The NewsVendorFacings.lng Model

The how many facings problem

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Given

tsw = total shelf width available for facings,

for each product p:

c( p) = cost per unit,

r( p) = revenue or selling price per unit,

w( p) = width of a facing,

f( p) = items per facing, e.g., stacked behind each other,

mu( p) = mean demand per day (assume re-stock each night),

sd( p) standard deviation in demand per day,

Question:

How many facings should we allocate to each product?

Essential ideas:

total facings cannot exceed tsw,

Want to stock for each product mean demand + safety stock,

We tend to give more safety stock to product p for which:

r( p) - c( p) is high,

f( p) is high,

w( p) is low,

sd( p) is high.

This can be done to optimize total expected profit.

Computed parameters:

phi( s, p) = Prob{ demand for product p is >= s}

Variables:

z( p, s) = 1 if we stock at least s, (thus z(s+1,p) <= z(s,p))

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Keywords:

Uncertainty | Inventory | Newsboy Problem | Facings | Newsvendor | Planogram |