Batch machine production with perishability time windows and limited batch size

Alleviating bottlenecks in a microbiology laboratory

“…However, it can be used on the problems arising at PAS as only a few agars are involved. The general agar scheduling problem belongs to the class of p-batch scheduling problems with incompatible job families Uzsoy (1995), and even the problem with only one machine is so difficult that it is in the class of so called NP-hard problems Chakhlevitch et al (2010b). Consequently there is no known efficient algorithm which can construct a feasible schedule for large problems.…”

“…Both algorithms have been developed for the single machine case but can be generalized to accommodate more machines. Systematic testing on a range of benchmark problems Chakhlevitch et al (2010b) showed that the DP algorithm was restricted to instances of relatively small dimensions, approximately 6-7 agars (or columns), depending upon the length of the production horizon and density of demand for agar. However, it can be used on the problems arising at PAS as only a few agars are involved.…”

“…Theory of parallel machine scheduling, related to agar production A formal description of the problem of finding an efficient agar production schedule is given in Chakhlevitch et al (2011). A simple heuristic algorithm has been developed for establishing a quick solution, and a more complicated optimisation approach, using Dynamic Programming (DP) methodology for small problems.…”

Minimising the number of gap-zeros in binary matrices

“…In particular, we have successfully applied the approach developed in this paper in the context of microbiological food testing. The methodology is used to resequence food samples, and is combined with an optimisation approach for scheduling agar production presented in [7], to take account of the limited shelf life of agar. This approach provides a methodology for increasing efficiency of food testing in the laboratory by 20%.…”

“…The saving is achieved by judicious batching of agar production, following the approach to batching perishable goods described in [7]. It is only at this further stage of analysis that account is taken of the volume of the individual agar requirement of test samples.…”