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A robust optimisation model for aggregate and detailed planning of a multi-site procurement-production-distribution system

The planning problem in the context of a multi-site procurement-production-distribution system (MSPPDS) considered in this paper is motivated from a real life case of a multinational consumer goods company. A robust optimisation model considering model robustness and solution robustness in the objective function is developed for integrated planning in three dimensions. Detailed production, procurement and distribution plans are integrated; countrywide aggregate production plan is integrated with a detailed plan. Similarly the detailed production plans from the previous planning cycle are integrated with current production plans. Constraints on storage space, production capacity and the time lag between procurement, production and distribution activities are captured in the model. Procurement and production plans are treated as ‘here-and-now’ decisions and the distribution plans are treated as ‘wait-and-see’ decisions to be implemented based on the realised demand scenario. The model is illustrated using an example problem and also successfully applied to the data of a consumer goods company involving 104,000 variables (with 832 integer variables) and 21,000 constraints.