An inventory model for nonperishable items with warehouse mode selection and partial backlogging under trapezoidal-type demand

Abstract

Considering a nonperishable product which may be stored either in an own warehouse or in both the own and the rented warehouse, this paper deals with the ordering decisions under a generalized trapezoidal-type demand rate in an inventory system. Shortages are allowed and the unsatisfied demand is assumed to be partially backlogged. Furthermore, the existence and uniqueness of the optimal solution to each warehouse mode is proved and used in an easy-to-use algorithm, and a decision-making theorem for measuring whether to adopt a rented warehouse is developed. Finally, numerical examples and a case study are presented to illustrate the feasibility and efficiency of the proposed model and algorithm. The results show that, the storage capacity of the own warehouse and the unit rental cost have remarkable impact on determining whether to use the rented warehouse. When both the unit rental cost and the unit opportunity cost are higher in the external market, the profitability of the inventory system mainly relies on the storage capacity of the own warehouse. Meanwhile, the optimal profit performance is sensitive to the selling price and the purchasing cost, and the optimal rented warehouse’s ordering quantity is sensitive to the order cycle length. But overall, the proposed model is basically robust.

Keywords:

• Inventory
• warehouse mode selection
• trapezoidal-type demand
• time-varying
• two-warehouse
• partial backlogging

Acknowledgements

The authors would like to thank the Editor-in-Chief, Associate Editor and three anonymous referees for their instructive comments and valuable suggestions, which have improved the earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 In order to simplify the model, the case that the time points $t_0$ and $T_1$ fall in the interval $(\mu ,\gamma )$ at the same time is not considered, but by setting the relevant model parameters, the proposed model may reduce to the particular case. Thus, we here omit this case.

2 In order to investigate the impact of over or under estimation of the model parameters, we here adopt $(\Pi \prime -\Pi )/\Pi ,(Q^{r^{\prime }}-Q^r)/Q^r$ and $(Q^{B^{\prime }}-Q^B)/Q^B$ as measures of parameter’s sensitivity, where Π, Q^r and Q^B denote the true values, and $\Pi \prime ,Q^{r^{\prime }}$ and $Q^{B^{\prime }}$ denote estimated ones. As the bold numbers shown in Table 5, when p changes from −33% to 33%, the varying range of Π is from 67% to −67%; when c changes from −40% to 40%, the varying range of Π is from 34% to −34%; when M changes from −20% to 20%, the varying ranges of Π, Q^B and Q^r are from −25% to 28%, −34% to 35%, and −38% to 47%; when T changes from −11% to 11%, the varying range of Q^B is from −17% to 15%. Except for the previous parameters, the effects of other ones on the Π, Q^r and Q^B are not very significant.

Additional information

Funding

The study was supported by Humanities and Social Science Foundation of the Education of Ministry of China (No. 19YJC630188), the Research Program of Tianjin Municipal Education Commission (No. 2017KJ242) and the National Natural Science Foundation of China (No. 71571002).