Question

Nanuq has a women’s fashion store Larmington. The manager of this store is trying to decide how many Jill Cladess dresses to order for this summer season. Demand for the dresses is assumed to follow a normal distribution with mean 400 and standard deviation 100 dresses. The contract for the purchase and delivery of dresses between Larmington and Cladess is as follows: At the beginning of October, manager of Larmington reserves Ұ dresses, called as capacity Ұ by both parties. Larmington must take delivery for at least 0.8 Ұ dresses and can, if desired, take delivery on up to its reserved capacity of Ұ dresses. Each dress sells for $160 and Cladess charges $70 per dress. If Larmington does not take delivery of all Ұ dresses they reserved, it owes Cladess a $12 penalty for each unit of reserved capacity that is unused (not delivered to store). Use Ұ as 400 first to calculate the profit to Larmington store.

Work out the average profit due to 100 simulations. Make sure to round off the demand, delivery, sale amounts, revenue, cost and penalty using ‘ROUND’ function in Excel

Now repeat the 100 simulations for each capacity of 450, 500 and 550.

Based on the above four reserved amounts, decide how many dresses Larmington should reserve (value of Ұ) to maximise its profit for the season. Justify your answer.

Answer 1

based on following simulation table order of 450 units will yield highest likely profit

Reserved Amount	400		Profit	30150		550	28819
Mean Demand	400		S.P	160		500	30298
Std. Demand	100		B.P	70		450	30474
Order	400		Penalty	12		400	29906
S.No	Demand	Reserved	Delivery	Unfulfilled	Penalty	Fulfillment cost	Total Cost	Total Sold Units	Total Revenue	Profit
1	318	400	320	80	960	22400	23360	318	50880	27520
2	640	400	400	0	0	28000	28000	400	64000	36000
3	478	400	400	0	0	28000	28000	400	64000	36000
4	498	400	400	0	0	28000	28000	400	64000	36000
5	485	400	400	0	0	28000	28000	400	64000	36000
6	539	400	400	0	0	28000	28000	400	64000	36000
7	444	400	400	0	0	28000	28000	400	64000	36000
8	379	400	320	80	960	22400	23360	320	51200	27840
9	441	400	400	0	0	28000	28000	400	64000	36000
10	421	400	400	0	0	28000	28000	400	64000	36000
11	508	400	400	0	0	28000	28000	400	64000	36000
12	243	400	320	80	960	22400	23360	243	38880	15520
13	485	400	400	0	0	28000	28000	400	64000	36000
14	431	400	400	0	0	28000	28000	400	64000	36000
15	367	400	320	80	960	22400	23360	320	51200	27840
16	566	400	400	0	0	28000	28000	400	64000	36000
17	343	400	320	80	960	22400	23360	320	51200	27840