A belief-rule-based inference method for aggregate production planning under uncertainty

Finding high-performance solutions for aggregate production planning (APP) poses a significant challenge for both academics and practitioners alike. In real-world problems, severe demand fluctuations make forecasts hardly reliable. Forecast errors can be biased and magnifying from immediate to distant periods, and unstable demands are usually forecast in uncertain forms. For APP under uncertain demands, a new hierarchical belief-rule-based inference (BRBI) method is proposed. As an expert system with a belief-rule structure, BRBI can assist decision-makers in planning production, workforce and inventory levels with corresponding information representation, causal inference and identification algorithms. Operational data and expert knowledge can be employed to construct, initialise, and adjust the belief-rule base (BRB). An inference engine algorithm is developed to handle both deterministic and interval inputs. In order to make the method applicable to both continuous and discrete production settings, continuous mode and switching mode for BRBI are proposed using different transformation techniques. To approximate hidden patterns in APP situations, simultaneous identification and two-step identification for structure and parameter of BRB are developed. The two-step identification contains a belief k-means (BKM) clustering algorithm extended from k-means and fuzzy c-means. BKM ensures that an optimal cluster can both facilitate human cognition and improve accuracy of identification and inference. A paint-factory example is utilised to conduct comparative studies and sensitivity analyses in deterministic forecast context, and an automotive production example is implemented to illustrate BRBI's advantage in interval forecast context and to contrast simultaneous identification and two-step identification.