基于“云排队”的经济效益分析

随着各种云智能排队预约系统的推出，顾客“排队难”的问题得到了极大的缓解。其简便的操作方式，受到了大量商家与顾客的好评。本文基于当下热门服务行业的运营模式，建立排队博弈模型，从理论上分析了“云排队”平台对顾客以及服务商的影响。本文主要得到了以下几个结果：(1) 给出了两类顾客的纳什均衡策略(包括进队策略与最优到达间隔)；(2) 发现当前的预约机制能够提高“线上”顾客的效用，并刺激更多的线上顾客购买该产品，但同时也降低了“线下”顾客的进队意愿；(3) 发现在云排队机制下服务商的收益将大大提高，同时该机制将刺激服务商收取更高的服务费用。     

Economic Manufacturing Quantity and Its Integrating Implications

Several contradictions are noted among the Economic Order Quantity (EOQ), Just‐In‐Time (JIT), and Optimized Production Technology (OPT) approaches and the economic framework for profit maximization. A fundamental model referred to as the Economic Manufacturing Quantity (EMO) is developed and examined for its integrating implications for the three approaches. An implication for the classic EOQ approach is that the balance between setup and inventory carrying costs is valid when a production facility is operating at or below a certain critical level but not when operating above that level. An implication for the JIT approach is that one must reduce setup cost at non‐bottlenecks and setup time at bottlenecks to reduce inventory. An implication for the OPT approach is that trade‐offs between setup and inventory carrying costs may indeed be ignored while determining process batch sizes, provided each facility in a production system is operating at or above Its critical level. Economic theoretic analysis of the EMO model provides a basis for unification of JIT which advocates stability in operating level as a key to improved productivity and quality, and OPT that advocates maximizing operating level with resultant emphasis on bottlenecks as a key to increased profits. This unifying basis states that a profit‐maximizing production facility or system will operate at the full and stable level as long as market demand remains relatively sensitive to price and operating at the full (maximum) level provides positive unit contribution.     

Optimal Control of Replenishment and Substitution in an Inventory System with Nonstationary Batch Demand

We study an inventory system in which a supplier supplies demand using two mutually substitutable products over a selling season of T periods, with a single replenishment opportunity at the beginning of the season. As the season starts, customer orders arrive in each period, for either type of products, following a nonstationary Poisson process with random batch sizes. The substitution model we consider combines the usual supplier‐driven and customer‐driven schemes, in that the supplier may choose to offer substitution, at a discount price, or may choose not to; whereas the customer may or may not accept the substitution when it is offered. The supplier's decisions are the supply and substitution rules in each period throughout the season, and the replenishment quantities for both products at the beginning of the season. With a stochastic dynamic programming formulation, we first prove the concavity of the value function, which facilitates the solution to the optimal replenishment quantities. We then show that the optimal substitution follows a threshold rule, and establish the monotonicity of the thresholds over time and with respect to key cost parameters. We also propose a heuristic exhaustive policy, and illustrate its performance through numerical examples.