A bundling strategy for items with different quality based on functions involving the minimum of two random variables

Abstract

A common strategy to increase sales and profit is to combine different types of products into bundles and sell at a discounted price. In this study, we consider the case where a wholesaler offers to sell two types of products through discount bundles. Each of the two types of products is purchased from a producer in lots that contain a percentage of imperfect quality items, which is a random variable having a known probability density function. Items received from the producer are inspected for imperfect quality using a 100% screening process. The perfect quality items are used to make the discount bundles, while the imperfect quality items are sold at a discounted price at the end of the screening period. Items of perfect quality of one type that are not bundled are kept in stock to be used in the next inventory cycle. A mathematical model is developed to determine the total profit function. A closed-form formula for the wholesaler's optimal order quantity of each type of product is determined by maximizing the profit function. The optimal solution is given in terms of the expected values of functions involving the two random variables representing the percentages of perfect quality items. Numerical examples are provided to illustrate the model, and simulation is used to calculate the optimal solution.

An economic production model with imperfect quality components and probabilistic lead times

“…For future research we suggest examining the effect of probabilistic lead times on the aforementioned models (El-Kassar et al , 2020; Yassine and Singh, 2020; Khan and Jaber, 2011; Yassine et al , 2018). In another direction, we suggest incorporating monetary factors in the model considered in this paper.…”

“…In case that all components received in a lot are of a perfect quality, the 4th assumption remains valid by setting the percentage of imperfect quality items in this lot equal to zero. Similarly, the mentioned above previous research studies that dealt with incorporating the effect of components used in production process (Yassine, 2018; Salameh and El-Kassar, 2007; El-Kassar et al , 2012) or an inventory situation (Yassine et al , 2018) did not consider lead times. Hence, the model presented in this paper generalizes these studies.…”

“…Moreover, recent results (Yassine, 2016, 2018; Yassine and El-Rabih, 2019) are used to show that the optimal policy of the proposed model depends on the maximum of the lead times and the minimum of the percentages of perfect components. Recent works based on the modeling approach of Yassine (2016) for the treatment of excess perfect components (Yassine, 2018; Yassine et al , 2018, 2020) did not consider the effect of the lead times. Moreover, Yassine and El-Rabih (2019) incorporated the effect of lead times on the classical production model.…”

Economic production quantity model with variable machining rates and product quality

“…Effect of change in the machining constant, k k appears in three terms of HðvÞ as well as constraint (4). Figure 4 shows that as the machining constant, k, increases, the optimal production quantity decreases the cutting speed and the fraction of nonconforming products.…”

“…2 Many researchers studied different settings and extensions of this classical problem. These include, but are not limited to, integrated models, 3 bundling strategies, 4 variable lead-time, 5 variable production rate, 6 and variable holding cost. 7 Several survey papers can be found on this problem and its variations, as examples: Glock,8 Ramasesh, 9 Drexl and Kimms, 10 and Zoller and Robrade.…”