transport winqsb

7/22/2019 Transport WinQSB

1/12

Application of WinQSB for Transportation Problem: An Example

Source book: An Introduction to Management Science, By: Anderson, Sweeney, and Williams

Software: WinQSB by Yih!ong "hang

#re$ared by: %r& #arisay

%ate: 'o(ember )***, !ast u$dated: 'o( )**+

Problem:

oster -enerators needs to trans$ort $roducts from three $lants to four distribution center&

Information on $roduction $lants and their a(ailable ca$acities for the ne.t / months is gi(en

on the left hand side of the following table& 0he distribution centers and their forecasted

demand is listed on the right hand side of the following table&

Plant Production Capacity Distribution Center Demand Forecast"le(eland +*** Boston 1***

Bedford 1*** "hicago 2***

York )+** St& !ouis )***

0otal 3/+** !e.ington 3+**

0otal 3/+**

0he trans$ortation cost $er unit from each $lant to each distribution center is gi(en the table

below:

Destination

ri!in Boston "hicago St& !ouis !e.ington

"le(eland / ) 4 1Bedford 4 + ) /

York ) + 2 +

Management would like to determine how much of its $roduction should be shi$$ed from each$lant to each distribution center with a minimum total cost&

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2/12

Enter t"e problem:

Select 5'etwork module6 from WinQSB& "lick on 5ile6 and 5'ew #roblem6& Select

50rans$ortation #roblem6 and in$ut information that are asked for as below&

You do not need to consider balancing the trans$ortation $roblem 7dummy su$$ly or dummy

demand8& 0he software will do that& 9owe(er, if you ha(e information for $enalty costs you

need to define a dummy su$$ly $oint& You can 5dit6 the names for source and demand $oints7node names8& nter unit cost and ca$acity information as below:

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3/12

Sol#e t"e problem:

"lick on 5Sol(e and Analy;e6 then select 5sol(e the $roblem6& Below is the solution&

btain more information:

"lick on 5results$timality6, 5=ange of

easibility6, 5-ra$hic Solution6, and 5#erform #arametric Analysis6&

Belo$ is t"e result for %&rap"ic Solution':

/


4/12

(ere is t"e result for %)an!e of ptimality':

0hat is coefficients in ob?ecti(e function 7unit cost of shi$ment8& It $ro(ides the range7Allowable Min and Allowable ma.8 that the coefficient 7@nit "ost8 can change and still ha(e

the same solution 7i?8 but with different minimum cost 7refer to your slides on sensiti(ity

analysis for !#8& 'otice that similar to !inear #rogramming you ha(e 5basic6 and 5at bound67nonbasic8 (ariables& or at bound (ariables you ha(e 5=educed "ost6 information similar to

!inear #rogramming&

(ere is t"e result for %)an!e of Feasibility':

0hat is ca$acities of su$$ly and demand $oints& It $ro(ides the range 7Allowable Min and

Allowable ma.8 that the ca$acity can change and still ha(e the same basis 7shi$ from one node

to the other8 but with different amount of shi$ment and minimum cost 7refer to your slides onsensiti(ity analysis for !#8& 'otice that similar to !inear #rogramming you ha(e 5Shadow

#rice6 information&

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5/12

Application of %Perform Parametric Analysis':

You can select to $erform sensiti(ity analysis on a 5!ink6 or a 5'ode6& 5!ink6 means cost of

unit shi$ment, coefficient in ob?ecti(e function& 5'ode6 means ca$acity of demand or su$$ly

$oint&

In the following e.am$le, I selected the cost of unit shi$ment from "le(eland to Boston&

Select a range for your sensiti(ity analysis 7starting u and ending u8& Your 5starting u6 will bea negati(e (alue that indicates as much as you want to see below the current (alue& 9ere

starting u is ), which means start from /)3& Your 5ending u6 will be a $ositi(e (alue that

indicates as much as you want to see abo(e the current (alue& 9ere ending u is C3*, which

means go u$ to /C3*3/& 5Ste$s of u6 is selected to be 3 in this e.am$le&

+


6/12

Below is the result of sensiti(ity analysis for changing coefficient of ob?ecti(e function as a

table:

0he same result is $resented as a gra$h below:

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7/12

In the following e.am$le you can see the result for 5#erform #arametric Analysis6 on ca$acity

7here "le(eland8& You should select the range 7starting u and ending u8 for ca$acities of su$$lyor demand $oints& Your 5starting u6 will be a negati(e (alue that indicates as much as you

want to see below the current (alue& 9ere starting u is 3)**, which means start from +***

3)**/D**& Your 5ending u6 will be a $ositi(e (alue that indicates as much as you want to seeabo(e the current (alue& 9ere ending u is C3D**, which means go u$ to+***C3D**1D**&

5Ste$s of u6 is selected to be 3** in this e.am$le&

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8/12

0he result of sensiti(ity analysis for changing ca$acity as a table:

D


9/12

0he result of sensiti(ity analysis for changing ca$acity as a gra$h:

E


10/12

Another e.am$le on sensiti(ity analysis of ca$acity of Bedford:

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11/12

Select "euristic met"od for initial basic feasible solution *optional+:

You can select a heuristic method for obtaining the Initial Solution& If you do not make a

selection the software will use its default method& 0he heuristic method will not affect the finalsolutionF ?ust the number of iterations to sol(e the $roblem may be different&

I selected 'orthwest "orner method below:

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12/12

Below is the first iteration towards solution&

After sol(ing the $roblem you can select 5Show run time and iterations6 from 5=esults6 in to$

menu& You will get the following& 72 iterations for 'W" method and ) iterations for =M, butsame o$timal solution8

3)

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