2020/
2021
Besliskunde
Opgaves
JAAR 1 – BLOK 4
BEDRIJFSKUNDE / RSM
,INHOUDSOPGAVE
WEEK 1 ....................................................................... 3
oefenopgaves ......................................................................................................................... 3
opgave 3.17 – maximax criterium ............................................................................................ 3
opgave 3.18 – maximin criterium ............................................................................................. 3
opgave 3.19 – EMV / beslissen met risico .................................................................................. 4
opgave 3.20 – EMV / prijs perfecte voorspelling ......................................................................... 4
opgave 3.21 – minimize opportunity loss ................................................................................... 5
opgave 3.22 – decision table.................................................................................................... 5
opgave 3.23 – willing to pay .................................................................................................... 6
opgave 3.24 – max regret / spijt .............................................................................................. 7
opgave 3.25 – resthoeveelheid................................................................................................. 7
opgave 3.26 – inkopen ............................................................................................................ 8
opgave 3.27 – inkopen ............................................................................................................ 9
opgave 3.30 - decisions ........................................................................................................ 10
opgave 3.31 – evaluate options .............................................................................................. 11
opgave 3.32 – minimax / opportunity loss ............................................................................... 12
bonus opgave ....................................................................................................................... 13
opgave 1 – Algemene vergelijking + beslistabel ....................................................................... 13
opgave 2 – Hurwicz criterium ................................................................................................. 13
opgave 3 – waarde van perfecte informatie ............................................................................. 13
WEEK 2 ...................................................................... 15
oefenopgaves ....................................................................................................................... 15
Opgave 3.36 – beslissingsboom voor probleem ........................................................................ 15
Opgave 3.37 – emv / expected value of sample information / efficiency ...................................... 15
opgave 3.38 – beslissingsboom .............................................................................................. 16
opgave 3.39 – market research / change probability without changing decision............................ 17
opgave 3.40 – advice ............................................................................................................ 18
opgave 3.41 – marketing research (un)favorable / probability of succesful .................................. 19
opgave 3.42 – probability of a favorable market ....................................................................... 19
opgave 3.43 – value to be indifferent ...................................................................................... 20
opgave 3.47 – utility theory / emv criterium ............................................................................ 21
opgave 3.48 – expected utility / risk seekers / risk avoiders ...................................................... 21
opgave 3.49 – maximize expected utility , change dicision ........................................................ 22
opgave 3.50 – utility / expected time ...................................................................................... 22
opgave 3.53 – revised probabilitys / EVSI .............................................................................. 23
bonus opgave ....................................................................................................................... 25
opgave 1 – beslissingsboom tekenen ...................................................................................... 25
opgave 2 – Vanaf welke waarde verandert de beslissing ............................................................ 25
opgave 3 – EMV berekenen.................................................................................................... 26
WEEK 4 ...................................................................... 27
oefenopgaves ....................................................................................................................... 27
opgave 13.14 – conduct the simulation ................................................................................... 27
opgave 13.15 – cumulative probability distribution / random numbers ........................................ 28
opgave 13.16 – expected value formula .................................................................................. 28
opgave 13.19 – simulate / what profit if they decide … .............................................................. 29
, opgave 13.20 – forecast % / simulate ..................................................................................... 30
opgave 13.21 – weekly stockout costs / weekly holding costs .................................................... 31
bonusopgaves ...................................................................................................................... 32
opgave 1 – verwachte aantal klanten per uur ........................................................................... 32
opgave 2 – bezettijd kassa / tabel invullen .............................................................................. 32
opgave 3 – totale wachttijd ................................................................................................... 33
WEEK 6 ...................................................................... 34
oefenopgaves ....................................................................................................................... 34
