### Table 1 summarizes the e ect of increase in opportunity cost of utilizing a unit of capacity which is equivalent to a decrease in available capacity levels on the optimal Sr depending on the conditions on unit cost and unit capacity requirements that are given in Theorem 2, and 3.

2003

"... In PAGE 11: ...Table 1 summarizes the e ect of increase in opportunity cost of utilizing a unit of capacity which is equivalent to a decrease in available capacity levels on the optimal Sr depending on the conditions on unit cost and unit capacity requirements that are given in Theorem 2, and 3. Place Table1 here Theorem 2 shows that, if the remanufacturing option is inferior to manufacturing with re- spect to both unit cost and capacity requirement, it is never utilized in the optimal solution under the substitution scheme considered. From the same theorem, it can be observed that for the cases where manufacturing has unit cost and remanufacturing has the capacity requirement advantages, as the available capacity gets tighter, remanufacturing option is utilized since the unit cost of utilizing one unit of capacity will increase.... In PAGE 27: ... Technical report 2002;02-02,Department of Industrial Engineering, Middle East Technical University. Table1 : The Behavior of S r with respect to an increase in , ( 0 = cr cm am ar ) cr lt; cm cr gt; cm non decreasing - S r = 0 up-to 0 , ar lt; am - non decreasing -non increasing S r = 0 ar gt; am -hits zero at 0 Table 2: Available Capacity Levels under which the Utilization Ratio of Remanufacturing Option Drops to Zero under Substitution (ar = 2) Scenario Case A Case B Case C S1 39 45 1 S2 8 8 1 S3 20 1 1 S4 4.21 5.... ..."

### Table 1: Gain in Erlang capacity by slowing transmission rates by a factor of a

"... In PAGE 6: ... Using Theorem 2 we see that the Erlang capacity of the system is = 1:361, which means that for having at most 1% of losses the rate of arrival of sessions should be limited to = = 21:8 calls per second. Table1 shows the gain by slowing the transmission rates by a factor of a. For each a it gives the Erlang Capac- ity EC(1%) as well as the rate of arriving calls that the system can handle without exceeding 1% of blocking.... ..."

### Table 1: The Behavior of S r with respect to an increase in , ( 0 = cr cm am ar )

2003

"... In PAGE 11: ... Proof : See Appendix II. Table1 summarizes the e ect of increase in opportunity cost of utilizing a unit of capacity which is equivalent to a decrease in available capacity levels on the optimal Sr depending on the conditions on unit cost and unit capacity requirements that are given in Theorem 2, and 3. Place Table 1 here Theorem 2 shows that, if the remanufacturing option is inferior to manufacturing with re- spect to both unit cost and capacity requirement, it is never utilized in the optimal solution under the substitution scheme considered.... In PAGE 11: ... Table 1 summarizes the e ect of increase in opportunity cost of utilizing a unit of capacity which is equivalent to a decrease in available capacity levels on the optimal Sr depending on the conditions on unit cost and unit capacity requirements that are given in Theorem 2, and 3. Place Table1 here Theorem 2 shows that, if the remanufacturing option is inferior to manufacturing with re- spect to both unit cost and capacity requirement, it is never utilized in the optimal solution under the substitution scheme considered. From the same theorem, it can be observed that for the cases where manufacturing has unit cost and remanufacturing has the capacity requirement advantages, as the available capacity gets tighter, remanufacturing option is utilized since the unit cost of utilizing one unit of capacity will increase.... ..."

### Table 1 shows where our result fits in in the context of previous work.

2006

"... In PAGE 3: ...Table1 : Table of Results about Rationality of Equilibrium in Capacity Allocation markets. The table also notes the existence of min-max theorems.... ..."

Cited by 3

### Table 3. Composition Theorems

1999

"... In PAGE 7: ...2 Composition theorems In this section we discuss some useful theorems, that can be proved exploiting the semantics in Table 2 and the de nitions in the previous subsection. We distinguish liveness ( Table3 , 1{6) and safety (Table 3, 7{15). (1) Reliable Communication: this theorem characterizes remote writings, linking the su cient cause in the sender to the e ect in the recipient.... ..."

Cited by 4

### Table 4. Composition Theorems.

1999

"... In PAGE 7: ...4 Composition Theorems In this section we discuss some useful theorems, that can be proved exploiting the semantics in Table 3 and the de nitions in the previous subsection. We distinguish liveness ( Table4 , 4{8) and safety (Table 4, 9{15). Most theorems refer to the new operators, and only few of them refer to Unity operators: the former are those needed to prove the re nement templates presented in this paper.... ..."

Cited by 4

### lable capacity.

2005