In this study, an optimal maintenance policy is developed for a k-out-of-n: G system subject to two types of maintenance services, preventive maintenance and corrective maintenance. We investigate the optimal replacement age when a component failure is not detected immediately until a k-out-of-n: G system fails. The optimal maintenance policy is determined to minimize the expected total system cost when a generalized block replacement model is developed using downtime period. It is assumed that component failures are not monitored until a system failure, thus, a k-out-of-n: G system failure occurs. The downtime period of each failed component using order statistics for life time and age distributions for a k-out-of-n: G system is investigated. Numerical examples are discussed in order to demonstrate the applicability of the methodology derived from this paper.

In this study, we consider a carbon emission cap-and-trade system in which the policymaker decides the cap for carbon emissions for each company and also has the power to regulate the carbon price in the carbon trading market for the purpose of minimizing total carbon emissions. We assume that there are n companies regulated in terms of carbon emissions by the policymaker, each of which emits carbon when producing its own product. After learning the carbon cap and carbon price regulated by the policymaker, each company makes simultaneous pricing and production decisions using the quick response strategy, and can trade some of its carbon emissions in the carbon market at the carbon price set by the policymaker, if the carbon emissions are below the cap. We model this non-cooperative game between the policymaker and companies as a Stackelberg game in which the policymaker is the leader and the companies are the followers. We show that there exists an equilibrium for the policymaker’s carbon pricing decisions and each company’s production and pricing decisions. From this equilibrium, we derive a carbon cap for the company at which the amount of traded carbon emissions is zero. This implies that some company’s production and pricing decisions, even under carbon emission restrictions, will be equal to those without the carbon emission restrictions. Also, we find that companies participating in the carbon cap-and-trade system would reduce their carbon emissions through reduced production, but can have a chance to improve profit through control of the product’s selling price.

This paper considers a carbon emission cap and trade market, where the carbon emission cap for each entity (either government or firm) is allocated first and then the carbon trading price is decided interdependently in the carbon trading market among the non-cooperative entities which make their production decision. We assume that there are n entities emitting carbon during the production process. After allocating the carbon (emission) cap for each participating entity in the carbon cap and trade market, each participant makes a production decision using the Newsvendor model given carbon trading price determined in the carbon trading market and trades some amount of its carbon emission, if its carbon emission is below or above its own carbon cap. Here, the carbon trading price depends on how carbon caps over the entities are allocated, since the carbon trading price is determined through the carbon (emission) trading market, which considers total amount of carbon emission being equal to total carbon caps over entities and some fraction of total carbon emission should be from each entity participating in the carbon cap and trade market. Thus, we can see the interdependency among the production decision, carbon cap and carbon trading price. We model this as a non-cooperative Stackelberg game in which carbon cap for each entity is allocated in the first stage and each entity’s production quantity is decided in the second stage considering the carbon trading price determined in the carbon trading market. First, we show the monotonic property of the carbon trading price and each entity’s production over the carbon cap allocation. In addition, we show that there exists an optimality condition for the carbon cap allocation. Using this optimality condition, we provide various results for carbon cap and trade market.

To optimize the firm’s profit during a finite planning horizon, a dynamic programming model is used to make joint pricing and inventory replenishment decision assuming that customers are loss averse and the firm is risk averse. We model the loss averse customer’s demand using the multinomial choice model. In this choice model, we consider the acquisition and transition utilities widely used by a mental accounting theory which also incorporate the reference price and actual price. Then, we show that there is an optimal inventory policy which is base‐stock policy depending on the accumulated wealth in each period.

Traditionally, in the area of production and operations management, the financial states and decision-makers’ behaviour regarding loss have been ignored in the supply chain, which may lead to infeasible or unrealistic practices or even catastrophic losses in practical supply chain operations. Therefore, this study aims to provide a model for operational efficiency in a financially constrained supply-chain system consisting of a financially deficient retailer, a supplier, and a bank, and to analyse the impact of the behaviour of the bank and the supplier on the operational decision. It is assumed that the bank provides a loan to the retailer considering the supplier’s credit guarantee for the retailer. The supplier’s credit guarantee implies that, if the retailer goes bankrupt after the sales season, then a pre-guaranteed proportion of the retailer’s loan is repaid by the supplier. Moreover, to capture the decision-makers’ behaviour regarding loss, it is assumed that the supplier and the bank are loss-averse in their risk preference on the final profit. Under this circumstance, it is intended to draw the theoretical implications by analysing a loss-averse behaviour model for a supplier and a bank, in which a kinked piecewise linear and concave utility function is considered. The optimal decision is analytically derived for the retailer (the optimal order quantity), the supplier (the optimal wholesale price), and the bank (the optimal interest rate). In addition, a sensitivity analysis is conducted to investigate how the model parameters affect the optimal decision for the retailer, the supplier, and the bank under different degrees of loss-aversion. The optimal decisions are shown to be highly affected by the degree of the loss-aversion coefficient of the bank and the supplier and to be more conservative than the result in the traditional case which optimises the risk-neutral expected profit (the unit degree of loss-aversion). The analytical results can be summarised as follows. First, as the wholesale price and the interest rate increase, the optimal order quantity decreases. Second, the more loss-averse the supplier is, the higher the optimal wholesale price that is offered to the retailer by the supplier. Third, the larger the credit guarantee that is provided to the retailer by the supplier, the higher the optimal wholesale price that is provided to the retailer. Fourth, the more loss-averse the bank is, the higher the interest rate that is offered to the retailer; and the larger the credit guarantee that is provided by the supplier, the lower the interest rate that is offered to the retailer.