This study investigates a two-stage stochastic facility location game (2-SFLG), in which clients collaboratively share the combined costs of facility opening and client connection. As strategic players, the clients aim to minimize the total cost through jointly decisions on which facilities to open and how to assign connections in the most cost-effective way. We focus on designing cross-monotonic cost-sharing strategies that incentivize client cooperation by revealing their true value. To this end, an approximation method utilizing the primal-dual technique is developed, which achieves a 6-approximation cost-sharing ratio, effectively balancing cost distribution and cooperation incentives. Furthermore, we introduce a novel variant, the 2-SFLG with penalties (2-SFLGP), which generalizes both the FLGP and the 2-SFLG. Crucially, our cost-sharing method for the 2-SFLGP preserves the same approximation guarantee while demonstrating competitive performance.

This paper investigates a platform supply chain consisting of a manufacturer and a platform and explores the impact of the manufacturer’s altruistic preference on the platform’s decision to introduce blockchain technology in reselling and agency models. The results indicate that, firstly, when the investment cost of blockchain technology is low, both the manufacturer and the platform prefer to use blockchain in the reselling model, and when the investment cost and the commission are high, both parties opt for an agency sales model. Then, the reselling model is a better option when consumer traceability demand is high, but for the additional unit information cost expended on products, the platform will not introduce blockchain technology in the agency model when the demand weakening effect from this unit cost exceeds 5.7% of the total demand. Finally, considering the manufacturer’s altruistic preference behavior, it is not feasible to simultaneously boost the revenue of both parties under either sales model. However, in the agency model, the manufacturer’s altruistic preference can incentivize the platform to introduce blockchain technology.

The application of Blockchain Technology (BT) makes consumers trace more product information and enhances their trust in the product brand, but it also brings cost pressure to some participants who adopt the technology. Thus, it is particularly important how to encourage and support more enterprises to participate in BT. This study incorporates the altruistic preference into a BT-enabled three-echelon supply chain consisting of a powerful retailer, a supplier, and a manufacturer. We investigate the optimal strategies of the supply chain in different scenarios: without and with the BT, and without and with the altruistic preference. Then, we explore the effects of the BT and the retailer’s altruistic preference on the profit performance of the supply chain system. The results show that the retailer, the manufacturer, and the supplier do not always benefit from the traceability of the BT, and while the powerful retailer’s altruistic preference decreases his or her own profit but increases the profits of the manufacturer, the supplier, and the entire supply chain. Finally, a profit redistribution mechanism is designed to coordinate the supply chain with the retailer’s altruistic preference under the BT.

Capacitated facility location problem (CFLP) is a classical combinatorial optimization problem that has various applications in operations research, theoretical computer science, and management science. In the CFLP, we have a potential facilities set and a clients set. Each facility has a certain capacity and an open cost, and each client has a spliitable demand that need to be met. The goal is to open some facilities and assign all clients to these open facilities so that the total cost is as low as possible. The CFLP is NP-hard (non-deterministic polynomial-hard), and a large amount of work has been devoted to designing approximation algorithms for CFLP and its variants. Following this vein, we introduce a new variant of CFLP called capacitated uniform facility location problem with soft penalties (CUFLPSP), in which the demand of each client can be partially rejected by paying penalty costs. As a result, we present a linear programming-rounding (LP-rounding) based 5.5122-approximation algorithm for the CUFLPSP.

Based on the retail inventory operation of Heilan Home, this study incorporates the price factor into inventory environment involving trapezoidal time-varying products. A joint pricing and ordering issue with deteriorating items under partial backlogged shortages is firstly explored in a fixed selling cycle. The corresponding optimization model aiming at maximizing profit performance of inventory system is developed, the theoretical analysis of solving the model is further provided, and the modelling frame generalizes some inventory models in the existing studies. Then, a solving algorithm for the model is designed to determine the optimal price, initial ordering quantity, shortage time point, and the maximum inventory level. Finally, numerical examples are presented to illustrate the model, and the results show the robustness of the proposed model.