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This article investigates methods for reallocation of service capacities in open Jackson networks in order to minimize either a system's mean total work-in-process or its response time. The focus is mainly on a method callednode generation, by which capacity can be transferred from a node in echelonjto a newly generated node in echelonj+ 1. The proposed procedure is compared with the more conventional capacity redistribution method, by which capacity can be transferred from any node in echelonjto existing successor nodes in echelonj+ 1. Formulation of each method as a mathematical programming problem reveals the structure of the optimal solution for both problems. The motivation for considering these approaches stems from real-life settings, in particular, from a production line or supply chains where the two types of capacity reallocation are applied. Heuristic methods are developed to solve relatively large networks in tractable time. Numerical results and analyses are presented. [ABSTRACT FROM PUBLISHER]

The risk of infection from the COVID-19 virus dictates businesses, such as supermarkets and department stores, to impose limits on the maximal number of customers allowed inside a store at any given time. These social distancing constraints generate long queues of waiting customers outside such businesses. This work investigates the impact of infection risk on arriving customers' strategic decisions regarding joining such queues. We consider a typical store where the floor is divided into two separate areas: (i) a shopping area with at most K shoppers allowed, and (ii) a payment area with c ≥ 1 parallel servers and an adjacent limited waiting space of size N ≥ 0. When the shopping area is full, a newly arriving customer observes only the outside queue and decides whether to join or balk. We investigate customers' individual joining strategies, as well as social optimization, with a utility function that takes into account not only the cost associated with waiting times (as in Naor's (1969) celebrated model), but also the cost related to the risk of infection. We propose an innovative risk measure that is a function of both the number of customers already in line, and those that a tagged customer 'meets' while waiting to enter the store. Consequently, expressions for mean waiting times and infection risk are derived and explicit formulas are obtained for limit values of the parameters. Our results can be used by authorities and customers alike to determine the maximal allowed queue sizes that ensure safety and reduce the risk of infection while minimizing associated costs. [ABSTRACT FROM AUTHOR]

The COVID-19 pandemic has forced numerous businesses such as department stores and supermarkets to limit the number of shoppers inside the store at any given time to minimize infection rates. We construct and analyze two models designed to optimize queue sizes and customer waiting times to ensure safety. In both models, customers arrive randomly at the store and, after receiving permission to enter, pass through two service phases: shopping and payment. Each customer spends a random period of time shopping (first phase) and then proceeds to the payment area of the store (second phase) where cashiers are assigned to serve customers. We propose a novel approach by which to calculate the risk of a customer being infected while queueing outside the store, while shopping, and while checking out with a cashier. The risk is proportional to the second factorial moment of the number of customers occupying the space in each phase of the shopping route. We derive equilibrium strategies for a Stackelberg game in which the authority acts as a leader who first chooses the maximum number of customers allowed inside the store to minimize the risk of infection. In the first model, store' management chooses the number of cashiers to provide to minimize its operational costs and its customers' implied waiting costs based on the number allowed in the store. In the second model, the store partitions its total space into two separate areas – one for shoppers and one for the cashiers and payers – to increase cashiers' safety. Our findings and analysis are useful and applicable for authorities and businesses alike in their efforts to protect both customers and employees while reducing associated costs. [ABSTRACT FROM AUTHOR]