Unitary Owen Points in Cooperative Lot-Sizing Models with Backlogging

This paper analyzes cost sharing in uncapacitated lot-sizing models with backlogging and heterogeneous costs. It is assumed that several firms participate in a consortium aiming at satisfying their demand over the planning horizon with minimal operating cost. Each individual firm has its own ordering channel and holding technology, but cooperation with other firms consists in sharing that information. Therefore, the firms that cooperate can use the best ordering channels and holding technology among members of the consortium. This mode of cooperation is stable. in that allocations of the overall operating cost exist, so that no group of agents benefit from leaving the consortium. Our contribution in the current paper is to present a new family of cost sharing allocations with good properties for enforcing cooperation: the unitary Owen points. Necessary and sufficient conditions are provided for the unitary Owen points to belong to the core of the cooperative game. In addition, we provide empirical evidence, through simulation, showing that, in randomly-generated situations, the above condition is fulfilled in 99% of the cases. Additionally, a relationship between lot-sizing games and a certain family of production-inventory games, through Owen’s points of the latter, is described. This interesting relationship enables easily constructing a variety of coalitionally stable allocations for cooperative lot-sizing models.The research authors is supported from Spain’s Ministerio de Ciencia, Innovación y Universidades (MCIU), from the Agencia Estatal de Investigación (AEI) and from the Fondo Europeo de Desarrollo Regional (FEDER) under the projects MTM2016-74983-C02-01 and PGC2018-097965-B-I00. The research of the third author is also partially supported from projects FEDER-US-1256951, CEI-3-FQM331 and NetmeetData: Ayudas Fundación BBVA a equipos de investigación científica 2019

From Cost Sharing Mechanisms to Online Selection Problems

We consider a general class of online optimization problems, called online selection problems, where customers arrive sequentially, and one has to decide upon arrival whether to accept or reject each customer. If a customer is rejected, then a rejection cost is incurred. The accepted customers are served with minimum possible cost, either online or after all customers have arrived. The goal is to minimize the total production costs for the accepted customers plus the rejection costs for the rejected customers. These selection problems are related to online variants of offline prize collecting combinatorial optimization problems that have been widely studied in the computer science literature. In this paper, we provide a general framework to develop online algorithms for this class of selection problems. In essence, the algorithmic framework leverages any cost sharing mechanism with certain properties into a poly-logarithmic competitive online algorithm for the respective problem; the competitive ratios are shown to be near-optimal. We believe that the general and transparent connection we establish between cost sharing mechanisms and online algorithms could lead to additional online algorithms for problems beyond the ones studied in this paper.National Science Foundation (U.S.) (CAREER Award CMMI-0846554)United States. Air Force Office of Scientific Research (FA9550-11-1-0150)United States. Air Force Office of Scientific Research (FA9550-08-1-0369)Solomon Buchsbaum AT&T Research Fun

The linear dynamic lot size problem with minimum order quantities

This paper continues the analysis of a special uncapacitated single item lot sizing problem where a minimum order quantity restriction, instead of the setup cost, guarantees a certain level of production lots. A detailed analysis of the model and an investigation of the particularities of the cumulative demand structure allowed us to develop a solution algorithm based on the concept of minimal sub-problems. We present an optimal solution to a minimal sub-problem in an explicit form and prove that it serves as a construction block for the optimal solution of the initial problem. The computational tests and the comparison with the published algorithm confirm the efficiency of the solution algorithm developed here. --lot sizing problem,minimum order quantity,dynamic programming

Mitigating the Cost of Anarchy in Supply Chain Systems

In a decentralized two-stage supply chain where a supplier serves a retailer who, in turn, serves end customers, operations decisions based on local incentives often lead to suboptimal system performance. Operating decisions based on local incentives may in such cases lead to a degree of system disorder or anarchy, wherein one party's decisions put the other party and/or the system at a disadvantage. While models and mechanisms for such problem classes have been considered in the literature, little work to date has considered such problems under nonstationary demands and fixed replenishment order costs. This paper models such two-stage problems as a class of Stackelberg games where the supplier announces a set of time-phased ordering costs to the retailer over a discrete time horizon of finite length, and the retailer then creates an order plan, which then serves as the supplier's demand. We provide metrics for characterizing the degree of efficiency (and anarchy) associated with a solution, and provide a set of easily understood and implemented mechanisms that can increase this efficiency and reduce the negative impacts of anarchic decisions

The impact of freight transport capacity limitations on supply chain dynamics

We investigate how capacity limitations in the transportation system affect the dynamic behaviour of supply chains. We are interested in the more recently defined, 'backlash' effect. Using a system dynamics simulation approach, we replicate the well-known Beer Game supply chain for different transport capacity management scenarios. The results indicate that transport capacity limitations negatively impact on inventory and backlog costs, although there is a positive impact on the 'backlash' effect. We show that it is possible for both backlog and inventory to simultaneous occur, a situation which does not arise with the uncapacitated scenario. A vertical collaborative approach to transport provision is able to overcome such a trade-off. © 2013 Taylor & Francis

Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review

[EN] The increase in the complexity of supply chains requires greater efforts to align the activities of all its members in order to improve the creation of value of their products or services offered to customers. In general, the information is asymmetric; each member has its own objective and limitations that may be in conflict with other members. Operations managements face the challenge of coordinating activities in such a way that the supply chain as a whole remains competitive, while each member improves by cooperating. This document aims to offer a systematic review of the collaborative planning in the last decade on the mechanisms of coordination in mathematical programming models that allow us to position existing concepts and identify areas where more research is needed.Rius-Sorolla, G.; Maheut, J.; Estelles Miguel, S.; García Sabater, JP. (2020). Coordination mechanisms with mathematical programming models for decentralized decision-making, a literature review. 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