An exact algorithm for a milk tanker scheduling and sequencing problem

In rural areas, milk tankers collect milk from farms for processing at a central base. Collection runs are assigned to tankers, each tanker performing a series of runs. After each run, the tankers need to be emptied by pumps, which are limited in number. A scheduling system has been devised to allocate runs to tankers, despatch the tankers and determine when the tanker may be emptied on its return in order to minimise the total time taken (makespan) for all runs to be completed. The joint problem of scheduling and sequencing is posed as a linear integer programming (IP) problem with additional nonlinear constraints. The problem is then solved by embedding an IP algorithm within an overall branch and bound approach. The results of testing this algorithm will be discussed and compared to a proposed heuristic approach.