FPTAS for Hardcore and Ising Models on Hypergraphs

Hardcore and Ising models are two most important families of two state spin systems in statistic physics. Partition function of spin systems is the center concept in statistic physics which connects microscopic particles and their interactions with their macroscopic and statistical properties of materials such as energy, entropy, ferromagnetism, etc. If each local interaction of the system involves only two particles, the system can be described by a graph. In this case, fully polynomial-time approximation scheme (FPTAS) for computing the partition function of both hardcore and anti-ferromagnetic Ising model was designed up to the uniqueness condition of the system. These result are the best possible since approximately computing the partition function beyond this threshold is NP-hard. In this paper, we generalize these results to general physics systems, where each local interaction may involves multiple particles. Such systems are described by hypergraphs. For hardcore model, we also provide FPTAS up to the uniqueness condition, and for anti-ferromagnetic Ising model, we obtain FPTAS where a slightly stronger condition holds

What Should be Known to Conduct in the Travel Industry? Extending to Knowledge-based View

The purpose of this study is to explore what market knowledge of the travel industry involves. Although there has been consensus that market knowledge is drawn from the market orientation theory, little insight into the nature and issue of market knowledge from the knowledge-based view is identified. Thus, our aim is to fill this gap in the market knowledge of tourism literature. To this end, this study adopts the discovery-oriented approach of qualitative study to delineate the domain of the market knowledge construct in the travel industry setting. The study interviewed two companies and summarized four categories of 4C market knowledge: Knowledge of external customer (customer) including customer profile, traveler’s psychology and behavior, and customer relationships management; internal customer (employee) including employee equity, workforce management, and performance control; competitor, including competitive status and competitive response; and partner client (supplier and distributor), including partners’ characteristics and supply chain management. This study provides operational definitions and a legible framework of market knowledge for directing future research

Optimal control of decoupling point with deteriorating items

Purpose: The aim of this paper is to develop a dynamic model to simultaneously determine the optimal position of the decoupling point and the optimal path of the production rate as well as the inventory level in a supply chain. With the objective to minimize the total cost of the deviation from the target setting, the closed forms of the optimal solution are derived over a finite planning horizon with deterioration rate under time-varying demand rate. Design/methodology/approach: The Pontryagin's Maximum Principle is employed to explore the optimal position of decoupling point and the optimal production and inventory rate for the proposed dynamic models. The performances of parameters are illustrated through analytical and numerical approaches. Findings: The results denote that the optimal production rate and inventory level are closely related to the target setting which are highly dependent on production policy; meanwhile the optimal decoupling point is exist and unique with the fluctuating of deteriorating rate and product life cycle. The further analyses through both mathematic and numerical approaches indicate that the shorten of product life cycle shifts the optimal decoupling point forward to the end customer meanwhile a backward shifting appears when the deterioration rate increase. Research limitations/implications: There is no shortage allowed and the replacement policy is not taken into account. Practical implications: Solutions derived from this study of the optimal production-inventory plan and decoupling point are instructive for operation decision making. The obtained knowledge about the performance of different parameters is critical to deteriorating supply chains management. Originality/value: Many previous models of the production-inventory problem are only focused on the cost. The paper introduces the decoupling point control into the production and inventory problem such that a critical element-customer demand, can be taken into account. And the problem is solved as dynamic when the production rate, inventory level and the position of the decoupling point are all regarded as decision variables.Peer Reviewe

Optimal control of decoupling point with deteriorating items

Purpose: The aim of this paper is to develop a dynamic model to simultaneously determine the optimal position of the decoupling point and the optimal path of the production rate as well as the inventory level in a supply chain. With the objective to minimize the total cost of the deviation from the target setting, the closed forms of the optimal solution are derived over a finite planning horizon with deterioration rate under time-varying demand rate. Design/methodology/approach: The Pontryagin's Maximum Principle is employed to explore the optimal position of decoupling point and the optimal production and inventory rate for the proposed dynamic models. The performances of parameters are illustrated through analytical and numerical approaches. Findings: The results denote that the optimal production rate and inventory level are closely related to the target setting which are highly dependent on production policy; meanwhile the optimal decoupling point is exist and unique with the fluctuating of deteriorating rate and product life cycle. The further analyses through both mathematic and numerical approaches indicate that the shorten of product life cycle shifts the optimal decoupling point forward to the end customer meanwhile a backward shifting appears when the deterioration rate increase. Research limitations/implications: There is no shortage allowed and the replacement policy is not taken into account. Practical implications: Solutions derived from this study of the optimal production-inventory plan and decoupling point are instructive for operation decision making. The obtained knowledge about the performance of different parameters is critical to deteriorating supply chains management. Originality/value: Many previous models of the production-inventory problem are only focused on the cost. The paper introduces the decoupling point control into the production and inventory problem such that a critical element-customer demand, can be taken into account. And the problem is solved as dynamic when the production rate, inventory level and the position of the decoupling point are all regarded as decision variables.Peer Reviewe