Production, Manufacturing and Logistics Inventory models with ramp type demand rate, partial backlogging and Weibull deterioration rate K. Skouri a, * , I. Konstantaras a , S. Papachristos b , I. Ganas c a Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece b Department of Agribusiness, University of Ioannina, 45110 Ioannina, Greece c Department of Accounting, Technological Education Institute of Epirus, 48100 Preveza, Greece Received 14 September 2006; accepted 1 September 2007 Available online 11 September 2007 Abstract In this paper, an inventory model with general ramp type demand rate, time dependent (Weibull) deterioration rate and partial back- logging of unsatisfied demand is considered. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The model is fairly general as the demand rate, up to the time point of its stabilization, is a general function of time. The backlogging rate is any non-increasing function of the waiting time up to the next replenishment. The opti- mal replenishment policy for the model is derived for both the above mentioned policies. Ó 2007 Elsevier B.V. All rights reserved. Keywords: Inventory; Ramp type demand; Deteriorating items; Partial backlogging 1. Introduction Maintenance of inventories of deteriorating items is a problem of major concern in the supply chain of almost any business organizations. Many of the physical goods undergo decay or deterioration over time. Commodities such as fruits, vegetables, foodstuffs, are subject to direct spoilage while kept in store. Highly volatile liquids such as gasoline, alcohol, turpentine, undergo physical depletion over time through the process of evaporation. Electronic goods, radio- active substances, photographic film, grain, deteriorate through a gradual loss of potential or utility with the passage of time. A model with exponentially decaying inventory was initially proposed by Ghare and Schrader (1963). Covert and Philip (1973) and Tadikamalla (1978) developed an economic order quantity model with Weibull and Gamma distributed dete- rioration rates, respectively. The assumption of constant demand rate is usually valid in the mature stage of a product’s life cycle. In the growth and/ or end stage life cycle, demand rate may well be approximated by a linear function. Resh et al. (1976) and Donaldson (1977) were the first who studied a model with linearly time varying demand. Since then, several researchers have studied deteriorating inventory models with time varying demand under a variety of modeling assumptions (e.g. Dave and Patel, 1981; Sachan, 1984; Goyal, 1987; Datta and Pal, 1988; Goswami and Chaudhuri, 1991; Hariga, 1996; Yang et al., 2001). 0377-2217/$ - see front matter Ó 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2007.09.003 * Corresponding author. Tel.: +30 26510 98230. E-mail address: kskouri@cc.uoi.gr (K. Skouri). www.elsevier.com/locate/ejor Available online at www.sciencedirect.com European Journal of Operational Research 192 (2009) 79–92