Solving multi-item multi-period capacitated lot sizing problem with considerations of backorders and setups

In this work we introduce an innovative procedure to solve the capacitated lot sizing problem with backorders and setup times, called CLSP_BS. The procedure formulates CLSP_BS as a mixed integer programming (MIP) problem, reduces it to the structure of a bounded variable linear program; and then calculates some ratios of the coefficients to determine an approximate solution to the problem. This initial solution is further improved using an intelligent enumeration procedure. Adopting this procedure, we solve the NP hard MIP differently and easily, by mere calculation of a few ratios and without actually using any traditional solution approaches, viz. simplex, interior point method, etc.