Optimal resource investment and scheduling of tests for new product development

Abstract

Previous optimization models for the scheduling of tests for pharmaceuticals and agrochemicals assume that the resources available for testing such as laboratories and scientists are constant throughout the testing horizon, and that all testing tasks have fixed cost, duration and resource requirements. In order to be able to handle more effectively a number of potential products in the R&D pipeline a company may consider the option to install/hire additional resources. Also, the type and amount of resources can be chosen for some tests to reduce their duration. In this paper we propose a new scheduling MILP model that addresses these issues to optimize the overall costs. More specifically, the model (a) allows for installation of new resources during the course of testing, and (b) handles cost and duration of tests as functions of the type and amount of the resources assigned to each test. To enhance the solution of the model we develop: (a) a reformulation with disaggregated variables, (b) a procedure for the tightening of the big- M constraints, (c) a procedure that fixes some of the sequencing binary variables, and (d) logic cuts. The solution of a single large-scale problem is avoided with a heuristic decomposition algorithm that relies on solving a reduced mixed-integer program that embeds the optimal schedules obtained for the individual products. The proposed algorithm is shown to be one to two orders of magnitude faster than the full space method yielding solutions that are optimal or near optimal.