An EOQ model for a deteriorating item with time-varying demand and time-dependent partial backlogging

This paper describes an EOQ model for a deteriorating item considering time-dependent demand and time-dependent partial backlogging, which depends on the length of the waiting time for the next replenishment over a finite time horizon and variable replenishment cycle. Equal replenishment cycle length in case of fixed planning horizon is relaxed in this model. Also, backlogging rate is taken to be dependent on waiting time of the customers, instead of waiting line of the customers. This seems to be better representation since impatient customers naturally want to know how long time they have to wait for receiving their goods, not how many customers are ahead. The model is solved analytically to obtain the optimal solution of the problem for a general time-dependent demand pattern. It is then illustrated with the help of numerical examples.

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