An Optimization Approach to Edge Reinforcement

1 a a 2 a a 2 ~~~~~~a C 3 a c 4 b b 5 b b 6 a a 7 c c 8 d d 9 50% of the times b;SO% of the times e e 10 c c 11 b b 12 d d 13 c c 14 b or d bor d 15 d 25% of the times b; .75% of the times d 16 b b 17 c (and b) b 18 d (and e)t e 19 c c 20 c c 21 c or d* c or d* 22 b b 23 d d 24 e e 25 b or d* b or d* *Choice can be done arbitrarily. tOther optimal solutions exist where either 17 or 18 obtains mixed service. facility b). Table II includes also the optimal solution for p = 25 percent. V. SUMMARY We have considered problems with two objectives, which are quite typical to several service systems. The first objective took into account the cost of operating the system whereas the second one was a measure of "customers' suffer" that is required to be less than some unbearable level T. Two closely related models were included. In one problem we minimized the expected cost of operating the system subject to an upper bound constraint on the percentage of customers that will not be reached within time period T while in the second model we did the opposite. An exact and fast algorithm (linear in the dimensions of the problem) was presented for the first model. For medium size problems the algorithms can even be solved manually. The same algorithm can be used to solve the integer version of the problem.Response area for two emergency units," Oper. Abstract-A steepest descent method is used to iteratively adjust edge magnitudes and thereby enhance the distinction between edge and nonedge pixels. The results appear to be better than those obtained from relaxation methods based on edge probabilities, using either Bayesian probability adjustment or optimization methods.