Knowledge that Transforms

Two types of customer behavior are considered: (1) if a customer is acquired for service before he has waited a time τ0, he remains in the queue until served irrespective of whether or not his total waiting time exceeds τ0. Only those customers who wait for a time τ0 without being acquired for service become “lost” customers, and (2) a customer whose total waiting time is τ0 becomes a lost customer irrespective of whether he is acquired for service or not.

This paper reviews some recent successes in the use of linear programming methods for the solution of discrete-variable extremum problems. One example of the use of the multistage approach of dynamic programming for this purpose is also discussed.

In his interesting paper on discrete-variable extremum problems, George Dantzig (Dantzig, G. 1957. Discrete-variable extremum problems. Opns Res. 5 266–277.) discusses the “knapsack” problem. He presents two approximate methods based upon linear programming techniques, and an exact solution based upon the functional equation method of dynamic programming (Bellman, R. 1957. Dynamic Programming. Princeton University Press.).