opgave 7.14 – best combi / corner point graphical approach ...................................................... 34
opgave 7.15 – slack or surplus ............................................................................................... 35
opgave 7.16 – welke hoeveelheid gebruiken ............................................................................ 36
opgave 7.17 – hoe veel produceren / LP Approach .................................................................... 37
opgave 7.18 ........................................................................................................................ 37
opgave 7.27 – formulation / unbounded / onbegrens / correct / feasible ..................................... 38
bonus opgaves ..................................................................................................................... 39
opgave 1 – LP probleem ........................................................................................................ 39
opgave 2 – hoekpuntenmethode ............................................................................................ 39
WEEK 7 ...................................................................... 41
oefenopgaves ....................................................................................................................... 41
opgave 7.31 – lp problem / optimal solution ............................................................................ 41
opgave 7.32 – LP formulation / constraint change .................................................................... 42
opgave 7.33 – computer output ............................................................................................. 42
opgave 7.34 – dual prices / constraints / resources .................................................................. 43
opgave 7.35 – chage constrains / right hand / left hand value ................................................... 44
opgave 7.37 ........................................................................................................................ 45
bonusopgaves ...................................................................................................................... 47
opgave 1 – waarden parameter a ........................................................................................... 47
opgave 2 – nieuwe optimale doelstellingswaarde ...................................................................... 47
opgave 3 – nieuwe optimale doelstellingswaarde ...................................................................... 48
opgave 3 – nieuwe optimale doelstellingswaarde ...................................................................... 48
WEEK 8 ...................................................................... 49
oefenopgaves ....................................................................................................................... 49
opgave 8.2 – investment decision problem .............................................................................. 49
opgave 8.3 – restairamt work scheduling problem .................................................................... 50
opgave 8.4 – animal feed mix problem .................................................................................... 50
opgave 8.5 – linear programming to determine production ........................................................ 51
opgave 8.10 – high school busing problem .............................................................................. 52
opgave 10.11 – 0-1 programming problem .............................................................................. 53
opgave 10.14 – write constraints ............................................................................................ 53
opgave 10.17 – npv .............................................................................................................. 54
opgave 10.18 - constraints .................................................................................................... 55
bonusopgaves ...................................................................................................................... 56
opgave 1 – ILP probleem ....................................................................................................... 56
opgave 2 – ILP probleem ....................................................................................................... 56
,WEEK 1
OEFENOPGAVES
OPGAVE 3.17 – MAXIMAX CRITERIUM
Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken
has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced
to consider purchasing some more equipment for Brown Oil because of competition. His alternatives
are shown in the following table:
For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of
$300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. But Ken
has always been a very optimistic decision maker.
(a) What type of decision is Ken facing?
Beslissen bij onzekerheid
(b) What decision criterion should he use?
Maximax criterium
(c) What alternative is best?
Volgens het maximax criterium is sub 100 de beste keuze
OPGAVE 3.18 – MAXIMIN CRITERIUM
Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob
iscredited with making the company a financial success. Bob is vice president of finance. Bob attributes
his success to his pessimistic attitude about businesS and the oil industry. Given the information from
Problem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should
Bob use, and what alternative will he select?
Nu maken we gebruim van het Maximin criterium
Volgens het maximin criterium is Texan de beste keuze
, OPGAVE 3.19 – EMV / BESLISSEN MET RISICO
The Lubricant is an expensive oil newsletter to which many oil giants subscribe, including Ken Brown
(see Problem 3-17 for details). In the last issue, the letter described how the demand for oil products
would be extremely high. Apparently, the American consumer will continue to use oil products even if
the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chance
of a favorable market for oil products was 70%, while the chance of an unfavorable market was only
30%. Ken would like to use these probabilities in determining the best decision.
(a) What decision model should be used?
Er is nu sprake van beslissen met risico. We gebruiken de Expected Monetary Value als criterium
(b) What is the optimal decision?
Dus de beste keuze is sub 100
(c) Ken believes that the $300,000 figure for the Sub 100 with a favorable market is too
high. How much lower would this figure have to be for Ken to change his decision made in
part (b)?
