Abstract
The previous efforts toward single period inventory problem with price-dependent demand only investigate the optimal order quantity to minimize the total inventory costs; however, there is no method in the literature to avoid unwanted costs due to the deviation between the actual demand and the previously estimated demand. To fill this gap, the present paper supposes that stochastic demand rate with normal distribution is sensitive to the selling price; this means that increasing the selling price would decrease the demand rate and vice versa. After monitoring the consumption trend within a section of the period, a new selling price is implemented to change the demand rate and reduce the shortage or salvage costs at the end of the period. Three functions were suggested to represent the demand rate as a function of selling price, and the numerical analysis was implemented to solve the proposed problem. Finally, an illustrative numerical example was solved for different configurations in order to show the advantages of the proposed model. The results revealed that there is a significant improvement in the system costs when price revision is considered.
Highlights
Inventory management is an important task in the business operations. e classical single period problem (SPP) deals with the purchasing inventory problem for single-period products, such as perishable or seasonal goods. e SPP has been popularly researched in the last decade, because of its extensive application in the inventory management of the products with short life cycles. e authors made extensions to incorporate real world situations in SPP; there are two important problems in SPP; the rst one is how to be in front of demand’s uncertainty in the real dynamic global condition and the other one is how to deal with the demand pattern which is dependent to the selling price
The columns of pp∗E and NPV∗E indicate the optimum solutions based on the estimated demand rate within proposed approach), the columns tohfeppi∗AntaenrdvaNl [P0V, t∗At0]sh(io.ew., the the optimum solutions based on the actual demand rate, with the mean 18 and variance 25, tsthhheeowcaocslttuuhmaelnrdeoleafmtiNvaePndVgaArpa(bptpee∗Et)fwoserheopnpw∗EN,s PathnVedAe( xpnpp∗Eae)cllatyenddthNeexPplaVesctbtecadoselNudmPoVnn without the price revision included in the last row of Table
We presented a price-dependent model for the single period inventory problem
Summary
Inventory management is an important task in the business operations. e classical single period problem (SPP) deals with the purchasing inventory problem for single-period products, such as perishable or seasonal goods. e SPP has been popularly researched in the last decade, because of its extensive application in the inventory management of the products with short life cycles (e.g., fashion clothes and electronic products [1]). e authors made extensions to incorporate real world situations in SPP (for further information refer to Khouja [2]); there are two important problems in SPP; the rst one is how to be in front of demand’s uncertainty in the real dynamic global condition and the other one is how to deal with the demand pattern which is dependent to the selling price. To overcome the problem of difference between the real demand and estimated demand, that causes overstock or understock at the end of period, Bitran and Mondschein [12] characterized the optimal pricing policies as functions of time and inventory to present a continuous time model where the seller faces a stochastic arrival of customers with different valuations of the product. In order to obtain optimal order quantity and adjusted price a er the review time, they considered a zero salvage value, small variance a er review time, deterministic function of price, and information before review time. Sinha and Sarmah [20] developed a single-vendor multibuyer discount pricing model under stochastic demand information In this model, the vendor offers multiple pricing schedules to encourage the buyers to adopt the global optimal policy instead of their individual optimal ordering policy. A numerical example is solved for various con gurations, and sensitivity analysis is performed to show the efficiency of the proposed approach
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