Optimal Replenishment Strategy for Inventory Mechanism with a Known Price Increase and Backordering in Finite Horizon

Table 1

Notation.

Parameters	Descriptions
	Demand rate
	Fixed order cost
	Regular purchasing price
	Purchasing price after increase
	Regular holding cost per item per unit time
	Holding cost per item per unit time under increased price
	Backorder cost per unit item per unit time
	Planning horizon of the inventory system
	The time when purchasing price changes
	Remaining stock at time
	Order size before
	Maximum shortage level for a normal order at the current price before
Decision variables
	Special order size
	Order size after when the special order is not placed
	Order size after special order
	Maximum shortage level for a special order at the current price
	Maximum shortage level for an order at the new price after when the special order is not placed
	Maximum shortage level for an order at the new price when a special order is placed
Other variables
	Inventory cost over interval without special order
	Inventory cost over interval with special order