Dus zodra de winst voor sub 100 bij een positieve markt kleiner is dan 292 857 zal de beslissing van
Ken veranderen
OPGAVE 3.20 – EMV / PRIJS PERFECTE VOORSPELLING
Mickey Lawson is considering investing some money that he inherited. The following payoff table gives
the profits that would be realized during the next year for each of three investment alternatives Mickey
is considering:
2021
Besliskunde
Opgaves
JAAR 1 – BLOK 4
BEDRIJFSKUNDE / RSM
,INHOUDSOPGAVE
WEEK 1 ....................................................................... 3
oefenopgaves ......................................................................................................................... 3
opgave 3.17 – maximax criterium ............................................................................................ 3
opgave 3.18 – maximin criterium ............................................................................................. 3
opgave 3.19 – EMV / beslissen met risico .................................................................................. 4
opgave 3.20 – EMV / prijs perfecte voorspelling ......................................................................... 4
opgave 3.21 – minimize opportunity loss ................................................................................... 5
opgave 3.22 – decision table.................................................................................................... 5
opgave 3.23 – willing to pay .................................................................................................... 6
opgave 3.24 – max regret / spijt .............................................................................................. 7
opgave 3.25 – resthoeveelheid................................................................................................. 7
opgave 3.26 – inkopen ............................................................................................................ 8
opgave 3.27 – inkopen ............................................................................................................ 9
opgave 3.30 - decisions ........................................................................................................ 10
opgave 3.31 – evaluate options .............................................................................................. 11
opgave 3.32 – minimax / opportunity loss ............................................................................... 12
bonus opgave ....................................................................................................................... 13
opgave 1 – Algemene vergelijking + beslistabel ....................................................................... 13
opgave 2 – Hurwicz criterium ................................................................................................. 13
opgave 3 – waarde van perfecte informatie ............................................................................. 13
WEEK 2 ...................................................................... 15
oefenopgaves ....................................................................................................................... 15
Opgave 3.36 – beslissingsboom voor probleem ........................................................................ 15
Opgave 3.37 – emv / expected value of sample information / efficiency ...................................... 15
opgave 3.38 – beslissingsboom .............................................................................................. 16
opgave 3.39 – market research / change probability without changing decision............................ 17
opgave 3.40 – advice ............................................................................................................ 18
opgave 3.41 – marketing research (un)favorable / probability of succesful .................................. 19
opgave 3.42 – probability of a favorable market ....................................................................... 19
opgave 3.43 – value to be indifferent ...................................................................................... 20
opgave 3.47 – utility theory / emv criterium ............................................................................ 21
opgave 3.48 – expected utility / risk seekers / risk avoiders ...................................................... 21
opgave 3.49 – maximize expected utility , change dicision ........................................................ 22
opgave 3.50 – utility / expected time ...................................................................................... 22
opgave 3.53 – revised probabilitys / EVSI .............................................................................. 23
bonus opgave ....................................................................................................................... 25
opgave 1 – beslissingsboom tekenen ...................................................................................... 25
opgave 2 – Vanaf welke waarde verandert de beslissing ............................................................ 25
opgave 3 – EMV berekenen.................................................................................................... 26
WEEK 4 ...................................................................... 27
oefenopgaves ....................................................................................................................... 27
opgave 13.14 – conduct the simulation ................................................................................... 27
opgave 13.15 – cumulative probability distribution / random numbers ........................................ 28
opgave 13.16 – expected value formula .................................................................................. 28
opgave 13.19 – simulate / what profit if they decide … .............................................................. 29
, opgave 13.20 – forecast % / simulate ..................................................................................... 30
opgave 13.21 – weekly stockout costs / weekly holding costs .................................................... 31
bonusopgaves ...................................................................................................................... 32
opgave 1 – verwachte aantal klanten per uur ........................................................................... 32
opgave 2 – bezettijd kassa / tabel invullen .............................................................................. 32
opgave 3 – totale wachttijd ................................................................................................... 33
WEEK 6 ...................................................................... 34
oefenopgaves ....................................................................................................................... 34
opgave 7.14 – best combi / corner point graphical approach ...................................................... 34
