Decision Trees Tasks

Decision trees task are provided here without solution. See if you can solve them. Discuss your solution in seminaries of course Modeling of Decision Processes.

Task 1

Your company decides if it should participate on tender for two contracts (Z1 and Z2) based on request of government’s office – to supply some components. If the company sends its offer, it will have to use, some of its resources.

The costs of resources for Z1 are 50 000,- but can be used also for the coverage of the Z2. Costs of production will be 18 000,-. Production costs for contract Z2 will be 10 000,-.

If the company participates only on tender for Z2, then it will have to use resources costing 24 000,- and production costs will be 12 000,-.

It is estimated, that the costs of tender preparation will be 2 000,- for Z1 or Z2 and 3 000,- if they try to win both contracts.

For every contract the price has been estimated, with probability of winning at different price levels. The company can send only one offer (so it can not send two offers with different price levels).

Price and probability of success

Z1 only

  • 120 000,- 30%
  • 110 000,- 85%

Z2 only

  • 70 000,- 10%
  • 65 000,- 60%
  • 60 000,- 90%

Z1 and Z2

  • 190 000,- 5%
  • 140 000,- 65%
  • 100 000,- 95%

If the company offers for Z1 and Z2 it will either win or lose both (the offer is evaluated altogether). 

What should the company do?

Task 2

Firm ABCD Ltd. Develops plan to build new production hall, which will be equipped with technologies with total value of 25 mil. EUR. Firm is deciding upon which security measures it will project into it. Legislative minimum requires investing 3 mil. EUR into security procedures and technologies.

Firm may also choose to invest to retrofit local fire brigade to perform more effective on site intervention. Such retrofit would be one time investment of 6 mil. EUR.

If there is fire in production hall, we can presume, that the whole production process will halt and that will have financial impacts on firm economics:

  • Small fire (5%) – loss of 150 000 EUR
  • Average fire (70%) – loss of 1 000 000 EUR
  • Large fire (25%) – loss of 10 000 000 EUR

Probability, that there will be the fire is estimated 3% (per 10 years). If there is a fire, there is also certain probability that the fire will spread into nearby warehouse:

  • Legislative minimum 60%
  • Retrofit of fire brigade 20%

If the fire spreads into the warehouse – it is presumed, that the fire will damage all the goods in it (goods value 15 000 000 EUR).

What should the firm do in the time horizon of 10 years.

Task 3

The firm introduces new product to the marker and needs to decide if it should modernize its packaging technology and improve the printing on it or it should buy new packaging line with attractive print (in this case it has possibility to choose between producers A and B). The choice is determined by following:

  • Modernization of packaging line used today – 3 mil. EUR
  • Buying the line from producer A – 5 mil EUR
  • Buying the line from producer B – 6 mil EUR

Probabilities of large demand on new product

  • Modernization of packaging line used today – 0.5
  • Buying the line from producer A – 0.7
  • Buying the line from producer B – 0.8

Monthly revenue at high demand is estimated to 13 mil EUR and 7 mil EUR for low demand. If the firm decides to buy line from producer B, the packaging will be se attractive, that the firm estimated revenue of 15 mil EUR at high demand and 9 mil EUR at low demand.

What will you recommend to firm?

Task 4

House owner tries to decide if (and how) should he arrange insurance of his house against thievery. He estimates, that replacement of the house’s depository will cost him 20 000 EUR. Statistic of criminality in the neighborhood shows, that there is 0.03 probability, that there will be burglary in the house in the next year. In such case the damages on depository would be 10%, 20% or 40% with probabilities of 0.5, 0.35 and 0.15.

Insurance from insurance company A costs 150 EUR yearly but it guarantees full cover of the damages. Insurance from company B costs only 100 EUR per year, but the owner of the house has participates by X EUR of any damage. Insurance from company C costs only 75 EUR per year, but the insurance company covers only Y% of the damages.

Presuming that there can be only one burglary per year.

