Abstract

A modified Economic Manufacturing Quantity (EMQ) model under the imperfect product quality has been presented. For measuring the product quality, Taguchi’s quadratic loss function has been used. Total loss to the society has been denoted by the modified EMQ model which includes the producer’s loss and consumer’s loss. The set-up cost, the holding cost and the product cost are used to calculate the total inventory cost of the modified EMQ. The perfect and imperfect reworks of product are considered in the modified EMQ model. In order to have minimum loss to society the optimum combination of EMQ and process mean can be obtained by solving the modified EMQ model.

Nomenclature

TC Total inventory cost per unit time.
D Demand quantity in units per time.
Q Economic manufacturing quantity.
S_t Set-up cost for each production run.
O Demand rate in units per day.
I Production rate in units per day.
h Holding cost per unit item per unit time.
P_I The cost function of product under the perfect rework.
A Inspection cost per unit.
k Quality loss coefficient.
Δ Tolerance.
B Rework cost.
t Target value.
S Scrap cost per unit.
Φ(z) The probability density function of the standard normal variable.
Φ(z) The cumulative distribution function of the standard normal variable z.
P_II Cost function of product under imperfect rework.
E(P_II) Expected cost of a product.