| 1. |
- Strömberg, Ann-Brith, 1961, et al.
(författare)
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Mixed-Integer Linear Optimization: Primal–Dual Relations and Dual Subgradient and Cutting-Plane Methods
- 2020
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Ingår i: Numerical Nonsmooth Optimization: State of the Art Algorithms. - Cham : Springer International Publishing. ; , s. 499-547, s. 499-547
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Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- This chapter presents several solution methodologies for mixed-integer linear optimization, stated as mixed-binary optimization problems, by means of Lagrangian duals, subgradient optimization, cutting-planes, and recovery of primal solutions. It covers Lagrangian duality theory for mixed-binary linear optimization, a problem framework for which ultimate success—in most cases—is hard to accomplish, since strong duality cannot be inferred. First, a simple conditional subgradient optimization method for solving the dual problem is presented. Then, we show how ergodic sequences of Lagrangian subproblem solutions can be computed and used to recover mixed-binary primal solutions. We establish that the ergodic sequences accumulate at solutions to a convexified version of the original mixed-binary optimization problem. We also present a cutting-plane approach to the Lagrangian dual, which amounts to solving the convexified problem by Dantzig–Wolfe decomposition, as well as a two-phase method that benefits from the advantages of both subgradient optimization and Dantzig–Wolfe decomposition. Finally, we describe how the Lagrangian dual approach can be used to find near optimal solutions to mixed-binary optimization problems by utilizing the ergodic sequences in a Lagrangian heuristic, to construct a core problem, as well as to guide the branching in a branch-and-bound method. The chapter is concluded with a section comprising notes, references, historical downturns, and reading tips.
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| 2. |
- Fotedar, Sunney, 1989, et al.
(författare)
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A criterion space decomposition approach to generalized tri-objective tactical resource allocation
- 2023
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Ingår i: Computational Management Science. - : Springer Science and Business Media LLC. - 1619-697X .- 1619-6988. ; 20:1
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Tidskriftsartikel (refereegranskat)abstract
- We present a tri-objective mixed-integer linear programming model of the tactical resource allocation problem with inventories, called the generalized tactical resource allocation problem (GTRAP). We propose a specialized criterion space decomposition strategy, in which the projected two-dimensional criterion space is partitioned and the corresponding sub-problems are solved in parallel by application of the quadrant shrinking method (QSM) (Boland in Eur J Oper Res 260(3):873–885, 2017) for identifying non-dominated points. To obtain an efficient implementation of the parallel variant of the QSM we suggest some modifications to reduce redundancies. Our approach is tailored for the GTRAP and is shown to have superior computational performance as compared to using the QSM without parallelization when applied to industrial instances.
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| 3. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Scheduling the repair and replacement of individual components in operating systems: a bi-objective mathematical optimization model
- 2024
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Ingår i: Journal of Scheduling. - 1099-1425 .- 1094-6136. ; 27:1, s. 87-101
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Tidskriftsartikel (refereegranskat)abstract
- Preventive maintenance (PM) is performed so that failure is avoided while corrective maintenance is performed after a failure has occurred in order to restore the system back to an operational state. This research aims at scheduling PM activities for a multi-component system within a finite time horizon. We consider a setting with two stakeholders, being the system operator and themaintenanceworkshop, and two different contract types governing their joint activities, namely an availability contract and a turn-around time contract. Components in the systems that are to be maintained are sent to the maintenance workshop, which needs to schedule and perform all maintenance activities while at the same time satisfying the contract and not exceeding the workshop capacity. Our modelling is based on a mixed-binary linear optimization model of a PM scheduling problem with so-called interval costs over a finite and discretized time horizon.We enhance this scheduling model with the flow of individual components through the maintenance workshop, including stocks of spare components, both those components that need repair and the repaired ones. The resulting scheduling model is then utilized in the optimization of two main contracts, namely maximizing the availability of repaired (or new) components and minimizing the deviation from the contracted turn-around times for the components in the maintenance loop. Each of these objectives is combined with the objective to minimize the costs for maintenance of the operating system, leading to two bi-objective optimization problems. We analyse the two contracting forms between the stakeholders by studying and comparing the Pareto fronts resulting from different parameter settings, regarding minimum allowed stock levels and investments in repair capacity of the workshop. Our bi-objective mixed-binary linear optimization model is able to capture important properties of the results from the contracting forms as well as to show that, in our setting, an availability contract performs better than a turn-around time contract in terms of tractability.
