A two-echelon inventory model with lost sales
Creators: name: Seifbarghy, Mehdi
name: Hill, Roger M.
name: Smith, David K.
Publisher: name: figshare
Year: 2020
Subjects: subject: 90603 Industrial Electronics
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: FOS: Electrical engineering, electronic engineering, information engineering
subject: 90505 Infrastructure Engineering and Asset Management
subject: FOS: Civil engineering
subject: FOS: Civil engineering
subject: 91599 Interdisciplinary Engineering not elsewhere classified
subject: FOS: Other engineering and technologies
subject: FOS: Other engineering and technologies
subject: 91003 Machine Tools
subject: 91004 Machining
subject: 91099 Manufacturing Engineering not elsewhere classified
subject: 91005 Manufacturing Management
subject: 91006 Manufacturing Processes and Technologies (excl. Textiles)
subject: 91007 Manufacturing Robotics and Mechatronics (excl. Automotive Mechatronics)
subject: 91008 Manufacturing Safety and Quality
subject: 91199 Maritime Engineering not elsewhere classified
subject: FOS: Environmental engineering
subject: FOS: Environmental engineering
subject: 91299 Materials Engineering not elsewhere classified
subject: FOS: Materials engineering
subject: FOS: Materials engineering
subject: Mechanical Engineering
subject: FOS: Mechanical engineering
subject: FOS: Mechanical engineering
subject: 91399 Mechanical Engineering not elsewhere classified
subject: 90304 Medical Devices
subject: FOS: Medical engineering
subject: FOS: Medical engineering
subject: 90404 Membrane and Separation Technologies
subject: FOS: Chemical engineering
subject: FOS: Chemical engineering
subject: 91207 Metals and Alloy Materials
subject: 91306 Microelectromechanical Systems (MEMS)
subject: 90604 Microelectronics and Integrated Circuits
subject: 91009 Microtechnology
subject: 91404 Mineral Processing/Beneficiation
subject: 91405 Mining Engineering
subject: 91102 Naval Architecture
subject: 90904 Navigation and Position Fixing
subject: 90405 Non-automotive Combustion and Fuel Engineering (incl. Alternative/Renewable Fuels)

description: This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, Ri) control policy. The warehouse operates an (SQ, (S - 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for retailer i is the fixed transportation time Li from the warehouse to that retailer. Otherwise retailer orders are met, after a delay, on a first-come first-served basis. The lead time on a warehouse order is fixed. Two further assumptions are made: that each retailer may only have one order outstanding at any time and that the transportation time from the warehouse to a retailer is not less than the warehouse lead time. The performance measures of interest are the average total stock in the system and the fraction of demand met in the retailers. Procedures for determining these performance measures and optimising the behaviour of the system are developed.