[公告]OR講義
LP-related Vocabulary, Concept & Notation
Prepared by 台大工管 賴聰乾 教授
Vocabulary & Concept: (1) algorithm, (2) simplex, (3) convex set,
(4) extreme point, (5) line segment, (6) convex combination, (7) bounded set,
(8) (optional) open set, closed set, compact set, (9) functional constraints,
(10) non-negativity constraints, (11) original form (space),
(12) augmented form (space), (13) standard form (of the original space),
(14) model parameters, (15) decision variable, (16) slack variable,
(17) artificial variable, (18) surplus variable,
(19) constraint boundary equation, (20) constraint boundary, (21) boundary,
(22) indicating variable, (23) feasible solution, (24) feasible region,
(25) optimal solution, (26) Corner-Point (CP) solution,
(27) Corner-Point Feasible (CPF) solution,
(28) defining equations (of a CP or CPF solution), (29) basic solution,
(30) Basic Feasible (BF) solution, (31) Basic Variable (BV),
(32) Non-Basic Variable (NBV), (33) basis, (34) edge (of the feasible region),
(35) adjacent (CPF solutions, BF solutions), (36) origin,
(37) initial CPF solution, (38) initial BF solution,
(39) optimality test (conditions), (40) iteration,
(41) entering basic variable, (42) leaving basic variable,
(43) minimum ratio rule, (44) pivot column, (45) pivot row, (46) pivot number,
(47) elementary row operations (ero), (48) degenerate BF solution,
(49) multiple optimal solutions, (50) unbounded Z, (51) primal problem,
(52) dual problem, (53) weak duality property, (54) strong duality property,
(55) complementary solutions property,
(56) complementary optimal solutions property, (57) symmetry property,
(58) duality theorem, (59) complementary basic solutions property,
(60) complementary slackness property,
(61) complementary optimal basic solutions property, (62) SOB method,
(63) post-optimality analysis, (64) sensitivity analysis (what-if analysis),
(65) shadow price, (66) reduced cost, (67) allowable range to stay optimal,
(68) allowable range to stay feasible, (69) binding constraint,
(70) the 100 percent rule for simultaneous changes in right-hand sides,
(71) the 100 percent rule for simultaneous changes in objective function
coefficients, (72) big M method, (73) two-phase method,
(74) revised simplex algorithm, (75) dual simplex algorithm,
(76) interior-point algorithm.
Notation: (1) n, (2) m, (3) c (1 x n row vector), (4) A (m x m matrix),
(5) b (m x 1 column vector), (6) x (n x 1 column vector),
(7) x* (n x 1 column), (8) y (1 x m row vector), (9) y* (1 x m) row vector,
(10) Z, (11) W, (13) z (1 x n row vector), (14) B (m x m matrix),
(15) S* (m x m matrix), (16) c_B (m x 1 row vector in the augmented space),
(17) x_B (1 x m column vector in the augmented space).
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