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| 4. |
- Laksman, Efraim, 1983, et al.
(författare)
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The stochastic opportunistic replacement problem, part III: improved bounding procedures
- 2020
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 292:2, s. 711-733
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Tidskriftsartikel (refereegranskat)abstract
- We consider the problem to find a schedule for component replacement in a multi-component system, whose components possess stochastic lives and economic dependencies, such that the expected costs for maintenance during a pre-defined time period are minimized. The problem was considered in Patriksson et al. (Ann Oper Res 224:51–75, 2015), in which a two-stage approximation of the problem was optimized through decomposition (denoted the optimization policy). The current paper improves the effectiveness of the decomposition approach by establishing a tighter bound on the value of the recourse function (i.e., the second stage in the approximation). A general lower bound on the expected maintenance cost is also established. Numerical experiments with 100 simulation scenarios for each of four test instances show that the tighter bound yields a decomposition generating fewer optimality cuts. They also illustrate the quality of the lower bound. Contrary to results presented earlier, an age-based policy performs on par with the optimization policy, although most simple policies perform worse than the optimization policy.
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| 5. |
- Fotedar, Sunney, 1989, et al.
(författare)
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Mathematical optimization of the tactical allocation of machining resources for an efficient capacity utilization in aerospace component manufacturing
- 2019
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Ingår i: Proceedings of the 10th Aerospace Technology Congress. - : Linköping University Electronic Press. - 1650-3686 .- 1650-3740. - 9789175190068 ; , s. 183-188
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Konferensbidrag (refereegranskat)abstract
- In the aerospace industry, with low volumes and many products, there is a critical need to efficiently use available manufacturing resources. Currently, at GKN Aerospace, resource allocation decisions that in many cases will last for several years are to some extent made with a short-term focus so as to minimize machining time, which results in a too high load on the most capable machines, and too low load on the less capable ones. This creates an imbalance in capacity utilization that leads to unnecessary queuing at some machines, resulting in long lead times and in an increase in tied-up capital. Tactical resource allocation on the medium to long-range planning horizon (six months to several years) aims to address this issue by allocating resources to meet the predicted future demand as effectively as possible, in order to ensure long range profitability. Our intent is to use mathematical optimization to find the best possible allocations.
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| 6. |
- Obradovic, Gabrijela, 1994, et al.
(författare)
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Simultaneous scheduling of replacement and repair of common components in operating systems A multi-objective mathematical optimization model
- 2022
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 0254-5330 .- 1572-9338. ; 322, s. 147-65
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Tidskriftsartikel (refereegranskat)abstract
- In order for a system to stay operational, its components need maintenance. We consider two stakeholders-a system operator and a maintenance workshop-and a contract governing their joint activities. Components in the operating systems that are to be maintained are sent to the maintenance workshop, which should perform all maintenance activities on time in order to satisfy the contract. The maintained components are then sent back to be used in the operating systems. Our modeling of this system-of-systems includes stocks of damaged and repaired components, the workshop scheduling, and the planning of preventive maintenance for the operating systems. Our modeling is based on a mixed-binary linear optimization (MBLP) model of a preventive maintenance scheduling problem with so-called interval costs over a finite and discretized time horizon. We generalize and extend this model with the flow of components through the workshop, including the stocks of spare components. The resulting scheduling model-a mixed-integer optimization (MILP) model-is then utilized to optimize the main contract in a bi-objective setting: maximizing the availability of repaired (or new) components and minimizing the costs of maintaining the operating systems over the time horizon. We analyze the main contract and briefly discuss a turn-around time contract. Our results concern the effect of our modeling on the levels of the stocks of components over time, in particular minimizing the risk for lack of spare components.
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| 7. |
- Åblad, Edvin, 1991, et al.
