This paper presents a binary particle swarm optimization algorithm for the lot sizing problem. The problem is to find order quantities which will minimize the total ordering and holding costs of ordering decisions. Test problems are constructed randomly, and solved optimally by Wagner and Whitin Algorithm. Then a binary particle swarm optimization algorithm and a traditional genetic algorithm are coded and used to solve the test problems in order to compare them with those of optimal solutions by the Wagner and Whitin algorithm. Experimental results show that the binary particle swarm optimization algorithm is capable of finding optimal results in almost all cases.