opgave 7.15 – slack or surplus ............................................................................................... 35
opgave 7.16 – welke hoeveelheid gebruiken ............................................................................ 36
opgave 7.17 – hoe veel produceren / LP Approach .................................................................... 37
opgave 7.18 ........................................................................................................................ 37
opgave 7.27 – formulation / unbounded / onbegrens / correct / feasible ..................................... 38
bonus opgaves ..................................................................................................................... 39
opgave 1 – LP probleem ........................................................................................................ 39
opgave 2 – hoekpuntenmethode ............................................................................................ 39
WEEK 7 ...................................................................... 41
oefenopgaves ....................................................................................................................... 41
opgave 7.31 – lp problem / optimal solution ............................................................................ 41
opgave 7.32 – LP formulation / constraint change .................................................................... 42
opgave 7.33 – computer output ............................................................................................. 42
opgave 7.34 – dual prices / constraints / resources .................................................................. 43
opgave 7.35 – chage constrains / right hand / left hand value ................................................... 44
opgave 7.37 ........................................................................................................................ 45
bonusopgaves ...................................................................................................................... 47
opgave 1 – waarden parameter a ........................................................................................... 47
opgave 2 – nieuwe optimale doelstellingswaarde ...................................................................... 47
opgave 3 – nieuwe optimale doelstellingswaarde ...................................................................... 48
opgave 3 – nieuwe optimale doelstellingswaarde ...................................................................... 48
WEEK 8 ...................................................................... 49
oefenopgaves ....................................................................................................................... 49
opgave 8.2 – investment decision problem .............................................................................. 49
opgave 8.3 – restairamt work scheduling problem .................................................................... 50
opgave 8.4 – animal feed mix problem .................................................................................... 50
opgave 8.5 – linear programming to determine production ........................................................ 51
opgave 8.10 – high school busing problem .............................................................................. 52
opgave 10.11 – 0-1 programming problem .............................................................................. 53
opgave 10.14 – write constraints ............................................................................................ 53
opgave 10.17 – npv .............................................................................................................. 54
opgave 10.18 - constraints .................................................................................................... 55
bonusopgaves ...................................................................................................................... 56
opgave 1 – ILP probleem ....................................................................................................... 56
opgave 2 – ILP probleem ....................................................................................................... 56
,WEEK 1
OEFENOPGAVES
OPGAVE 3.17 – MAXIMAX CRITERIUM
Kenneth Brown is the principal owner of Brown Oil, Inc. After quitting his university teaching job, Ken
has been able to increase his annual salary by a factor of over 100. At the present time, Ken is forced
to consider purchasing some more equipment for Brown Oil because of competition. His alternatives
are shown in the following table:
For example, if Ken purchases a Sub 100 and if there is a favorable market, he will realize a profit of
$300,000. On the other hand, if the market is unfavorable, Ken will suffer a loss of $200,000. But Ken
has always been a very optimistic decision maker.
(a) What type of decision is Ken facing?
Beslissen bij onzekerheid
(b) What decision criterion should he use?
Maximax criterium
(c) What alternative is best?
Volgens het maximax criterium is sub 100 de beste keuze
OPGAVE 3.18 – MAXIMIN CRITERIUM
Although Ken Brown (discussed in Problem 3-17) is the principal owner of Brown Oil, his brother Bob
iscredited with making the company a financial success. Bob is vice president of finance. Bob attributes
his success to his pessimistic attitude about businesS and the oil industry. Given the information from
Problem 3-17, it is likely that Bob will arrive at a different decision. What decision criterion should
Bob use, and what alternative will he select?
Nu maken we gebruim van het Maximin criterium
Volgens het maximin criterium is Texan de beste keuze
, OPGAVE 3.19 – EMV / BESLISSEN MET RISICO
The Lubricant is an expensive oil newsletter to which many oil giants subscribe, including Ken Brown
(see Problem 3-17 for details). In the last issue, the letter described how the demand for oil products
would be extremely high. Apparently, the American consumer will continue to use oil products even if
the price of these products doubles. Indeed, one of the articles in the Lubricant states that the chance
of a favorable market for oil products was 70%, while the chance of an unfavorable market was only
30%. Ken would like to use these probabilities in determining the best decision.
(a) What decision model should be used?
Er is nu sprake van beslissen met risico. We gebruiken de Expected Monetary Value als criterium
(b) What is the optimal decision?
Dus de beste keuze is sub 100
(c) Ken believes that the $300,000 figure for the Sub 100 with a favorable market is too
high. How much lower would this figure have to be for Ken to change his decision made in
part (b)?
Dus zodra de winst voor sub 100 bij een positieve markt kleiner is dan 292 857 zal de beslissing van
Ken veranderen
OPGAVE 3.20 – EMV / PRIJS PERFECTE VOORSPELLING
Mickey Lawson is considering investing some money that he inherited. The following payoff table gives
the profits that would be realized during the next year for each of three investment alternatives Mickey
is considering:
