Arbitrary-order economic production quantity model with and without deterioration: generalized point of view

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 2 EPQ model with deterioration

Notations	Units	Descriptions
\(c_{h}\)	/unit	Holding cost per unit time
\(c_{0}\)	/unit	Ordering cost per unit time
\(c_{p}\)	/unit	Production cost per unit time
K	Units	Production rate per cycle
D	Units	Demand rate per cycle
T	Year	Total time cycle
\(t_{1}\)	Year	Production time
\(q_{\mathrm{max}}\)	Units	Highest level of inventory
\(\theta _{1}\)	Constant	Rate of deterioration in \([0, t_{1}]\)
\(\theta _{2}\)	Constant	Rate of deterioration in \([t_{1}, T]\)
TAC	/Year	Total average cost
\(\mathrm{TAC}_{\alpha ,\beta }\)	/Year	Total generalized average cost
α	Constant	The order of integration
β	Constant	The order of differention
Decision variable for integer/arbitrary-order model
T	Year	Total time cycle
\(t_{1}\)	Year	Production time