An entrepreneur who operates a cellular phone store orders inventory of cell phones based on four internal memory specifications - 8 GB, 16 GB, 32 GB, and 64 GB. She wants to evaluate her inventory ordering policy for the phones with four different amounts of internal memory. Any phone unsold at the end of a period is kept in inventory for the next sales period and incurs a holding cost expressed as 10% of the cost per unit per period. If demand during a period exceeds supply for a phone, then the sale is lost. The data on the cost and selling prices of the cell phones categorized by these memory specifications are known, and representative data on the past sales are also available.
Internal Memory Cost ($)Selling Price ($)8 GB420
430
16 GB500
520
32 GB590
620
64 GB670
700
Past Sales:
Period
8 GB
16 GB
32 GB
64 GB
1
276
274
327
332
2
302
211
264
329
3
299
276
306
239
4
261
258
232
277
5
260
244
278
220
6
306
252
262
252
7
227
213
290
253
8
228
217
308
250
9
205
215
246
277
10
236
237
272
284
11
279
251
301
282
12
303
271
271
282
13
266
252
276
317
14
263
306
285
310
15
210
250
328
253
16
247
230
317
340
17
314
285
289
332
18
283
304
312
256
19
283
245
294
272
20
252
237
262
323
a. Construct a spreadsheet simulation model to estimate the total profit the entrepreneur earns in a period when ordering 300 units of each cell phone. To model the respective cell phone demands, fit a realistic distribution to the sales data. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period?b. Using Spearman rank correlation, compute the correlations between the demands for the cells phones based on the four memory specifications. Incorporate a correlation matrix to capture the interrelationships between the demands for each cell phone type. What is the average total profit? What is the estimated likelihood that the entrepreneur makes less than $10,000 next period? Comparing these answers to part (a), conclude how the correlated demand affects the model's implications.
What will be an ideal response?
The spreadsheet simulation model is shown below. The average total profit earned by the entrepreneur is about $17,515. Also, the estimated probability that the entrepreneur makes less than $10,000 next period is 0.0278.
b. The calculation of ranks, using sales data, for computing the correlations between the demands for the cells phones based on the four memory specifications is given below:
The average total profit earned by the entrepreneur is about $17,515. Also, there is a 0.0435 probability that the total profit made by the entrepreneur is less than $10,000 next period.
Comparing these results with the answers in part (a), we see that considering the correlation between demands does not have a large impact on the profit estimation, but correlated demand does suggest a slightly higher chance of more extreme outcomes.
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