Approximation algorithms for scheduling single batch machine with incompatible deteriorating jobs

Motivated by the soaking process under separate heating mode in iron and steel enterprises, we study the parallel batch machine scheduling problem with incompatible deteriorating jobs. The objective is to minimize makespan. A soaking furnace can be seen as a parallel batch processing machine. In order to avoid the thermal stress caused by excessive temperature difference, initial temperature is needed for the ingot before processing. With the increasing of waiting time, the ingot temperature decreases and the soaking time increases. This property is called deterioration. Setup time is needed between incompatible jobs. We show that if jobs have the same sizes, an optimal solution can be found within O(nlogn) time. If jobs have identical processing times, the problem is proved to be NP-hard in the strong sense. We propose an approximate algorithm whose absolute and asymptotic worst-case ratios are less than 2 and 11/9, respectively. When the jobs have arbitrary sizes and arbitrary processing times, the model is also NP-hard in the strong sense. An approximate algorithm with an absolute and asymptotic worst-case ratio less than 2 is proposed. The time complexity is O(nlogn)

Fashion retail competition on product greenness with overconfidence

In this paper, we study the impacts of overconfidence in a competitive retailer setting of green fashion. We model a green fashion supply chain comprising one unbiased manufacturer and two biased retailers, to explore how overconfidence affects greenness level of fashion products and expected profit of retailers. An overconfident retailer has a cognitive bias in which it believes consumers are more sensitive to greenness of fashion products than it really is. Our findings show that the competition between two retailers discourages greenness level of fashion products, while overconfidence can provide a counterbalance to the negative impact caused by competition. We also find, a retailer's overconfidence is not only conducive to the greenness level of its own fashion products, but also can benefit to its rival. Moreover, it shows a low level of overconfidence can be a comparative advantage of the retailer's profit. Even though one of the retailers is unbiased and has an advantage of information, it can still earn less than its overconfident rival

Optimal decision in MC supply chain with overconfident retailer based on the newsvendor model

In this paper, we analyze the optimal order-quantity decisions in a supply chain with mass customization (MC) manufacturer and overconfident retailers. First, we consider a newsvendor model in which an unbiased retailer sells mass customized products. The retailer needs to make order quantity decisions before the selling season. Meanwhile, the supplier is a mass customization manufacturer and implements modular production. The supply process is uncertain, as the real quantity the retailer received is the order quantity multiplied by a random yield rate. Second, two overconfident models are considered and theorems are proposed. In the first model, the behavioral bias of overconfidence only affects the retailer’s judgment of variance of market demand. In the second model, the behavior bias of overconfidence affects not only the retailer’s cognition of the variance of market demand, but also his cognition of the expectation of market demand. In addition, the relationship between the optimal decisions and the modularity level is obtained. Finally, we provide managerial insights for the decision makers of the retailers and the manufacturers on order quantity and modularity level, respectively