EOQ inventory model for perishable products under uncertainty
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PRODUCTION MANAGEMENT
EOQ inventory model for perishable products under uncertainty R. Patriarca1 · G. Di Gravio1 · F. Costantino1 · M. Tronci1 Received: 29 May 2020 / Accepted: 22 September 2020 © The Author(s) 2020
Abstract Perishable products require accurate inventory control models as their effect on operations management can be critical. This assumption is particularly relevant in highly uncertain and dynamic markets, as for the ones generated by the pandemic era. This paper presents an inventory control model for perishable items with a demand rate variable over time, and dependent on the inventory rate. The model also considers the potential for backlogging and lost sales. Imperfect product quality is included, and deterioration is modelled as a time-dependent variable. The framework envisages the possibility to define variables affected by uncertainty in terms of probability distribution functions, which are then jointly managed via a Monte Carlo simulation. This paper is intended to provide an analytical formulation to deal with uncertainty and time-dependent inventory functions to be used for a variety of perishable products. The formulation is designed to support decision-making for the identification of the optimal order quantity. A numerical example exemplifies the outcomes of the paper and provides a cost-based sensitivity analysis to understand the role of main parameters. Keywords Inventory management · Deteriorated products · Defective products · Disposal cost · COVID19 List [ of] symbols Demand rate in D (t = 0) (a > 0) a unit [ t ] b unit Demand rate coefficient (b ≠ 0) 2 ] [t C Unit backorder cost bc unit∗t [ ] c unit Demand rate coefficient (c ≠ 0) 3 [t ] C {\rm unit} deteriorating cost d unit [ ] C Constant coefficient of the holding cost g unit ] [ C Variable coefficient of the holding cost h unit∗t [ ] C Unit lost sale cost ls unit [ ] C Unit screening cost s unit t1 [t] Screening process starting time t2 [t] Stock-out starting time
* R. Patriarca [email protected] 1
Department of Mechanical and Aerospace Engineering, Sapienza University of Rome, Via Eudossiana, 18, 00184 Rome, Italy
α Percentage of defective products [ ] θ unit Deterioration rate [ t ] λ unit Screening rate t
μ[[t]] Deterioration process starting time φ 1t Backlogging parameter (𝜑 > 0) Br(t) Backlogging rate [ ] unit D(t) t Demand rate [ ] Db unit Demand rate when inventory is null [t ] C Holding cost function H(t) unit
I0 [unit] Maximum inventory level I1(t) [unit] Inventory level in the time interval [0, t1] I1′(t) [unit] Inventory level in the time interval [t1, μ] I2(t) [unit] Inventory level in the time interval [μ, t2] I3(t) [unit] Inventory level in the time interval [t2, T] Id [unit] Inventory level in t1, considering defective products Is [unit] Inventory level in t1, without defective products Iμ [unit] Inventory level in μ Q [unit] Ordered quantity Qb [unit] Maximum backorder quantity T [t] Inventory cycle length
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