A Three-dimensional Matching Model for Perishable Production Scheduling

In the production of perishable goods particular stress is often given to performance indi cators generally less critical in such manufacturing settings as metal cutting or mechan ical electronic assembly For instance in food or biochemical productions a prominent interest of the producer is to reduce the time from distribution to the so called best before end A scheduling problem with a goal of this sort is here addressed The decision vari ables considered are launching and completion times of parts in a production line with critical aspects in the initial and or nal stages The basic problem is to nd an assign ment of a maximum number of jobs to launching and completion times so that no two jobs are assigned the same launching or completion time feasible solutions have therefore the form of three dimensional matchings The problem is studied under two independent respects assuming either i the relative perishability of products or ii the feasibility of launching completion time pairs not a ected by the intermediate transformation stage We show that the problem is NP Complete even under such a ranking assumption as i whereas is in P under assumption ii Polynomial time algorithms are also proposed to solve several optimization versions of the problem