{"title":"Robust Batch Process Scheduling in Pharmaceutical Industries: A Case Study","authors":"Tommaso Adamo, Gianpaolo Ghiani, Antonio D. Grieco, Emanuela Guerriero","country":null,"institution":"","volume":103,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":401,"pagesEnd":405,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10002269","abstract":"Batch production plants provide a wide range of\r\nscheduling problems. In pharmaceutical industries a batch process\r\nis usually described by a recipe, consisting of an ordering of tasks\r\nto produce the desired product. In this research work we focused\r\non pharmaceutical production processes requiring the culture of\r\na microorganism population (i.e. bacteria, yeasts or antibiotics).\r\nSeveral sources of uncertainty may influence the yield of the culture\r\nprocesses, including (i) low performance and quality of the cultured\r\nmicroorganism population or (ii) microbial contamination. For\r\nthese reasons, robustness is a valuable property for the considered\r\napplication context. In particular, a robust schedule will not collapse\r\nimmediately when a cell of microorganisms has to be thrown away\r\ndue to a microbial contamination. Indeed, a robust schedule should\r\nchange locally in small proportions and the overall performance\r\nmeasure (i.e. makespan, lateness) should change a little if at all.\r\nIn this research work we formulated a constraint programming\r\noptimization (COP) model for the robust planning of antibiotics\r\nproduction. We developed a discrete-time model with a multi-criteria\r\nobjective, ordering the different criteria and performing a\r\nlexicographic optimization. A feasible solution of the proposed\r\nCOP model is a schedule of a given set of tasks onto available\r\nresources. The schedule has to satisfy tasks precedence constraints,\r\nresource capacity constraints and time constraints. In particular\r\ntime constraints model tasks duedates and resource availability\r\ntime windows constraints. To improve the schedule robustness, we\r\nmodeled the concept of (a, b) super-solutions, where (a, b) are input\r\nparameters of the COP model. An (a, b) super-solution is one in\r\nwhich if a variables (i.e. the completion times of a culture tasks)\r\nlose their values (i.e. cultures are contaminated), the solution can be\r\nrepaired by assigning these variables values with a new values (i.e.\r\nthe completion times of a backup culture tasks) and at most b other\r\nvariables (i.e. delaying the completion of at most b other tasks).\r\nThe efficiency and applicability of the proposed model is\r\ndemonstrated by solving instances taken from a real-life\r\npharmaceutical company. Computational results showed that\r\nthe determined super-solutions are near-optimal.","references":null,"publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 103, 2015"}