Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random working cycle, rebate and charge into warranty theory, a random free repair warranty with rebate and charge (RFRW-RC) is devised to ensure system reliability during the warranty stage. Under RFRW-RC, the rebate removes manufacturers’ responsibility for continuing to ensure system reliability, while the charge is a support where manufacturers continue to ensure system reliability. The warranty cost of RFRW-RC is derived, and a random discrete free repair warranty (RDFRW) is presented by simplifying RFRW-RC. By mixing random age replacement last (RARL) and classic age replacement (CAR), a random hybrid age replacement (RHAR) is designed in order to ensure system reliability during the post-warranty stage. In such an RHAR, RARL is applied to extend the replacement time during the post-warranty stage in order to maximize the remaining life of the system through warranty, and CAR is used to lower the maintenance cost of the system through warranty. The cost rate of RHAR is modeled, and the cost rate of RDFRW is offered as well by discussing parameter values. The decision variable is optimized by minimizing the cost rate model. The properties of the presented models are explored from numerical perspectives.

This paper investigates a dual-channel retailer’s inventory and pricing integrated decision-making problem over multiple periods. The quantity-sales mode is adopted in the online channel while the unit-sales mode is used offline. The customer demand of each sales channel is stochastic, and depends on visit costs, customer return costs, sales modes and pricing levels. To achieve the long-term profit maximization, the dual-channel retailer needs to optimize the pricing levels of both channels and the ordering quantity. For this problem, we first formulate a stochastic dynamic programming model, and then prove the joint concavity and the supermodularity of the objective function. With these properties, the optimality of the base-stock policy is proved, and the optimum price policy is characterized. Specifically, if the retailer’s optimum stock is neither too low nor too high, both sales channels need to be operated simultaneously, otherwise, only operating one channel is optimal. The online price is invariant with the retailer’s stock level while the offline price is decreasing in the retailer’s stock level. Finally, numerical results show that the quantity-sales mode, dual-channel sales model, and the multi-period dynamic decisions could benefit the dual-channel retailer. In addition, influences of cost parameters on the total profit are verified numerically.

Predicting future promotion information on markdowns, customers can maximize their utilities by deciding when to buy. With this strategic behavior, this paper investigates a downside-risk-averse retailer’s integrated stock and pricing problem using a single case study method. Analyzing effects of the downside risk aversion and strategic customers is our purpose. By exploring a two-phase newsvendor model with a retailer selling to strategic customers, our work determines the downside-risk-averse retailer’s equilibrium ordering level and selling price. On this basis, effects of the downside risk aversion and the strategic behavior on the retailer’s optimum decisions and profit are analyzed. We find that the reverse effect of the strategic behavior can be mitigated by the retailer’s downside risk constraint. We also extend the model to a decentralized supply chain case. It is found that a low (high) downside risk aversion would mean that the supply chain profit in the decentralized case can (cannot) dominate the centralized under some (any) wholesale price contracts when customers are strategic. In addition, for different risk aversions, we also construct contracts to optimize the supply chain profit. Our results will provide reference evidence of making operational management decisions for the downside-risk-averse retailer in the case of strategic customers.