Stability analysis and optimization of an inventory system with bounded orders |
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| Institution: | 1. Hydraulic Engineering and Environmental Research Group, Universidad Nacional de Colombia Sede Manizales, Cra 27 64-60 Bloque H Palogrande, Manizales, Colombia;2. Departamento de Ingeniería Mecánica, Universidad Técnica Federico Santa María, Vicuña Mackenna 3939, Santiago, Chile;1. School of Environmental Science and Engineering, Shandong University, Qingdao, China;2. Institute of Science and Technology for Development of Shandong, Qilu University of Technology (Shandong Academy of Sciences), Jinan, China;3. School of Environmental Science and Engineering, Shanghai Jiao Tong University, Shanghai, China;1. Department of Basic Science and Humanities, University of Engineering and Management Kolkata, Kolkata-700091, West Bengal, India;2. Department of Mathematics, The University of Burdwan, Burdwan 713104, India;3. Department of Industrial Engineering, Seoul National University, Seoul 08826, Republic of Korea;1. Department of Earth, Environmental and Physical Sciences, Ecodynamics Group, University of Siena, Pian dei Mantellini 44, 53100 Siena, Italy;2. Provincial Agency for Energy, Environment and Sustainable Development (APEA srl), Via Massetana Romana 106, 53100 Siena, Italy |
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| Abstract: | This paper addresses the control of a one-item inventory system subject to random order lead time and random demand. The key parameter of the control policy is the objective inventory. In each period, the order to be placed brings the inventory position as close as possible to the objective inventory. The order of each period is kept between a lower bound and an upper bound. We show that the distribution of the inventory level converges to its stationary distribution provided that the lower bound is smaller than the average demand, the upper bound is greater than the average demand and some regularity conditions hold. The average inventory cost is shown to be a convex function of the objective inventory level. A simulation-based approach is proposed for the determination of the optimal objective inventory. A method of bisection with derivative is then used to determine the optimal objective inventory. The derivatives needed in various iterations of this method are estimated using a single sample path with respect to a given objective inventory. Numerical results are provided. |
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