  • develop the decision tree
  • recommend optimal insurance policy when X = 50 and Y = 40%

Task 5

Firm ABCD is subsidiary of large international company, which demands the ABCD to sign insurance contract with same insurance company as she. Insurance company Assure Everything Ltd., after performing on site evaluation, presented two variants of insurance policy: 

  1. ABCD will implement additional measures to increase safety of its operation with total cost of 75 mil. EUR. The Implementation will require postponing the commercial production by one year, but after finishing of implementation the insurance will be only 1,5 mil EUR per year.
  2. The company will not implement any additional protective measures and starts the production immediately, but the insurance fee will be 6 mil EUR per year.

As alternative to these options, ABCD asked local insurance company Vše pojistíme to evaluate its production. If the ABCD did use insurance of Vše pojistíme, it would cost 1 mil. EUR per year only, but there is risk of 3%, that the insurance company won’t be capable to process the event in time. For ABCD it would mean additional problems evaluated by 750 mil. EUR.

Marketing research and company’s experience on market show, that the projected profit of selling will be 30 mil. EUR per year.

Help ABCD company to decide which insurance policy it should use. Use 10-year invest horizon.

Task 6

Firm ABC Ltd. built new production facility with storage space nearby and tries to decide how it should deal with the risk connected to the used production technologies and to presence of valuable goods and raw materials.

It is considering the insurance of production facility against fire. The technology catches fire usually 2x per year, but only in 1% of the cases the personnel is not capable to extinguish it in time. In that case there is 50% risk that the fire will spread to nearby storage and will damage the goods of total value 15 mil EUR. In the production facility itself the fire will cause damages on technology 35 mil EUR and will result in stopping of the production for 3 months. 

Expected profit from the selling is 5 mil EUR per month. If the storage does not catch the fire, the company may use it to fill in missing production.

The insurance company is willing to insure production facility for 1 mil EUR per year against fire, and the storage space for 2 mil EUR per year. Insurance policy says that the insurance will cover 90% of the damages. Alternatively the insurance company is willing to cover 100% of the damages, but at the price of 2 mil EUR per year for production facility and 4 mil EUR per year for storage space.

What should ABC Company do in investing horizon of 10 years.

Task 7

Planner with cooperation with tenant of the part of the building is deciding on possible safety measures. He can let be inner division of the building as is – but if there will be larger fire, it will spread into whole building including the rental unit of the tenant with total damages of 3 mil EUR. Such fire happens once per 30 years.

Planner can also separate the unit from the rest of the building by protective fire resistant blind, which will cost 300 000 EUR, but will protect the unit against the fire. The blind is not resistant to extremely intensive fires, which happen usually once per 60 years. In such case the fire will burn through the blind and expected damages in the unit are 3 mil EUR.

Planner can also recommend the tenant to (with cooperation with the building owner) invest into sprinklers, costing 750 000 EUR. In case of the fire in the unit – the sprinklers would extinguish the fire, but the water would damage the goods (750 000 EUR).

Recommend for investing horizon of 10 years, if it is economically useful to invest into bind, bind + sprinkler or not invest at all.

Task 8

Xanadu traders is private American company dealing with trading of raw materials (minerals). There is possibility for the company to buy 1 mil kg of partially processed ore from Zeldavidian government at price of 5EUR per kg. The ore may then be processed in several different ways and used for example to produce semiconductors. George Xanadu – company’s owner, estimates, that he will be capable to sell the ore at price of 8EUR per kg.

Unfortunately at present time government of USA is deciding upon setting trade embargo on the Zeldavidian products, due to its suspicion of price dumping. If the suspicion will be confirmed, the government of the USA will ball all implorts from Zeldavidia including the ore. If the USA government will not grant import permit after Xanadu Traders brought the ore, Xanadu Traders will not be capable to finish the business with Zaldavian government and will have to pay fine 1EUR per kg of the ore. The chances of ban are estimated to be 50:50.

Alternatively the Xanadu Traders can wait on how the USA government will decide and realize the buy after it gets import permit. In such case there is 70% chance that the ore will not be available at that time (someone else will buy it in mean time).

What should the Xanadu Traders do?