In order to solve this problem, your spreadsheet programwill need to have a function that produces random numbers [@RAND in Lotus 1–2–3 and RAND ( ) in Excel]. The purpose of this exercise is to construct a simulation of a periodic-

review inventory system with random demand. We assume that the reader is familiar with the fundamentals of Monte Carlo simulation.

Your spreadsheet should allow for cell locations for storing values of the holding cost, the penalty cost, the proportional order cost, the order-up-to point, the initial inventory, and the mean and the standard deviation of periodic demand.

An efficient means of generating an observation from a standard normal variate is the formula Z  [2 ln (U1)]0.5 cos(2U2), where U1 and U2 are two independent draws from a (0, 1) uniform distribution. (See, for example, Fishman, 1973.) Note that two independent calls of @RAND are required. Since Z is approximately standard normal, the demand X is given by X  Z  

where  and  are the mean and the standard deviation of one period’s demand.

A suggested layout of the spreadsheet is NEWSVENDOR SIMULATOR Holding cost  Mean demand 

Order cost  Std. dev. demand 

Penalty cost  Initial inventory 

Order-up-to point 

Starting Order Ending Holding Penalty Order Period Inventory Quantity Demand Inventory Cost Cost Cost 1

2 3

.

.

.

20 Totals Each time you recalculate, the simulator will generate a different sequence of demands.

A set of suggested parameters is h  2, c  5, p  20,

  100,

  20, I0  50, Order-up-to point  150.