In this work, we study customer equilibrium balking strategies in single-server Markovian queueing systems with a single working vacation and vacation interruption. That is, the server undertakes workload with a lower service rate rather than completely stops working during the vacation period. At the instant of completing the service during a vacation period, if there are any customers in the system, the server ends the vacation compulsively and returns to the normal working level, i.e. vacation interruption occurs. Upon arrival, the customers must make a decision whether to join or balk the system based on the information about the number of customers in the system and the server status, along with the reward–cost structure of the system. Accordingly, four cases with respect to different levels of information are introduced and the corresponding Nash equilibria are presented. In addition, the impact of the information levels, as well as of several system parameters, on the equilibrium thresholds and equilibrium joining probabilities is illustrated by numerical examples.

As awareness of environmental protection increases worldwide, enterprises have been building their supply chains in ways that conserve natural resources and minimize the creation of pollutants. One of the practical ways to make supply chains more sustainable is for enterprises to utilize green innovation strategies and to increase resource reuse. In this work, we focus on a closed-loop supply chain (CLSC) consisting of a manufacturer, a retailer, and a collector. In the investigated CLSC, the manufacturer and the retailer drive the green innovation strategy either individually or simultaneously to boost market demand. In the reverse flow of the CLSC, the collector is responsible for collecting consumers’ used products and transferring them to the manufacturer for remanufacturing. By combining two types of the market leadership and three types of green innovation strategies, we establish six different Stackelberg game models and solve them analytically. Through an extensive comparative analysis, we show who should have market leadership and who should drive the green innovation strategy in the CLSC. Various numerical examples are also given to support our major findings. One of our key findings suggests that the supply chain members must participate in green innovation activities at the same time to achieve a win-win scenario in the CLSC.

This work investigates the optimal pricing strategies of a server and the equilibrium behavior of customers in an unobservable M/M/1 queueing system with negative customers and repair. In this work, we consider two pricing schemes. The first is termed the ex‐post payment scheme, where the server charges a price that is proportional to the time spent by a customer in the system. The second scheme is the ex‐ante payment scheme, where the server charges a flat rate for all services. Based on the reward‐cost structure, the server (or system manager) should make optimal pricing decisions in order to maximize its expected profit per time unit in each payment scheme. This study also investigates equilibrium joining/balking behavior under the server’s optimal pricing strategies in the two pricing schemes. We show, given a customer’s equilibrium, that the two pricing schemes are perfectly identical from an economic point of view. Finally, we illustrate the effect of several system parameters on the optimal joining probabilities, the optimal price, and the equilibrium behavior via numerical examples.

Rapid economic growth and industrialization have brought material abundance and convenience, but also social and environmental problems such as global warming, climate change, and ozone depletion. For this reason, the public and governments have continued to make efforts to reduce carbon oxide emissions worldwide over the past few decades. To achieve this mission, cap-and-trade regulations have been introduced as one of the most effective market-based mechanisms to control carbon emissions. Accordingly, sustainability efforts, including the development of green products and innovating manufacturing technologies, are being made by companies in supply chains to reduce their carbon emissions. In the context of sustainability innovations and carbon emission constraints, this article investigates pricing decisions, the degree of sustainability efforts, and carbon caps under two different supply chain contracts—in this case, wholesale price contract and cost-sharing contract. This article establishes a Stackelberg game model under each of the supply chain contract types and presents the equilibrium decisions made by players of the game. Major findings of this article reveal that (i) the performance of the supply chain is considerably affected by the presence of a carbon cap; (ii) the higher the carbon cap set by a government is, the more sustainability innovation efforts the supply chain makes; and (iii) the supply chain can improve its profitability and its sustainability under a cost-sharing contract.

As awareness of climate change increases, diverse initiatives such as subsidies for remanufactured products and take-back programs for end-of-life products have been taken to conserve energies and materials. This paper explores how the subsidy program affects manufacturer’s take-back activity in a closed-loop supply chain and also analyzes how a coalition between a retailer and a remanufacturer affects the equilibrium decisions. Major findings of this paper reveal that (i) when a take-back program is implemented, the government imposes a high penalty on products that are not collected, thereby encouraging manufacturers to collect more used products, (ii) implementing a take-back program in conjunction with a subsidy program results in a greater reduction in environmentally negative impacts and an enhanced social welfare compared to implementing them separately, and (iii) a coalition between a retailer and a remanufacturer results in lowering the penalty imposed to a manufacturer, which leads to lowering the quantity of the collected and remanufactured products.

Environmental sustainability has become a critical indicator in evaluations of the success and efficiency of supply chain management. In this study, we consider a two-echelon supply chain composed of two competing manufacturers, two retailers, and one third-party logistics firm. The first manufacturer produces a green product, while the second manufacturer produces a nongreen product. Each of the two retailers can sell only a green product, only a nongreen product, or both green and nongreen products. All products are initially stored by the third-party logistics firm and delivered to the retailers. This study investigates product pricing, the degree of greenness of the first manufacturer’s product, and carbon emission reduction as carried out by the third-party logistics firm. Using a three-stage Stackelberg game framework, we present the equilibrium strategy on pricing, the degree of greenness, and carbon emission reduction for five different distribution channel structures. One of our major findings is that competition between the two manufacturers has a positive influence on the profitability of the supply chain. We also find that it is desirable for each manufacturer to choose a cross-distribution channel for its products considering the sustainability and profitability of the supply chain.