In this paper, we consider the well-known constant-batch lot-sizing problem, which we refer to as the single module capacitated lot-sizing (SMLS) problem, and multi-module capacitated lot-sizing (MMLS) problem. We provide sufficient conditions under which the (k,l,S,I) inequalities of Pochet and Wolsey (Math of OR 18: 767-785, 1993), the mixed (k,l,S,I) inequalities, derived using mixing procedure of Gunluk and Pochet (Math. Prog. 90(3): 429-457, 2001), and the paired (k,l,S,I) inequalities, derived using sequential pairing procedure of Guan et al. (Discrete Optimization 4(1): 21-39, 2007), are facet-defining for the SMLS problem without backlogging. We also provide conditions under which the inequalities derived using the sequential pairing and the n-mixing procedure of Sanjeevi and Kianfar (Discrete Optimization 9:216-235, 2012) are facet-defining for the MMLS problem without backlogging.
Technical Report#B9, Virginia Tech, 06/2017