Acquisition cost per pair = $ 40
Selling price per pair = $ 54
But Salvage value = 0.5 * $54 = $27 every boot
Demand mean (µ) = 400 pairs
But standard deviation (α) = 150 pairs
With regard to the provided data, we shall apply single-period stock model (Stevenson & Hojati, 2007).
Under-stocking cost (Cs) = shortage cost or demand estimation = price of sales per pair less cost per pair
Therefore Cs = 54 – 40= $14 per pair
Overstocking cost (Co) = cost of average (demand overestimation) = cost per pair less the salvage value per pair
Therefore Co = 40-27 = $13
The probability or the level of service of not running out of stock is prescribed at,
Level of service (critical ratio) = Under-stocking cost / (Under-stocking cost + Overstocking cost) =14/ (14+13)
Level of service or critical ratio = 0.5185
It is essential for Teddy Bower to look for the z-score for the demand normal distribution which generates a probability (equal to the service level) of 0.5185
Thus, 51.85% of the area under the normal curve should be to the right side of the maximum level of stocking. By use of the standard normal table, with an area of approximately 0.5185, our z-score shall be about 0.0464
Maximum inventory quantity = z + µ = (0.0464*150) +400 = 407 pairs
The company should order 407 pairs of boots from the suppliers since this is the optimal stock which will maximize the anticipated profit.
The case assuming Teddy Bower will order 450 pairs. Apparently, at this quantity level, there will be excess after the season ends. However, it is expected that a certain discount rate of that excess will not be 50% as it was in the original case. This can be determined as follows
Z-score at 450 pairs of boots
Inventory = z + µ
Z*150 + 400 = 450
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