Abstract
An order level inventory model for seasonable/fashionable products subject to a period of increasing demand followed by a period of level demand and then by a period of decreasing demand rate (three branches ramp type demand rate) is considered. The unsatisfied demand is partially backlogged with a time dependent backlogging rate. In addition, the product deteriorates with a time dependent, namely, Weibull, deterioration rate. The model is studied under the following different replenishment policies: (a) starting with no shortages and (b) starting with shortages. The optimal replenishment policy for the model is derived for both the above mentioned policies.
Highlights
It is observed that the life cycle of many seasonal products, over the entire time horizon, can be portrayed as a period of growth, followed by a period of relatively level demand and finishing with a period of decline
The purpose of the present paper is to study an order level inventory model when the demand is described by a three successive time periods that classified time dependent ramp-type function
The previous analysis shows that t∗1 is independent from the demand rate D t. This very interesting result agrees with the classical result, in many order level inventory systems, that the point t∗1 is independent from the demand rate Naddor 31, page 67
Summary
It is observed that the life cycle of many seasonal products, over the entire time horizon, can be portrayed as a period of growth, followed by a period of relatively level demand and finishing with a period of decline. Chen et al 30 proposed a net present value approach for the previous inventory system without shortages For both models, the demand rate is a revised version of the Beta distribution function and so is a differentiable with respect to time. The purpose of the present paper is to study an order level inventory model when the demand is described by a three successive time periods that classified time dependent ramp-type function. Any such function has points, at least one, where differentiation is not possible, and this introduces extra complexity in the analysis of the relevant models.
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