We study the problem of finding optimal space-time trajectories for two factory cranes or hoists ... more We study the problem of finding optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is a assigned a sequence of pickups and deliveries at specified locations that must be performed within given time windows. The cranes must be operated so as not to interfere with each other, although one crane may need to yield to another. The objective is generally to follow a production schedule as closely as possible. We show that only certain types of trajectories need be considered to obtain an optimal solution. This simplifies the operation of the cranes and enhances safety, because the cranes move according to predictable patterns. We present a specialized dynamic programming algorithm that solves the problem. To control the state space size we use an innovative state space representation based on a cartesian product of intervals of states and an array of two-dimensional circular queues. The algorithm solves medium-sized instanc...
Publisher Summary This chapter presents an approach for combining constraint programming (CP) wit... more Publisher Summary This chapter presents an approach for combining constraint programming (CP) with mixed-integer linear programming (MILP) when solving a multistage scheduling problem. The proposed hybrid approach relies on assigning orders to equipment with a MILP subproblem and sequencing with CP. Special cuts are proposed for the MILP subproblem. Results show that the order of magnitude reductions can be achieved in the computation. The chapter discusses the minimization of assignment cost of the orders to the equipment. The rigorous MILP optimization for this problem has proved to be intractable. A two-stage procedure is discussed in which the assignment of orders is performed in the first stage by minimizing the in-process time. In the second stage, the tardiness is minimized for that assignment. An alternate MILP model is developed in which the assignment and sequencing variables are treated separately, thereby reducing the number of binary variables but at the expense of introducing undesirable big-M constraints that exhibit poor linear programming (LP) relaxations. A decomposition strategy is used in which the assignment of orders to equipment is performed with a relaxed MILP master model while the sequencing is performed with a CP model. Solutions of the CP problem are used to generate cuts that are incorporated to the MILP master problem.
This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapte... more This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapted to different plant structures. Moreover, the flexibility allows for modeling individual characteristics of parallel equipment, particular processing and changeover times, scarce resources and maintenance requests. A small example illustrates the size and solution time of a typical model instance.
In Fortsetzung zu dem im Februar erschienenen ersten Heft [1] ist dieses at-Heft demselben Schwer... more In Fortsetzung zu dem im Februar erschienenen ersten Heft [1] ist dieses at-Heft demselben Schwerpunktthema gewidmet: Produktionsoptimierung befasst sich mit Methoden zur Erzielung technischer und wirtschaftlicher Verbesserungen des Betriebs von Produktionsanlagen. Verbesserungen der Effizienz, Geschwindigkeit und Sicherheit der Produktion gehören zu den dauerhaften Zielen der Fertigung. Das Gebiet der Produktionsoptimierung hat vor kurzem durch den 2007-IPCC-Sachstandsbericht1 an Aktualität und Relevanz gewonnen: So kann die Produktionsoptimierung wichtige Beiträge zum Erreichen der Reduktionsziele bezüglich des Energiebedarfs der Volkswirtschaften gemäß des Bali-Aktionsplans leisten.
Abstract In today's energy markets there is a growing effort in the alignment of the industri... more Abstract In today's energy markets there is a growing effort in the alignment of the industrial sector to the power grid for the sake of efficient energy distribution and consumption. The steel making industry, as one of the most energy-intensive stakeholders, may play an important role in this context. In this paper, we use the Resource Task Network (RTN) in order to provide a generic modeling framework for scheduling problems under energy constraints. We study the impact of fluctuating electricity prices on the scheduling of operations in the steel plant and the economic profits that can be obtained from the steel plant's participation in the incentive-based iDSM program.
Abstract This paper addresses a mixed integer linear programming model for the optimal utilizatio... more Abstract This paper addresses a mixed integer linear programming model for the optimal utilization of municipal solid waste in a multi-echelon supply chain network. The model focuses on tactical and operational level decisions including the supply, production, and distribution. It aims to maximize the annual net profit by optimizing the choice of waste-to-energy technologies through observing the related capacity and environmental constraints and market demands. The proposed sustainable waste management model not only reduces the burden on the environment, but also optimally distributes the solid waste through the system and converts it into electricity, thus contributing towards energy supply. Sensitivity analyses are conducted to investigate the effects of changes in waste separation rate, energy conversion rate, and energy efficiencies on the system performance and on the environment. The model is solved using GAMS/CPLEX.
