The mixing set with divisible capacities

Given rational numbers C_0,...,C_m and b_0,...,b_m, the mixing set with arbitrary capacities is the mixed-integer set defined by conditions s + C_t z_t  ≥ b_t , 0 ≤ t ≤ m, s ≥ 0, z_t integer, 0 ≤ t ≤ m. Such a set has applications in lot-sizing problems. We study the special case of divisible capacities, i.e. C_t /C_{t − 1} is a positive integer for 1 ≤ t ≤ m. Under this assumption, we give an extended formulation for the convex hull of the above set that uses a quadratic number of variables and constraints.