Production planning in furniture settings via robust optimization

Production planning procedures in small-size furniture companies commonly consists of decisions with respect to production level and inventory policy, while attempting to minimize trim-loss, backlogging and overtime usage throughout the planning horizon. Managing these decisions in a tractable way is often a challenge, especially considering the uncertainty of data. In this study, we employ robust optimization tools to derive robust combined lot-sizing and cutting-stock models when production costs and product demands are uncertainty parameters. Our motivation over the traditional two-stage stochastic programming approach is the absence of an explicit probabilistic description of the input data, as well as avoiding to deal with a large number of scenarios. The results concerning uncertainty in the cost coefficients were illustrative and confirmed previous studies. Regarding uncertainty in product demands, we provide some insights into the relationship between the budgets of uncertainty, fill rates and optimal values. Moreover, when uncertainty affects both costs and demands simultaneously, optimal values are worse for large variability levels. Numerical evidence indicated that less conservative budgets of uncertainty result in reasonable service levels with cheaper global costs, while worst-case deterministic approaches generate relatively good fill rates, but with prohibitive global costs.