## Introduction to Operations Research, Volume 1-- This classic, field-defining text is the market leader in Operations Research -- and it's now updated and expanded to keep professionals a step ahead -- Features 25 new detailed, hands-on case studies added to the end of problem sections -- plus an expanded look at project planning and control with PERT/CPM -- A new, software-packed CD-ROM contains Excel files for examples in related chapters, numerous Excel templates, plus LINDO and LINGO files, along with MPL/CPLEX Software and MPL/CPLEX files, each showing worked-out examples |

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Page 127

Frederick S. Hillier, Gerald J. Lieberman. TABLE 4.6 First two simplex tableaux

for the Wyndor Glass Co. problem Coefficient of :

Iteration Eq . Z X2 X3 X5 Z ( 0 ) 1 -3 0 0 0 X3 1 1 0 -5 0 2 2 0 0 0 0 0 0 0 4 12 18

X4 ( 2 ) ...

Frederick S. Hillier, Gerald J. Lieberman. TABLE 4.6 First two simplex tableaux

for the Wyndor Glass Co. problem Coefficient of :

**Basic Variable**Right SideIteration Eq . Z X2 X3 X5 Z ( 0 ) 1 -3 0 0 0 X3 1 1 0 -5 0 2 2 0 0 0 0 0 0 0 4 12 18

X4 ( 2 ) ...

Page 159

... ( with adjusted values ' for the

change in the other right - hand sides . ... Once again , this information obtained

algebraically also can be derived from graphical analysis for this two - variable ...

... ( with adjusted values ' for the

**basic variables**) remains feasible , assuming nochange in the other right - hand sides . ... Once again , this information obtained

algebraically also can be derived from graphical analysis for this two - variable ...

Page 375

Since Cij – U ; – v ; is required to be zero if xij is a

satisfy the set of equations Cij = U ; + y ; for each ( i , j ) such that Xij is basic .

There are mtn 1

Since the ...

Since Cij – U ; – v ; is required to be zero if xij is a

**basic variable**, u ; and v ;satisfy the set of equations Cij = U ; + y ; for each ( i , j ) such that Xij is basic .

There are mtn 1

**basic variables**, and so there are m + n - 1 of these equations .Since the ...

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activity additional algorithm alternative amount analysis apply assignment assumed basic variable begin BF solution calculate called changes coefficients column complete Consider constraints Construct corresponding cost CPF solution customers decision demand described determine developed distribution entering equations estimated example expected feasible FIGURE final flow formulation given gives hour identify illustrate increase indicates initial inventory iteration linear programming machine Maximize mean million Minimize month needed node objective function obtained operations optimal optimal solution original parameter path payoff plant player possible presented Prob probability problem procedure profit programming problem queueing respectively resulting shown shows side simplex method solution solve step strategy Table tableau tion transportation unit waiting weeks