A lost sales (r, Q) inventory control model for perishables with fixed lifetime and lead time Chaaben Kouki a,n , Zied Jemaï b , Stefan Minner c a Montpellier Business School/Montpellier Research in Management, France b Laboratoire Génie Industriel, Ecole Centrale Paris, France c TUM School of Management, Technische Universität München, Germany article info Article history: Received 19 March 2014 Accepted 9 June 2015 Available online 17 June 2015 Keywords: Perishable products Inventory control Deterministic lifetime Continuous review abstract We consider a perishable inventory system that operates under stochastic demand, constant lifetime and a constant lead time. The system employs a continuous review ðr; Q Þ inventory control policy where unfilled demands are lost. We investigate the properties of the cost function and present an approximation procedure to find the parameters r and Q that minimize the total cost. We then conduct a numerical analysis to examine the performance of the proposed model and study the sensitivity to changes in the system parameters. We demonstrate the suitability of the proposed approximations compared to optimal ðr; Q Þ parameters obtained by simulation and show that our proposal outperforms another approximation procedure from the literature, in particular for increasing ordering cost and demand variability. The proposed model contributes to the literature by providing a simple and efficient algorithm to compute the best (r, Q) parameters that minimize the total cost. Besides, it can be used in automated store ordering systems. & 2015 Elsevier B.V. All rights reserved. 1. Introduction Economic sectors such as pharmaceutics, medical goods and consumer goods industries are concerned with the management of perishable products' inventory. In fact, drugs and food, for example, are produced to be consumed within a limited period of time and consequently the impact of perishability on inventory management cannot be disregarded. To illustrate such impact, Roberti (2005) noted that roughly 10% of all perishable goods go to waste before consumers purchase them. In the health care sector, 10.9% of blood platelets processed in the United States outdated without being transfused in 2006 (Fontaine et al., 2009). However, despite the growing literature on perishable inventory control, the fixed life perishability problem remains a complex problem when the product lifetime is longer than two units of time in a periodic review scenario (Nahmias, 1982). Indeed, determining the optimal ordering policy for perishables with deterministic lifetime requires a recursive solution of multi-dimensional dynamic programs. The multi-dimensionality is caused by the need to track the different age categories in stock. Besides, the computation of an optimal policy turns out to be impractical for a real-life situation. The investigations developed so far underline the complexity caused by tracking the different items in inventory by age. We refer to the following literature reviews that give further details pertaining to this difficulty: Goyal and Giri (2001), Karaesmen et al. (2011) and Nahmias (1982). In this paper, we revisit the fixed life perishability problem and study continuous review ðr; Q Þ inventory systems where products have deterministic lifetimes and excess demands are lost. We derive bounds on the expected number of perished units and expected lost sales and use these bounds to obtain approx- imations for the expected on-hand inventory level and the expected total cost. Based on the properties of the total cost function, we propose an algorithm to compute the parameters r and Q that minimize the approximated total cost. We show that, compared to similar existing studies, the model we propose performs very well. Academic literature of inventory control for perishables with deterministic lifetime can be categorized into various classes depending on (i) whether the inventory is reviewed periodically or continuously, (ii) whether replenishment orders arrive instan- taneously or after a positive lead time, (iii) the cost components considered, e.g., ordering, inventory holding, outdating and short- age costs. Under periodic review schemes, several heuristics deal- ing with deterministic lifetime were proposed to avoid the Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/ijpe Int. J. Production Economics http://dx.doi.org/10.1016/j.ijpe.2015.06.010 0925-5273/& 2015 Elsevier B.V. All rights reserved. n Corresponding author at: 2300 Avenue des Moulins, 34080 Montpellier, France. Tel.: þ33 467102500; fax: þ33 467451356. E-mail addresses: chaaben.kouki@gmail.com (C. Kouki), zied.jemai@ecp.fr (Z. Jemaï), stefan.minner@tum.de (S. Minner). Int. J. Production Economics 168 (2015) 143–157