On the Optimization of Schedules of a Multitask Production Cell
Licentiate thesis, 2011

Volvo Aero has invested in a complex production cell containing a set of multipurpose machines. The problem of finding optimal schedules for this multitask cell is a complex combinatorial optimization problem which is recognized as a flexible job shop problem. This thesis proposes an approach to find such schedules using mathematical optimization. The mathematical models developed so far are presented together with a study of their interrelations, both from a computational and from a modelling perspective. One result of the study is that one of these models, a time-indexed model with nail variables, outperforms all the others presented. To our knowledge, this model is the first for the flexible job shop problem using this type of variables. In order to reduce the number of variables in the time-indexed models, a heuristic has been developed which finds an upper bound on the optimal value of the makespan. Computational results are presented for several variants of the time-indexed model and the engineer’s model, the latter belonging to a family of models widely used in job shop scheduling. The objective employed for the computations is the minimization of a weighted sum of the total tardiness and the sum of job completion times. A comparison is made between optimal schedules emanating from the timeindexed model and schedules resulting from the use of three well-known dispatching rules, using the data from 21 real production scenarios. The tardiness and the sum of job completion times are on average 6–22% larger in the schedules resulting from the use of the dispatching rules compared to those obtained in the optimal schedules. The first appended paper provides the results from a similar comparison for a number of scenarios, constructed by using data emanating from the multitask cell. The computational complexity of the problem of scheduling the multitask cell is also investigated. The second appended paper contains a proof of a complexity result for a related scheduling problem, namely flow-shop scheduling with deteriorating jobs. This thesis has been written in close cooperation with the Department of Logistics Development at Volvo Aero Corporation.

due date

mathematical modelling

total flowtime

dispatching rule

production planning

complexity analysis

release date

flexible job shop scheduling

total tardiness

mathematical optimization

mixed integer linear programming (MILP)

priority function

multi-purpose machine

Sal Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3, Chalmers Tekniska Högskola
Opponent: Stefan Engevall, Institutionen för Teknik och Naturvetenskap, Linköpings Universitet


Karin Thörnblad

University of Gothenburg

Chalmers, Mathematical Sciences

Optimization of schedules for a multitask production cell

Proceedings of The 22nd NOFOMA Conference in Kolding, Denmark, 10-11th of June 2010,; (2010)

Paper in proceeding

A note on the complexity of flow-shop scheduling with deteriorating jobs

Discrete Applied Mathematics,; Vol. 159(2011)p. 251-253

Journal article

Production planning facilitated by optimal scheduling of a multi-task production cell

GKN Aerospace Sweden, 2008-01-01 -- 2013-10-31.

VINNOVA, 2008-01-01 -- 2013-10-31.

Swedish Research Council (VR), 2008-01-01 -- 2012-12-31.

Subject Categories

Production Engineering, Human Work Science and Ergonomics

Computational Mathematics

Areas of Advance


Preprint - Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University: 2011:19



Sal Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3, Chalmers Tekniska Högskola

Opponent: Stefan Engevall, Institutionen för Teknik och Naturvetenskap, Linköpings Universitet

More information

Latest update

3/7/2023 1