Production - Inventory Policies for Deteriorating Items with Imperfect Production Process when Demand is Quadratic (pp. 1-15) 1 Nita H. Shah , 2 Ajay S. Gor and 3 Chetan A. Jhaveri 1 Department of Mathematics, Gujarat University, Ahmedabad-380009 2 Pramukh Swami Science & H. D. Patel Arts College, Kadi, Gujarat 3 S. L. Institute of Business Administration, Ahmedabad-380009, Gujarat, India Correspondence E-mail: nitahsh@gmail.com Abstract: This study is aimed at analysing integrated production - inventory policies for deteriorating items in supply chain when demand of product is subject to increase with time. The model assumes partial backlogging, imperfect production process and multiple deliveries. The elapsed time until the production process shifts is assumed to be exponentially distributed. It is observed that the joint decision lowers the total cost compared with an independent decisions made by the manufacturer and the retailer with the help of numerical data. The sensitivity analysis is carried out to study the variation in the decision variables and the total integrated cost. Key words: integrated production-inventory policy, deterioration, imperfect processes, multiple deliveries, quadratic demand. NOTATIONS R(t) Retailer’s demand rate (units/unit time) = a(1 + bt + ct 2 ), where a is fixed demand, b and c are linear and exponential rate of change of a demand with respect to time respectively with a > 0, a > > b, c and 0 < b, c < 1 P(t) = γR(t) ; production rate(units/unit time), where γ > 1 B Fraction of retailer’s demand back-ordered N The number of delivery per order (a decision variable) T 1 The production period (a decision variable) T 2 The non-production period (a decision variable) T 3 The period for which a retailer has the stock (a decision variable) T 4 The retailer’s stock-out period.(a decision variable) T ( = T 1 + T 2 = n(T 3 + T 4 ) ); the length of the cycle time (a decision variable) I rm (t 1 ) Raw material’s inventory level at any time t 1 , 0 ≤ t 1 ≤ T 1 I mfi (t i ) Manufacturer’s finished goods inventory level at any time t i , 0 ≤ t i ≤ T i , i = 1,2 I ri (t i ) Retailer’s inventory level at any time t i , 0 ≤ t i ≤ T i , i = 3, 4 A mo Manufacturer’s ordering cost per order cycle ($/cycle) A ms Manufacturer’s set-up cost per production cycle ($/cycle) A r Retailer’s ordering cost per order cycle ($/order) C mr Manufacturer’s raw material’s per unit cost ($/unit) C mrw Manufacturer’s finished goods per unit rework cost ($/unit) Journal of Innovative Research in Management and Humanities 1(1), October, 2010. Maiden Edition © Global Research Publishing, 2010. -1- Production - Inventory Policies for Deteriorating Items with Imperfect Production Process when Demand is Quadratic