##Company:

Hot Dog Stand

##Required product:

Program to evaluate best quantity of hotdogs with which to restock a stand in stochastic conditions (and how often these should be restocked).

##Parameters:

The input to the problem is 4 parameters:

  • Arrival rate (how often customers arrive wanting to buy a hotdog, assumed to follow an exponential distribution)
  • Service rate (how quickly the single server can make a hotdog, assumed to follow an exponential distribution)
  • The wholesale price of a hotdog (assumed constant)
  • The retail price of a hotdog (assumed constant)

There are 2 decision parameters:

  • The replenishment period (how often the hotdog stands orders hotdogs, assumed constant)
  • The replenishment quantity (how many hotdogs the hotdog stand orders, assumed constant)

##Particularities that need to be taken in to account:

  • Customers will be lost if they arrive at the queue and there are not sufficient hotdogs to feed them. Note that they do not join the queue if there is not sufficient stock at the time of their arrival.

As well as building a model of the system (consider that to be step one), if you can, obtain the best possible replenishment period and quantity for the following input parameters:

Scenario 1

  • Arrival rate: 1 per time unit.
  • Service rate: 2 per time unit.
  • Wholesale price: 3.
  • Retail price: 4.

Scenario 2

  • Arrival rate: 1 per time unit.
  • Service rate: 2 per time unit.
  • Wholesale price: 1.
  • Retail price: 8.

Scenario 3

  • Arrival rate: 1 per time unit.
  • Service rate: .9 per time unit.
  • Wholesale price: 3.
  • Retail price: 4.

Scenario 4

  • Arrival rate: 1 per time unit.
  • Service rate: .9 per time unit.
  • Wholesale price: 3.
  • Retail price: 40.

##Summary:

The following picture summarises your challenge:

##Evaluation:

Your code will be evaluated in terms of:

  • Precision (does it work and if so is it correct? - This is an objective criteria)
  • Performance (how fast is it? how does it handle bugs? - This is an objective criteria)
  • Time taken to submit solution (This is an objective criteria)
  • Clarity (is it well written/documented/tested - This is a subjective criteria)

##Suggestion:

I suggest you proceed by clearly defining independent programming tasks and attempting to work independently whilst ensuring that each piece of code produced is capable of talking to each other piece.