Analyzing Simultaneous Changes in R

Analyzing Simultaneous Changes in Right-Hand Sides. When multiple bi values
are changed simultaneously, the formula b*  S*b  can again be used to see how the right-
hand sides change in the final tableau. If all these right-hand sides still are nonnegative, the
feasibility test will indicate that the revised solution provided by this tableau still is feasi-
ble. Since row 0 has not changed, being feasible implies that this solution also is optimal.
Although this approach works fine for checking the effect of a specific set of changes in
the bi, it does not give much insight into how far the bi can be simultaneously changed from
their original values before the revised solution will no longer be feasible. As part of postop-
timality analysis, the management of an organization often is interested in investigating the
effect of various changes in policy decisions (e.g., the amounts of resources being made avail-
able to the activities under consideration) that determine the right-hand sides. Rather than
considering just one specific set of changes, management may want to explore directions of
changes where some right-hand sides increase while others decrease. Shadow prices are in-
valuable for this kind of exploration. However, shadow prices remain valid for evaluating the
effect of such changes on Z only within certain ranges of changes. For each bi, the allowable
range to stay feasible gives this range if none of the other bi are changing at the same time.
What do these allowable ranges become when some of the bi are changing simultaneously?
A partial answer to this question is provided by the following 100 percent rule, which
combines the allowable changes (increase or decrease) for the individual bi that are given
by the last two columns of a table like Table 6.22.
The 100 Percent Rule for Simultaneous Changes in Right-Hand Sides: The
shadow prices remain valid for predicting the effect of simultaneously changing
the right-hand sides of some of the functional constraints as long as the changes
are not too large. To check whether the changes are small enough, calculate for
each change the percentage of the allowable change (increase or decrease) for that
right-hand side to remain within its allowable range to stay feasible. If the sum of
the percentage changes does not exceed 100 percent, the shadow prices definitely
will still be valid. (If the sum does exceed 100 percent, then we cannot be sure.)
Example (Variation 3 of the Wyndor Model). To illustrate this rule, consider Vari-
ation 3 of the Wyndor Glass Co. model, which revises the original model by changing the
right-hand side vector as follows:
b   b   .
The calculations for the 100 percent rule in this case are
b2: 12  15. Percentage of allowable increase  100
 15 
6
12
 50%
b3: 18  15. Percentage of allowable decrease  100 18 
6
15
 50%
Sum  100%
Since the sum of 100 percent barely does not exceed 100 percent, the shadow prices
definitely are valid for predicting the effect of these changes on Z. In particular, since

Kết quả (Anh) 1:

Analyzing Changes in Simultaneous right-hand Sides. When multiple bi valuesare changed simultaneously, the formula b * S * b can again be used to see how the right-hand sides change in the final tableau. If all these right-hand sides still are nonnegative, thefeasibility test will indicate that the revised solution provided by this tableau still is feasi-ble. Since row 0 has not changed, being feasible implies that this solution also is optimal.Although this approach works fine for checking the effect of a specific set of changes inthe ball, it does not give much insight into how far the ball can be simultaneously changed fromtheir original values before the revised solution will no longer be feasible. As part of postop-timality analysis, the management of an organization often is interested in investigating theeffect of various changes in policy decisions (e.g., the equivalent of resources being made avail-able to the activities under consideration) that determine the right-hand sides. Rather thanconsidering just one specific set of changes, management may want to explore the directions ofchanges where some right-hand sides increase while others decrease. Shadow prices are in-valuable for this kind of exploration. However, shadow prices remain valid for evaluating thethe effect of such changes on the Z only within certain ranges of changes. For each bi, the allowablerange to stay feasible gives this range if none of the other balls are changing at the same time.What do these allowable ranges become when some of the marbles are changing simultaneously?A partial answer to this question is provided by the following 100 percent rule, whichcombines the allowable changes (increase or decrease) for the individual Marbles that are givenby the last two columns of a table like Table 6.22.The 100 Percent Rule for Simultaneous Changes in right-hand Sides: Theshadow prices remain valid for predicting the effect of simultaneously changingthe right-hand sides of some of the functional constraints as long as the changesare not too large. To check whether the changes are small enough, calculate foreach change the percentage of the allowable change (increase or decrease) for thatright-hand side to remain within its allowable range to stay feasible. If the sum ofthe percentage changes does not exceed 100 percent, the shadow prices definitelywill still be valid. (If the sum does exceed 100 percent, then we cannot be sure.)Example (Variation 3 of the Wyndor Model). To illustrate this rule, consider Vari-ation 3 of the Wyndor Glass Co. model, which revises the original model by changing theright-hand side vector as follows:b   b   .The calculations for the 100 percent rule in this case areB2:12 15. Percentage of allowable increase 100 1561250%B3:18 15. Percentage of allowable decrease 100 1861550%Sum 100%Since the sum of 100 percent barely does not exceed 100 percent, the shadow pricesdefinitely are valid for predicting the effect of these changes on Z. In particular, since

Kết quả (Anh) 2:

Simultaneous Analyzing Changes in Right-Hand Sides. When multiple bi values
​​are changed simultaneously, the formula b *? S * b? can be used to see how again the Right-
hand sides in the final tableau change. If all these right-hand sides still are nonnegative, the
Feasibility test solution will indicate rằng revised Provided by this tableau is still feasi-
ble. Since row 0 hasnt changed, this being feasible solution là có cũng is Optimal.
Although this approach works fine for checking the effect of a specific set of changes to print
the ball, it does not give much insight Into how far the ball can be simultaneously changed from
original chúng trước revised values ​​will no longer be feasible solution. As part of postop-
timality analysis, the management of an organization is interested print often Do Investigating the
effects of various policy changes print Decisions (eg, the resources being made ​​avail- tiền of
thể the Activities under Consideration) is the right-hand quyết Sides. Thay
considering just one specific set of changes, management muốn explore sewing directions of
changes where some right-hand sides while others Decrease tăng. Shadow prices are in-
Valuable for this kind of exploration. Tuy nhiên, shadow prices Remain valid for Evaluating the
effect of such 'changes on Z only trong Certain ranges of changes. For each ball, the Allowable
range to stay this Gives feasible if none of the other range balls at the same time thay are.
What do những Allowable ranges trở khi thay are some of the balls simultaneously?
A partial answer to this question is provided by sau 100 percent rule, mà
combines the Allowable changes (tăng or Decrease) for the the individual bi được given
by the last two columns of a table like Table 6:22.
The 100 Percent Rule for Simultaneous Changes in Right-Hand Sides: The
shadow Remain prices valid for predicting the effect of simultaneously thay
the right-hand sides of some of the functional constraints as Long as the changes
are not too large. To check the changes are small enough nếu, calculate for
each change the percentage of the Allowable change (tăng or Decrease) for that
right-hand side to Remain its trong Allowable range to stay feasible. If the sum of
the percentage changes does not Exceed 100 percent, the shadow prices definitely
will still be valid. (If the sum does Exceed 100 percent, then WE CAN not be sure.)
Example (Variation 3 of the Wyndor Model). To illustrate this rule, như Vari-
ation 3 of the Wyndor Glass Co. model, revises the original model by mà đổi
right-hand side vector to as follows:
b? ? b? ? .
The calculations for the 100 percent rule in this case are
b2: 12? 15. Percentage of Allowable tăng? 100
?? 15?
6
12
??? 50%
b3: 18? 15. Percentage of Allowable Decrease? 100 ?? 18?
6
15
??? 50%
Sum? 100%
Since the sum of 100 percent does not Exceed 100 percent barely, the shadow prices
are valid for predicting definitely the effect of changes on Z. In Particular những, since