A closed-form solution to a class of quadratic knapsack problems

One important problem in data base management is checkpointing of computer systems which is the copying of primary memory into a secondary storage device. The tradeoffs in determining optimal checkpoints involve the system unavailability during the checkpoint operation versus the possibility of system failure leading to long recovery periods. Research in this area has led to optimal checkpoint intervals assuming that they are equally spaced. With a discrete optimization model it is shown that this assumption indeed holds. The same model has also been used in solving a batching problem in a simple manufacturing context. This problem can be viewed as a subproblem in understanding how batching helps alleviate bottlenecks. The solution to the discrete optimization model can be found in closed-form. It is felt that there are many other applications which lead to a similar formulation.