Models of inventory systems frequently consider the relationships among a beginn

Question

Models of inventory systems frequently consider the relationships among a beginning inventory,
a production quantity, a demand or sales, and an ending inventory. For a given
production period j, let
sj-1 = ending inventory from the previous period (beginning inventory for period j)
xj = production quantity in period j
dj = demand in period j
sj = ending inventory for period j

a. Write the mathematical relationship or model that shows ending inventory as a function
of beginning inventory, production, and demand.
b. What constraint should be added if production capacity for period j is given by Cj?
c. What constraint should be added if inventory requirements for period j mandate an
ending inventory of at least Ij?

Explanation / Answer

a.) Ending inventory for period j = ending inventory from the previous period (beginning inventory for period j) + production quantity in period j - demand in period j

Writing mathematically

sj = sj-1 + xj - dj

b) Constraint to be added; xj <= Cj (production can not be more than the capacity hence production is less than or equal to capacity)

c) Constraint to be added; sj >= lj (ending inventory to be greater than or equal to lj)

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