Linear Programming Constraints and Variables: Definitions and Effects

Binding Constraint: LHS equals to RHS at optimal ;  Non-binding constraint: LHS is not equal to RHS at optimal

Shadow Price: Amount by which OFV changes if RHS is increased by one unit

Basic Variable: A decision variable which has non-zero value at optimal ;  Non-basic Value: A decision variable which has a value of zero at optimal

Reduced cost: Amount by which the objective function coefficient needs to be decreased before the variable becomes basic

• Basic var: "Final Value" >0 and "Reduced cost"=0; With allow inc/dec, optimal solution (Final Value) doesn't change, OFV change by (change)*(Final Value); Beyond allow inc/dec, optimal solution and OFV changes by RESOLVE.
• Non basic var:  "Final Value"=0 and "Reduced cost"≠0; In a MIN,"Reduced cost"=allow dec(>0); allow inc=infinity; In a MAX,"Reduced cost"=(-allow inc)<0, allow dec=infinity; within allow inc/dec, optimal solution(final value) doesn't change, OFV doesn't change; beyond allow inc/dec, optimal solution(final value) and OFV change by >0,
• Binding: "Final Value"="RHS" and "Shadow Price"≠0; Within allow inc/dec, optimal solution(Final Value) changes and OFV changes by (change)*(Shadow Price); Beyond allow inc/dec, optimal solution(Final Value) and OFV changes by RESOLVE.

  Max problem and ≤ type constraint: shadow price is positive; Max problem and ≥ type constraint: shadow price is negative

  Min problem and ≤ type constraint: shadow price is negative; Min problem and ≥ type constraint: shadow price is positive

• Non-binding: have "Final Value"≠"RHS" and "Shadow Price"=0; Within allow inc/dec, optimal solution(Final Value) doesn't change, OFV doesn't change; Beyond inc/dec, optimal solution(Final Value) and OFV changes by RESOLVE.

  ≤ type constraint: Allowable increase: infinity, Allowable decrease: RHS-Final Value;  ≥ type constraint: Allowable increase: Final Value -RHS, Allowable decrease: infinity

• Deleting a non-binding constraint: optimal solution and OFV remain as before; Deleting a binding constraint: optimal solution and OFV change by RESOLVE

• If Adding constraint, optimal solution满足constraint, optimal sol and OFV remain same; Otherwise, the optimal sol and OFV change by RESOLVE.