(författare)
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Exact makespan minimization of unrelated parallel machines
- 2021
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Ingår i: Open Journal of Mathematical Optimization. - : Cellule MathDoc/CEDRAM. - 2777-5860. ; 2
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Tidskriftsartikel (refereegranskat)abstract
- We study methods for the exact solution of the unrelated parallel machine problem with makespan minimization, generally denoted as R||Cmax. Our original application arises from the automotive assembly process where tasks needs to be distributed among several robots. This involves the solutions of several R||Cmax instances, which proved hard for a MILP solver since the makespan objective induces weak LP relaxation bounds. To improve these bounds and to enable the solution of larger instances, we propose a branch–and–bound method based on a Lagrangian relaxation of the assignment constraints. For this relaxation we derive a criterion for variable fixing and prove the zero duality gap property for the case of two parallel machines. Our computational studies indicate that the proposed algorithm is competitive with state-of-the-art methods on different types of instances. Moreover, the impact of each proposed feature is analysed.
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| 8. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Scheduling optimization of a real flexible job shop including fixture availability and preventive maintenance
- 2015
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Ingår i: European Journal of Industrial Engineering. - 1751-5254 .- 1751-5262. ; 9:1, s. 126-145
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Tidskriftsartikel (refereegranskat)abstract
- The multitask cell at GKN Aerospace Sweden is a flexible job shop containing ten resources aimed at being flexible with regard to product mix and processing types. We present a time-indexed formulation of the problem of optimally scheduling the planned jobs on the resources, also considering a limited availability of fixtures as well as required preventive maintenance activities. The objective is to minimize a weighted sum of the completion times and tardiness for the jobs, where the tardiness weight for a given job is a non-increasing function of its due date. We propose a fast iterative approach to finding a suitable value of the length of the time horizon that needs to be set for the time-indexed formulation and which considerably influences the computation time. Computational results show that the method developed is able to produce optimal, or near-optimal, schedules for real data instances within an acceptable practical time frame.
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| 9. |
- Thörnblad, Karin, 1971, et al.
(författare)
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Scheduling optimization of a real flexible job shop including side constraints regarding maintenance, fixtures, and night shifts
- 2013
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- We present a generic iterative scheduling procedure for the scheduling of a real flexible job shop, the so-called multitask cell at GKN Aerospace Engine Systems in Sweden. A time-indexed formulation of the problem is presented including side constraints regarding preventive maintenance, fixture availability, and unmanned night shifts. This paper continues the work in [35], with an improvement of the iterative solution procedure and the inclusion of constraints regarding night shifts during which only unmanned processing is allowed. The resulting schedules are compared with schedules constructed using two priority dispatching rules. Computational results show that the gain of including the night shifts constraints is significant and that the methodology developed is able to produce near-optimal schedules for industrial data instances for the coming shift within an acceptable practical time frame.
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| 10. |
- Patriksson, Michael, 1964, et al.
(författare)
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The stochastic opportunistic replacement problem, part I: models incorporating individual component lives
- 2015
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Ingår i: Annals of Operations Research. - : Springer Science and Business Media LLC. - 1572-9338 .- 0254-5330. ; 224:1, s. 25-50
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Tidskriftsartikel (refereegranskat)abstract
- We consider an extension of the opportunistic replacement problem, which has been studied by Dickman et al. (The Journal of the Operational Research Society of India, 28:165–175, 1991), Andréasson (Optimization of opportunistic replacement activities in deterministic and stochastic multi-component systems, Licentiate thesis, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2004), and Almgren et al. (The opportunistic replacement problem: analysis and case studies, Preprint, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2011), that allows the individuals of the same component to have non-identical lives. Formulating and solving this problem constitute a first step towards solving the opportunistic replacement problem with uncertain component lives. We show that the problem is NP-hard even with time independent costs, and present two 0–1 integer programming models for the problem. We show that in model I the integrality requirement on a majority of the variables can be relaxed; this is in contrast to model II and the model from Andréasson (Optimization of opportunistic replacement activities in deterministic and stochastic multi-component systems, Licentiate thesis, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, Göteborg, Sweden, 2004). We remove all superfluous variables and constraints in model I and show that the remaining constraints are facet inducing. We also utilize a linear transformation of model I to obtain a stronger version of model II, i.e., model II+, which inherits the polyhedral properties of model I. Numerical experiments show that the solution time of model I is significantly lower than those of both model II and Andréasson’s model. It is also slightly lower than the solution time of model II+.
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