Hossein Alipour - Assistant Professor, Department of industrial Engineering, Khalkhal Branch, Islamic Azad University,Khalkhal, Iran

The production planning problems encountered in real- life situations are generally intractable due to a number of practical constraints. The decision maker has to find a good feasible solution in a reasonable execution time rather than an optimal one. The objective is to satisfy the requirementsin the production plan with minimum costs over a multi-period planning horizon. This paper proposes a new mixed integer programming model for multi-item capacitated lot-sizing problemwith setup times, safety stock and demand shortages. The problem is NP-hard and to solve it, aharmony search (HS) approach is used. To verify and validate the efficiency of the HS algorithm, the results are compared with those of the Lingo 8 software. Results suggest that the HS algorithm have good ability of solving the problem, especially in the case of large and medium-sized problems for which Lingo 8 cannot produce solutions

Lot-sizing, Safety stocks, Harmony search, Safety stock