Contributed Session Wed.2.H 2013

Wednesday, 13:15 - 14:45 h, Room: H 2013

Cluster 11: Integer & mixed-integer programming [...]

Scheduling II


Chair: Mahmut Ali Gokce



Wednesday, 13:15 - 13:40 h, Room: H 2013, Talk 1

Karin Thörnblad
A time-indexed formulation of a flexible job shop problem including preventive maintenance and availability of fixtures

Coauthors: Torgny Almgren, Michael Patriksson, Ann-Brith Strömberg


We study a real-world problem arising in the scheduling of a production cell for aero engine components. This problem can be described as a flexible job shop problem with ten resources, where some of the jobs are subject to precedence constraints with time lags. The objective is the minimization of a weighted sum of the completion times and the total tardiness. The scheduling of the cell must be fast and produce reliable and robust schedules, since the conditions are unceasingly changing with new jobs continuously
arriving at the queue.
During the production a number of preventive maintenance activities need to be regularly carried out in specific resources of the cell. Further, in the processing of a job, the corresponding component needs to be mounted into a certain fixture; only a limited number of fixtures are available and each fixture is compatible only with a subset of the jobs.
We present a time-indexed mathematical model of this flexible job shop problem including the scheduling of the preventive maintenance activities and subject to the fixture availability. Computational results for real instances collected during the spring of 2012 are also presented.



Wednesday, 13:45 - 14:10 h, Room: H 2013, Talk 2

Adam Wojciechowski
Opportunistic replacement scheduling with interval costs

Coauthors: Emil Gustafsson, Magnus Önnheim, Michael Patriksson, Ann-Brith Strömberg


The topic of this talk is replacement scheduling in a multicomponent system, where maintenance is associated with a set up or fixed cost. In such a system, replacing several components simultaneously is less expensive than replacing the components at different times. Hence, the replacement of one component is also an opportunity for the replacement of another. We have developed a 0-1 integer linear programming (ILP) model for the problem of scheduling replacement activities when the cost of the schedule depends on the length between replacements. In this model, the integrality restrictions on most variables can be relaxed without losing integrality, and the inequality constraints are facets of the convex hull of feasible solutions. We present numerical tests performed on the replacement scheduling of a turbine in an aircraft engine. We show that the ILP model can be utilized for the two-objective problem of minimizing the replacement cost and minimizing the probability of unexpected system halts. Further, by assigning a cost to unexpected system halts, we also use the ILP model for solving the problem of minimizing the expected cost.



Wednesday, 14:15 - 14:40 h, Room: H 2013, Talk 3

Mahmut Ali Gokce
Scheduling for disassembly systems

Coauthors: Burak Gokgur, Selin Ozpeynirci


Disassembly systems obtain valuable parts from end-of-life products to remanufacture, reuse or recycle them. This study deals with the disassembly scheduling and presents a mixed integer programming (MIP) model. Disassembly scheduling is the problem of determining quantity and schedule of items disassembled, held in inventory, sold, and incinerated on which resource over a planning horizon while satisfying at least the service level. The model presented includes a number of novelties including consideration of capacitated resources, environmental concepts and demand for items at all levels. Results from an experimental design are presented. After the statistical analysis of experimentation, research may be directed to develop exact algorithms or heuristics. Insights into the optimal solutions and alternative solution methods to large sized problems with which mathematical programming model has difficulty solving in acceptable times are discussed.


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