Esempi di problemi

Questa pagina propone alcuni esempi di descrizioni interpretabili come la base informale per la costruzione di modelli di sistemi dinamici (naturalmente potrebbero essere anche intesi come ispirazione per progetti per l'esame).

  1. The more that has been produced by a producer, the more experience that producer has gained, and as a consequence, the lower its production cost per product. Lower costs translate into lower prices which, in turn, increase the attractiveness of the product to the consumer and therefore the number of sold products per unit time.
  2. A capital of 1000 € is invested at the yearly interest rate of 2%; which will the capital amount be after 10 years, under the hypothesis that the interests are computed on a monthly basis and all reinvested, and no sums are withdrawn? Then solve the problem under the new hypothesis that each four months a sum of 100 € is added to the account; which will the capital amount be after 10 years in this case? Then solve the problem under the new hypothesis that at the beginning of each new year the bank gives a price of 500 € to some randomly chosen account owners; provided that the estimated probability to win is 0.1 for each year, which will the estimated capital amount be after 10 years in this case?
  3. The person responsible of the warehouse in a factory wants to compute (i) the stock level as a function of the inventory input and output, (ii) the change of the stock level under the hypothesis that items of a single product are stored in the warehouse. Then solve the problem under the new hypothesis that she wants then introduce the automatic reordering to the supplier (the supplier requires 1 time unit to deliver the ordered items), triggered when the stock level is lower than a fixed security level, with the reorder quantity required to fill the stock to the security level. Then solve the problem under the new hypothesis that, noticing that the previous strategy is generally ineffective, she wants to compute the reorder quantity in some adaptive way, e.g., as a function of the inventory output or the change of the stock level, with the aim of reducing the number of reorder operations.
  4. A classical macro-economical model: the relations between demand and supply as the determining factor of the dynamics of price. Create and simulate a model implementing the following specifications: (i) the demand is inverse function of the price; (ii) the price increases in function of the difference of demand and supply; (iii) the supply is direct function of the price of the previous instant (in all cases assume a linear dependence).‏ Perform some sensitivity analysis to explore the dependence of price on model calibration parameters.
  5. The management of a fast-food restaurant is re-defining the FFR organization: to this goal it identified the main variables affecting the FFR operations and their relations, as follows: decreasing the service time requires decreasing the cooking time, which implies decreasing the food quality, which is acceptable by increasing the number of customers, which is achievable by decreasing the service time, …
  6. Some experts have estimated that the market of the table lamp “Xlight” in Castellanza has 10000 potential buyers. Currently only 10 persons own this lamp. The distributor relies on the direct communication among customers as advertising strategy, under the hypothesis, suggested by the experts, that 2 persons will be contacted by each 10 owners per month. While some of the contacted people could be already owner of the lamp, the experts are confident that all the contacted persons who do not own the lamp will buy it immediately after the contact. On the basis of these specifications, create a model of the system and run the simulation to predict the number of months required to reach a 90% saturation of the market.
  7. Your client is worried about employee motivation and is debating the best ways to generate maximum effort from their people in the forthcoming six months. Indeed, in the past some consultants suggested that the greater the performance shortfall (the greater the gap between required performance and actual performance), the greater the motivation of employees will be. They argue that the secret of motivation is to set aggressive goals (the so called stretch objectives) to elicit maximum motivation and effort. Some others pointed out instead that too big a performance shortfall simply causes frustration as people conclude there is no chance to accomplish the goal. Furthermore, your client agreed to exploit financial incentives for her goal, and is wondering how they should be rewarded (to whom, with which schedule, with or without previous communications or requests), provided of course that a definite amount of money is available. Finally, your client is well aware that different employees might react in different ways to the decisions, and would like to minimize the risk of internal clashes.
  8. A Borgo Verde, un paese isolato di 100 abitanti, è stato recentemente aperto il Bar Bianco, un locale in cui una sera alla settimana si fa musica dal vivo. Ognuno dei 100 abitanti vorrebbe recarsi allo spettacolo tutte le settimane, ma è anche infastidito dall’eccessivo affollamento del locale, per cui giudica piacevole l’esperienza solo nel caso in cui al massimo 60 persone siano presenti complessivamente nel locale. Gli abitanti di Borgo Verde non hanno occasioni di comunicazione, e quindi non hanno la possibilità di scambiarsi informazioni circa chi intende partecipare allo spettacolo. D’altra parte, ognuno viene a sapere quante persone erano presenti a ogni spettacolo il giorno successivo a quello in cui si è tenuto lo spettacolo stesso. Posto che nelle prime cinque settimane dall’apertura del locale il numero dei partecipanti è stato rispettivamente di 35, 42, 69, 38, 76 persone, come dovrebbe comportarsi un abitante di Borgo Verde a proposito della sua eventuale partecipazione ai prossimi spettacoli?