Research Article

An Inventory Model for Perishable Items with Price-, Stock-, and Time-Dependent Demand Rate considering Shelf-Life and Nonlinear Holding Costs

Table 1

Notation.

ParametersDescription

Salvage cost of deteriorated item (currency symbol/unit)
Purchase cost (currency symbol/unit)
Deterioration cost (currency symbol/unit)
Holding cost (currency symbol/unit/unit of time)
Holding cost (currency symbol/unit/unit of time2)
Holding cost (currency symbol/unit/unit of time3)
Ordering cost (currency symbol/per cycle)
Shelf-life of the item upon which the remaining amount, if any, is withdrawn immediately from the storage (unit of time)
Maximum shelf space (units)
Salvage coefficient
Inventory deterioration rate
Sensitivity parameter to the current level of stock
Scale parameter for the part of price-dependent demand
Sensitivity parameter for the part of price-dependent demand

Functions
Price-dependent demand for the item, which can be linear, isoelastic, exponential, logit, logarithmic, or polynomial function (units/unit of time)
Stock level at time (units)
Price-, stock-, and age-dependent demand for the item at time (units/unit of time)
Quadratic holding cost function
Total profit per cycle (currency symbol/unit)
Total profit per unit of time (currency symbol/unit of time)
Age of the stock, which is the time passed since the last replenishment (unit of time)

Decision variables
Product selling price (currency symbol/unit)
Replenishment cycle length (unit of time)

Dependent decision variable
Order quantity (units)