This paper presents a study conducted on the minimum number of open stacks problem (MOSP) which occurs in various production environments where an efficient simultaneous utilization of resources (stacks) is needed to achieve a set of tasks. We investigate through this problem how classical look-back reasonings based on explanations could be used to prune the search space and design a new solving technique. Explanations have often been used to design intelligent backtracking mechanisms in Constraint Programming whereas their use in nogood recording schemes has been less investigated. In this paper, we introduce a generalized nogood (embedding explanation mechanisms) for the MOSP that leads to a new solving technique and can provide explanations.
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