A fixed point iterative approach to integer programming and its distributed computation

Table 1 The market split problem

Prob.	p	q	The method		The best CPLEX strategy
Prob.	p	q	NumLPs	Feasibility	NumLPs	Feasibility
1	5	40	9,640	Feasible	87,136	Feasible
2	5	40	32,015	Feasible	718,883	Feasible
3	5	40	22,221	Feasible	484,796	Feasible
4	5	40	12,670	Feasible	139,967	Feasible
5	5	40	49,709	Feasible	454,552	Feasible
6	5	40	54,525	Infeasible	677,463	Infeasible
7	5	40	105,670	Infeasible	1,644,945	Infeasible
8	5	40	90,204	Infeasible	1,593,382	Infeasible
9	5	40	93,751	Infeasible	1,061,334	Infeasible
10	5	40	67,565	Infeasible	1,039,454	Infeasible
11	5	40	90,218	Infeasible	1,134,168	Infeasible
12	5	40	36,204	Feasible	857,912	Feasible
13	5	40	106,082	Infeasible	2,189,829	Infeasible
14	5	40	33,699	Infeasible	649,045	Infeasible
15	5	40	64,368	Infeasible	808,468	Infeasible
16	5	40	38,577	Feasible	370,900	Feasible
17	5	40	26,167	Feasible	162,529	Feasible
18	5	40	75,633	Feasible	96,595	Feasible
19	5	40	86,061	Infeasible	964,038	Infeasible
20	5	40	36,737	Infeasible	801,745	Infeasible
21	5	40	67,556	Infeasible	881,563	Infeasible
22	5	40	16,170	Feasible	1,136,200	Feasible
23	5	40	33,848	Feasible	225,732	Feasible
24	5	40	78,172	Infeasible	784,658	Infeasible
25	5	40	75,375	Infeasible	1,412,998	Infeasible