Coordinating continuous-time distribution and sales planning of perishable goods with quality grades

A variety of industries handling perishable goods is faced with the challenge of reducing lead times in order to ensure the best possible freshness of products at the point of sales. Considering a short-term multi-day planning horizon, the implementation of quantitative optimisation approaches with a continuous-time representation is most appropriate for planning and scheduling. However, as the quality measures are usually standardised by discrete grades, coordination take thresholds of maximum delivery times into account. For this purpose, a new mixed-integer linear programming model is developed. It enables to assess complete material flows, whose formal composition originates in a method based on power sets on the one hand, but additionally allows for the exact scheduling of partial material flows between sites. Specific transportation conditions that need to be imposed with respect to shelf-life are included. The efficiency of the model is confirmed by comparison with an equivalent mixed-integer linear formulation that uses path variables for modelling complete material flows. Besides an illustrative example motivated by the real-life problem of a fresh produce company supplying a wholesaler group, both model formulations are validated within a numerical analysis composed of 10 scenarios with different numbers of suppliers, warehouses, markets and product variants. Each scenario includes six instances with randomly generated data. As a result of the computations using high-performance hardware and software, it was shown that the formulation based on power sets was superior in each instance, as it enabled determining optimal solutions within significantly reduced computation times.