Abstract
The classical newsboy problem considers the single product case to determine the optimal ordering quantity which maximises the expected profit. This paper attempts to develop a newsboy type model with multiple products and stochastic demand and determine the optimal ordering quantity based on the different time periods which maximise the expected profit subject to the budget constraints. In the modern market, each individual customer has his own freedom to choose the product independently. Accordingly, this paper assumes that the demand for each product is invariably independent and follows the lognormal distribution with different mean and variance. An effective method has been developed to determine the optimal ordering quantity for each product at different time period with different level of budget constraint. From the illustrations, it is quite clear that an optimal solution can be obtained for the proposed model. The analytical structure used in the proposed model shows that the multi-product extension of the newsboy problem with budget constraint and stochastic demand is a very challenging area of research.
Highlights
Under the traditional single period newsvendor type problem, the newsboy buys the newspaper at the start of the day and sells it during the day
To capture the increasing trend of demand in the case of single period news vender problem, some researchers (Huang, 2013; Yao, 2017) have considered that the demand for each commodity approximately follows log normal distribution. This strongly motivates us to develop a model with multiple item newsboy type problems with budget constraint and stochastic demand
This paper extends the existing newsboy model to incorporate multiple items with stochastic demand and budget constraint and determine the optimal ordering quantity which maximises the total expected profit
Summary
Under the traditional single period newsvendor type problem, the newsboy buys the newspaper at the start of the day and sells it during the day. Salazar (2018) discussed the single period newsboy model by considering changes in demand riskiness and fixed cost and analyse the effect of this on optimal ordering quantity. The multi-product newsboy model considering fuzzy demand and storage space constraint (Dutta, 2010) was discussed with an objective to maximise the total profit. Some researchers have extended the newsboy model to discuss the problem of minimising the cost to maximise the profit (Nobari et al, 2018; Liu et al, 2007), offering all-unit quantity discount in each product. To capture the increasing trend of demand in the case of single period news vender problem, some researchers (Huang, 2013; Yao, 2017) have considered that the demand for each commodity approximately follows log normal distribution This strongly motivates us to develop a model with multiple item newsboy type problems with budget constraint and stochastic demand.
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