We study the problem of finding optimal space-time trajectories for two factory cranes or hoists ... more We study the problem of finding optimal space-time trajectories for two factory cranes or hoists that move along a single overhead track. Each crane is a assigned a sequence of pickups and deliveries at specified locations that must be performed within given time windows. The cranes must be operated so as not to interfere with each other, although one crane may need to yield to another. The objective is generally to follow a production schedule as closely as possible. We show that only certain types of trajectories need be considered to obtain an optimal solution. This simplifies the operation of the cranes and enhances safety, because the cranes move according to predictable patterns. We present a specialized dynamic programming algorithm that solves the problem. To control the state space size we use an innovative state space representation based on a cartesian product of intervals of states and an array of two-dimensional circular queues. The algorithm solves medium-sized instanc...
Publisher Summary This chapter presents an approach for combining constraint programming (CP) wit... more Publisher Summary This chapter presents an approach for combining constraint programming (CP) with mixed-integer linear programming (MILP) when solving a multistage scheduling problem. The proposed hybrid approach relies on assigning orders to equipment with a MILP subproblem and sequencing with CP. Special cuts are proposed for the MILP subproblem. Results show that the order of magnitude reductions can be achieved in the computation. The chapter discusses the minimization of assignment cost of the orders to the equipment. The rigorous MILP optimization for this problem has proved to be intractable. A two-stage procedure is discussed in which the assignment of orders is performed in the first stage by minimizing the in-process time. In the second stage, the tardiness is minimized for that assignment. An alternate MILP model is developed in which the assignment and sequencing variables are treated separately, thereby reducing the number of binary variables but at the expense of introducing undesirable big-M constraints that exhibit poor linear programming (LP) relaxations. A decomposition strategy is used in which the assignment of orders to equipment is performed with a relaxed MILP master model while the sequencing is performed with a CP model. Solutions of the CP problem are used to generate cuts that are incorporated to the MILP master problem.
This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapte... more This paper discusses MILP-models for meltshop scheduling optimization that can be flexibly adapted to different plant structures. Moreover, the flexibility allows for modeling individual characteristics of parallel equipment, particular processing and changeover times, scarce resources and maintenance requests. A small example illustrates the size and solution time of a typical model instance.
In Fortsetzung zu dem im Februar erschienenen ersten Heft [1] ist dieses at-Heft demselben Schwer... more In Fortsetzung zu dem im Februar erschienenen ersten Heft [1] ist dieses at-Heft demselben Schwerpunktthema gewidmet: Produktionsoptimierung befasst sich mit Methoden zur Erzielung technischer und wirtschaftlicher Verbesserungen des Betriebs von Produktionsanlagen. Verbesserungen der Effizienz, Geschwindigkeit und Sicherheit der Produktion gehören zu den dauerhaften Zielen der Fertigung. Das Gebiet der Produktionsoptimierung hat vor kurzem durch den 2007-IPCC-Sachstandsbericht1 an Aktualität und Relevanz gewonnen: So kann die Produktionsoptimierung wichtige Beiträge zum Erreichen der Reduktionsziele bezüglich des Energiebedarfs der Volkswirtschaften gemäß des Bali-Aktionsplans leisten.
Abstract In today's energy markets there is a growing effort in the alignment of the industri... more Abstract In today's energy markets there is a growing effort in the alignment of the industrial sector to the power grid for the sake of efficient energy distribution and consumption. The steel making industry, as one of the most energy-intensive stakeholders, may play an important role in this context. In this paper, we use the Resource Task Network (RTN) in order to provide a generic modeling framework for scheduling problems under energy constraints. We study the impact of fluctuating electricity prices on the scheduling of operations in the steel plant and the economic profits that can be obtained from the steel plant's participation in the incentive-based iDSM program.
Abstract This paper addresses a mixed integer linear programming model for the optimal utilizatio... more Abstract This paper addresses a mixed integer linear programming model for the optimal utilization of municipal solid waste in a multi-echelon supply chain network. The model focuses on tactical and operational level decisions including the supply, production, and distribution. It aims to maximize the annual net profit by optimizing the choice of waste-to-energy technologies through observing the related capacity and environmental constraints and market demands. The proposed sustainable waste management model not only reduces the burden on the environment, but also optimally distributes the solid waste through the system and converts it into electricity, thus contributing towards energy supply. Sensitivity analyses are conducted to investigate the effects of changes in waste separation rate, energy conversion rate, and energy efficiencies on the system performance and on the environment. The model is solved using GAMS/CPLEX.
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