Production, Manufacturing and LogisticsAn EOQ model for perishable products with fixed shelf life under stochastic demand conditions
Section snippets
Introduction and literature review
Inventory models for deteriorating items have attracted considerable interest in recent decades. The problem of modeling the deterioration process was firstly tackled by Ghare and Schrader (1963) that developed an exponentially decaying inventory model. They observed that certain commodities deteriorate with time by a proportion which can be approximated by a negative exponential function of time. Successively, Covert and Philip (1973), considered a two parameters Weibull deterioration
Model formulation
The model here presented deals with products having a deterministic and constant SL. In the case of deterministic demand behaviour such an assumption would lead to the purchasing of the quantity sold within the time of the SL, i.e., EOQ = demand rate*SL and t1= Tc = SL. Conversely, the stochastic behavior of the demand here enforced leads two main results. First of all, it determines the possibility of stockout occasions due to the demand variability. Such problem can be partially overcome by
Cost function analysis
Under the hypothesis of symmetric distribution Eq. (15) becomes: Considering position (16), it can be shown that for t1 = 0 or t1 = Tc, Eq. (15) is simply to solve via analytic form. For t1 = 0 in (18) we have: By posing: The cost function is always convex and the optimality condition is:
Numerical example
In this section a numerical application is illustrated to confirm the practical applicability of the proposed model that can be taken as drive of decision-making process in the warehouse management field.
The input data are: A = 250€, h = 0.001€/unit*unit time, Cs = 0.02€/unit*unit time, Co = 0.01€/unit. The safety factor k is equal to 1.65 (corresponding to a CSL of 0.95). The SL of the products is equal to 30 unit time. The demand is normally distributed with μt = 30 unit/unit time and σt = 5
Sensitivity analysis
In this section a sensitivity analysis is proposed to show the impact of the variation of input factors, namely the SL, the LT, the costs and the demand values, on the optimal ETCu, t1, Tc and the EOQ. For the purpose of the model, the input factors are independent variables, while t1, Tc, EOQ and ETCu are dependent variables of the model. Of independent variables, μt, σt and SL are out of the control of supply chain's actors, as well as the costs, while the safety factor k is dependent on
Conclusions
The present paper addressed the topic of EOQ for perishable products. The study starts from the consideration that the perishability of products is to be put in relation with their SL. Moreover, in determining the optimal quantity to be stocked on hand, the current literature neglects of verifying that the SL has not been overcome during the cycle time. This leads that products remaining on hand at the end of the cycle time are considered outdated and consequently disposed off or rather sent to
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