We present a PTAS for the Multiple Subset Sum Problem (MSSP) with different
knapsack capacities. This is the selection of items from a given ground se
t and their assignment to a given number of knapsacks such that the sum of
the item weights in every knapsack does not exceed its capacity and the tot
al sum of the weights of the packed items is as large as possible. Our resu
lt generalizes the PTAS for the special case in which all knapsack capaciti
es are identical [1]. (C) 2000 Elsevier Science B.V. All rights reserved.