1.1 For a given (postulated) pair of production and demand distribution models, we want to estimate certain characteristics of the single-item inventory model based on simulated inventory balance equations over a sequence of weeks.

Input data:

Weekly production distribution: Uniform(60, 90) Weekly demand distribution: Normal(75,15) Inventory at the beginning of week 1: 10 items No. of weeks simulated: 50

Inventory balance equation, for each week:

Ending inventory = Beginning inventory + Production – Units sold

Observe that the number of units sold either equals the demand or the available inventory (whichever is smaller).

1.2 (15 points) We want to estimate the following quantities: average and standard deviation of the beginning inventory, production, demand, and units sold; we also estimate the stockout probability. Create the graphs of the following quantities as these evolve over 50 weeks: beginning inventory, production, demand, units sold, and ending inventory.

1.3 (5*4 = 20 points) Describe shortly the expected effect of changing the input parameters indicated below.

Production distribution: Uniform(Min, Max) Demand distribution: Normal(Mean, StdDev) Beginning inventory