Exam 10: Simulation Models

Titus Tronix is currently having a consumer electronics clearance sale.The store presently has 10 Gadzooks video cassette recorders on sale.Five are Standard, three are Economy, and two areTop-of-Line.Each day the firm expects between 0 and 3 customers interested in buying a VCR to arrive at the store according to the following probability distribution: P(0 arrivals) = .15 P(1 arrivals) = .40 P(2 arrivals) = .25 P(3 arrivals) = .20 For each customer interested in buying a VCR, there is a seventy percent chance that the customer will want to purchase one of the sale-priced Gadzooks models.Titus knows from past experience that sixty percent will want a Standard, twenty-five percent will want the Economy, and fifteen percent will desire the Top-of-Line.If the store is sold out of a particular price-level model, the customer who wanted it will leave the store without buying any other. Set up a model which will simulate five days of VCR sales at Titus. Use any set of random numbers, but clearly indicate how they were selected.What is your estimate of Titus' remaining inventory of the three Gadzooks models, at the end of five days?

Crystal Ball is:

A simulation study:

Monte Carlo simulation may be applied to problems in which a chance (random) process generates relevant occurrences.

What is the difference between a simulation language, such as GPSS, and a simulator program, such as Extend?

Why is the next-event approach preferred for discrete simulations?

A computer-created random number generator uses a mathematical formula and produces pseudo-random numbers, which are not truly random.

What proves the validity of a simulation model?

Pseudo-random numbers are often generated in groups, such as 07967 45929 85113 36308.What determines which specific digits to use in random number mapping?

Muchobucks Funding, a venture capital company, invests in a high-tech, pre-IPO startup.Assume the startup has an exponential distribution of income with a mean of $500,000 per year and one million dollars in expenses.That is, the company is expected to lose half a million dollars each year.Once a startup loses $2 million, Muchobucks pulls the plug, and the startup goes out of business.How long will the average startup last?

Repeat problem 2 using a next event approach.Assume the ship interarrival time is exponentially distributed with a mean of .5 days.

Papagayo Rum is produced on the island of the same name, and its entire output is exported by ship.There is only one pier capable of accommodating the freighters, which arrive empty, are then loaded with their cargo of rum, and then depart.The pier may service at most two ships at a time. Cargo ships arrive randomly according to the following distribution: Number of Ships per Day Probability 0 .10 1 .20 2 .40 3 .20 4 .10 If the pier is occupied by two freighters, a subsequent arrival drops anchor in the harbor and awaits its turn.The time required to load a ship is also variable, depending on the vessel's capacity and configuration as well as available dockside manpower and equipment. Loading Time in Days Probability .5 .35 1 .45 1.5 .15 2 .05 Do a ten day fixed time simulation and estimate the average number of ships waiting at anchor for an available pierside berth and the average amount of time a ship must wait at anchor.

In simulation studies, time may be represented as a fixed value or as a random variable.

How does simulation differ from analytical techniques, such as queuing theory or linear programming?