Modeling and solving the constrained multi-items lot-sizing problem with time-varying setup cost

The dynamic lot-sizing problem is highly complex and very important for the planning systems of manufacturing enterprises in time-varying environment, where production factors such as the production setup costs, unit storage costs, and production capacities may constantly rise or fall in different planning periods over the entire planning horizon. This paper proposed an extension model of the dynamic multi-product lot-sizing problem considering time-varying production setup cost and with dual constraints on dynamic capacities and resource limits, which carters for the actual situation of modern production and manufacturing systems in time-varying environments. Comparative experiments on synthesized problem instances were conducted by using the AMPL/CPLEX solver, which showed that the new model is efficiently on finding solutions with high qualities and the maximum size of test problems can be more than 500 products.