Cooperative lot sizing with transshipments and scarce capacities: solutions and fair cost allocations

Abstract

In this article, we study the cooperative capacitated lot sizing problem where the available resources of the players may be used in common and payable transshipments may take place to transport items from one player to the other. Two research questions are attacked. On the one hand, there is the hard-to-solve optimisation problem of deciding which player shall produce what amount of items at what point of time, how many items shall be kept in stock when, and when transport of what quantities shall take place among which players. The objective is to minimise the total cost of the supply chain taking into account thorny side constraints due to capacity limits. On the other hand, there is the hard-to-solve problem of distributing cost shares among the players such that the cost allocation is stable and fair. Both questions are discussed in detail and answers are given by proposing mathematical programming approaches.

Analysis of collaborative savings and cost allocation techniques for the cooperative carrier facility location problem

“…To compensate for this shortcoming, several extensions have been developed which relax inequalities that define the core. Examples are the least core (Drechsel and Kimms, 2010) and the minmax core (Drechsel and Kimms, 2011). In relation to this core, the excess can be computed for each coalition .…”

Pooling of critical, low-utilization resources with unavailability

“…Availability games are mostly overlapping with the last category. Recent publications in this category focus on economic order quantity situations (Meca et al 2004), economic lot sizing situations (Van Heuvel et al 2007;Drechsel and Kimms 2011), newsvendor situations (Özen et al 2008), truckload delivery situations (Hezarkhani et al 2016;Li et al 2016) and spare parts situations (Karsten et al 2012;Karsten and Basten 2014;Karsten et al 2015). Recently, Bachrach et al (2011Bachrach et al ( , 2012Bachrach et al ( , 2013 introduced and investigated a new class of operations research games, called cooperative reliability games, which comes closer to our work.…”

The subcoalition-perfect core of cooperative games

“…• the capacitated lot sizing problem, see Drechsel and Kimms (2008), and • the newsvendor model, see Zhang (2009), Dror et al (2008), Hartman et al (2000), Hartman and Dror (2005), Müller et al (2002), Özen et al (2008), and Slikker et al (2001).…”

“…A scenario where a cooperative game occurs and the characteristic function is not monotone is described by Drechsel and Kimms (2008). They consider a cooperative lot sizing problem where players may produce items in order to meet some known (or estimated) demand.…”

“…They consider a cooperative lot sizing problem where players may produce items in order to meet some known (or estimated) demand. The problem considered by Drechsel and Kimms (2008) is an extension of the well-known capacitated lot sizing problem (CLSP, see e.g. Billington et al 1983).…”