The Sample Analysis Machine Scheduling Problem: Definition and comparison of exact solving approaches

Nowadays there exists a wide variety of automatic machines that perform analytical tests on liquid samples, such as water, blood, urines, saliva, etc. A test can be modelled as a set of activities with given precedences and through sharing a set of limited resources. A scheduling process is therefore required to find a feasible or optimal execution of a set of tests. An important particularity of the machines performing tests are their storage areas of limited capacity. For instance, one activity may require a sample to be moved to an observation area, while another activity may later remove this sample from that observation area. In this paper, we introduce a real problem encountered in the analytical instrument industry known as the Sample Analysis Machine Scheduling Problem (SAMSP). We show that the SAMSP is a particular case of the Resource Constrained Project Scheduling Problem with Cumulative Resources (RCPSP-Cu), and present a successful application of optimization techniques for it. We are interested in exact approaches, since the models presented will be used to prove the maximum throughput of the selected machine layouts. In particular, we compare the performance of approaches based on Constraint Programming (CP), Satisfiability Modulo Theories (SMT), and Mixed Integer Linear Programming (MILP), on real instances of SAMSP.