires the execution of control recipes to achieve a set of production orders. For these reasons, PrODHyS is coupled to a scheduling module (ProSched) based on a MILP mathematical model in order to initialize various operational parameters and to ensure a proper completion of the simulation. This paper focuses on the procedure used to generate the simulation model corresponding to the realization of a scenario described through a particular scheduling. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Dynamic hybrid simulation Environment Batch processes Scheduling Petri nets mixed integer linear programming Object oriented modeling

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A heuristic block coordinate descent approach for controlled tabular adjustment

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COMPUTERS & OPERATIONS RESEARCH 2011年第12期38卷 1826-1835页

作者： Gonzalez, Jose A. Castro, Jordi Univ Politecn Cataluna Dept Stat & Operat Res ES-08034 Barcelona Catalonia Spain

One of the main concerns of national statistical agencies (NSAs) is to publish tabular data. NSAs have to guarantee that no private information from specific respondents can be disclosed from the released tables. The purpose of the statistical disclosure control field is to avoid such a leak of private information. Most protection techniques for tabular data rely on the formulation of a large mathematical programming problem, whose solution is computationally expensive even for tables of moderate size. One of the emerging techniques in this field is controlled tabular adjustment (CTA). Although CTA is more efficient than other protection methods, the resulting mixed integer linear problems (MILP) are still challenging. In this work a heuristic approach based on block coordinate descent decomposition is designed and applied to large hierarchical and general CTA instances. This approach is compared with CPLEX, a state-of-the-art MILP solver. Our results, from both synthetic and real tables with up to 1,200,000 cells, 100,000 of them being sensitive (resulting in MILP instances of up to 2,400,000 continuous variables, 100,000 binary variables, and 475,000 constraints) show that the heuristic block coordinate descent has a better practical behavior than a state-of-the-art solver: for large hierarchical instances it provides significantly better solutions within a specified realistic time limit, as required by NSAs in real-world. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： Statistical confidentiality Statistical disclosure control Controlled tabular adjustment mixed integer linear programming Heuristics Block coordinate descent Decomposition techniques

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Shift scheduling for tank trucks

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2011年第5期39卷 513-521页

作者： Knust, Sigrid Schumacher, Elisabeth Tech Univ Clausthal Inst Math D-38678 Clausthal Zellerfeld Germany Univ Osnabruck D-49069 Osnabruck Germany

In this paper we deal with shift scheduling of tank trucks for a small oil company. Given are a set of tank trucks with different characteristics and a set of drivers with different skills. The objective is to assign a feasible driver to every shift of the tank trucks such that legal and safety restrictions are satisfied, the total working times of the drivers are within desired intervals, requested vacation of the drivers is respected and the trucks are assigned to more favored drivers. We propose a two-phase solution algorithm which is based on a mixed integer linear programming formulation and an improvement procedure. Computational results are reported showing that the algorithm is able to generate feasible schedules in a small amount of time. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： Shift scheduling Tank trucks mixed integer linear programming

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Scheduling open shops with parallel machines to minimize total completion time

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2011年第5期235卷 1275-1287页

作者： Naderi, B. Ghomi, S. M. T. Fatemi Aminnayeri, M. Zandieh, M. Amirkabir Univ Technol Dept Ind Engn Tehran Iran Shahid Beheshti Univ GC Accounting & Management Fac Dept Ind Management Tehran Iran

This paper explores scheduling a realistic variant of open shops with parallel machines per working stage. Since real production floors seldom employ a single machine for each operation, the regular open shop problem is very often in practice extended with a set of parallel machines at each stage. The purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency. The objective is to find the sequence which minimizes total completion times of jobs. We first formulate the problem as an effective mixed integer linear programming model, and then we employ memetic algorithms to solve the problem. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm. To further enhance the memetic algorithm, we hybridize it with a simple form of simulated annealing as its local search engine. To assess the performance of the model and algorithms, we establish two computational experiments. The first one is small-sized instances by which the model and general performance of the algorithms are evaluated. The second one consists of large-sized instances by which we further evaluate the algorithms. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Scheduling Open shop Parallel machines Mathematical model mixed integer linear programming Memetic algorithm Taguchi method

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Optimal hoist scheduling of a deep level mine twin rock winder system for demand side management

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ELECTRIC POWER SYSTEMS RESEARCH 2011年第5期81卷 1088-1095页

作者： Badenhorst, Werner Zhang, Jiangfeng Xia, Xiaohua Univ Pretoria Dept Elect Elect & Comp Engn Ctr New Energy Syst ZA-0002 Pretoria South Africa

This paper presents a near optimal hoist scheduling and control program for rock winders found in South African deep level mines in the context of demand side management and time-of-use (TOU) tariffs. The objective is to achieve a set hoist target at minimum energy cost within various system constraints. The development of a discrete dynamic and constrained mixed integer linear programming model for a twin rock winder system is presented on which a half-hourly model predictive control (MPC) algorithm containing an adapted branch and bound methodology is applied for near optimal scheduling. Simulation results illustrate the effectiveness of the control program by minimising the energy costs through scheduling according to the TOU tariff and controlling output and ore levels within their boundaries even in the case of significant random delays in the system. Scheduling according to the TOU tariff shows a possible 30.8% reduction in energy cost while approximately 6h of delays in the system resulted in a mere 14% increase in energy cost. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Load scheduling Demand side management mixed integer linear programming Model predictive control

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