Line Balancing in Parallel M/M/1 Lines and Loss Systems as Cooperative Games

Abstract

We consider production and service systems that consist of parallel lines of two types: (i) M/M/1 lines and (ii) lines that have no buffers (loss systems). Each line is assumed to be controlled by a dedicated supervisor. The management measures the effectiveness of the supervisors by the long run expected cost of their line. Unbalanced lines cause congestion and bottlenecks, large variation in output, unnecessary wastes and, ultimately, high operating costs. Thus, the supervisors are expected to join forces and reduce the cost of the whole system by applying line‐balancing techniques, possibly combined with either strategic outsourcing or capacity reduction practices. By solving appropriate mathematical programming formulations, the policy that minimizes the long run expected cost of each of the parallel‐lines system, is identified. The next question to be asked is how to allocate the new total cost of each system among the lines' supervisors so that the cooperation's stability is preserved. For that sake, we associate a cooperative game to each system and we investigate its core. We show that the cooperative games are reducible to market games and therefore they are totally balanced, that is, their core and the core of their subgames are non‐empty. For each game a core cost allocation based on competitive equilibrium prices is identified.

Pricing strategy and collusion in a market with delay sensitivity

“…Yu, Benjaafar, and Gerchak (2015) also examine the incentives to form coalitions in order to serve customers using pooled capacity. Anily and Haviv (2017) use cooperative game theory to study the challenge of balancing systems consisting of parallel lines. These authors identify the optimal policy to minimize the system's cost as well as the way to allocate this cost among the line supervisors to achieve cooperation.…”

Quality control for a detected an appropriate queue from K‐independent M/M/C/N queueing models

“…The main idea of this model is based on the collaboration between servers to reduce the overall congestion by redistributing the total service capacity between individual servers. There is another interesting idea presented by Anily and Haviv 27 . This idea is based on controlling the customer access by dividing the total flow of access between the servers.…”

“…There is another interesting idea presented by Anily and Haviv. 27 This idea is based on controlling the customer access by dividing the total flow of access between the servers.…”

Core Nonemptiness of Stratified Pooling Games: A Structured Markov Decision Process Approach

“…Another possible technique is the reformulation of our game to another game with a non-empty core. For instance, Anily and Haviv [3] use this technique: they show that their game can be transformed to a so-called market game (see, e.g., Osborne and Rubinstein [16]). In a market game, each player is associated with a set of resources and a continuous, convex utility function, identifying the amount of profit realized for the given set of resources.…”