The material-handling systems for the Maltese distribution centre in La Valletta of Ekom makes use of hand transpallet trucks which can hold at most three roll containers, with a capacity of 15 packages each. Last January 9, at 10:15 AM, a picking list was created of eight orders to be retrieved from the storage zone, according to Table 1.
The Euclidean distances between the centres of gravity of such orders are reported in Table 2.
The Euclidean distance between the centres of gravity of order 7 and 8 can be obtained from Tables 3 and 4, reporting the list of packages and the corresponding Cartesian coordinates.
Determine a lower bound on the number of grouped orders. Identify how to group orders, based on a seed order, choosing orders on the basis of their number of packages.