An efficient optimal solution method for the joint replenishment problem with minimum order quantities

Abstract

We study the joint replenishment problem (JRP) for M items under deterministic demand, with a minimum order quantity constraint for each item in the replenishment order. We first study an iterative procedure that proves to be not efficient in this case. Further, we derive bounds on the basic cycle time and propose an efficient global optimisation procedure to solve the JRP with constraints. Moreover, we also consider the case where a correction is made for empty replenishment occasions. The algorithms are tested in a real case.

Synchronization in the single-manufacturer multi-buyer integrated inventory supply chain

“…Although others have studied the JRP considerably (cf. Hoque (2006), Chan et al (2006), Bayindir et al (2006), Porras and Dekker (2006), Moon and Cha (2006) for detail), they neglected vendor set-up and inventory costs, which were however considered by Joglekar and Tharthare (1990), Lu (1995) and Viswanathan and Piplani (2001). Although it may be assumed that the system benefits generated by a joint economic lot size policy can be shared among the buyer(s) and the seller in a costless way, Joglekar and Tharthare (1990) argued that negotiated benefit sharing is never costless.…”

A systematic literature review on the joint replenishment problem solutions: 2006-2015

“…Furthermore, there has been a trend in solving practical problems by considering additional situations such as capacity and resource constraints, in Hoque (2006); Porras & Dekker (2006), Wang & Cheng (2008), Amaya et al (2013), Li et al (2015). Studies of Zhang et al (2011Zhang et al ( , 2012 and Zhang (2012) presented the replenishment of a main individual item and its complementary products whose demand is correlated to the former.…”

“…By means of experiments in simulation, it was observed that the IGS was more efficient than the DGS when the ratio major/minor ordering costs was high, and the DGS presented better results mostly in computational time when the ratio was lower (Olsen, 2005;Porras & Dekker, 2006;Khouja & Goyal, 2008).…”

An O(T3) algorithm for the capacitated lot sizing problem with minimum order quantities

“…Only if these two conditions are fulfilled, do we solve SP it by means of algorithm (13) and remember the beginning of the sub-problem and its optimal switching period. In fact, we do not need to perform step 8 of the algorithm (13) in every iteration of the algorithm (14). It may happen that the solution found until now is sub-optimal and would be outperformed in some further iterations.…”

“…The MOQ constraint plays the role of minor set-up cost (Anderson and Cheah, 1993) and specifies that in every period one can produce either nothing or at least as much as MOQ. Such problems arise in an industrial context where, in order to derive an optimal production plan, production managers prefer to use a minimum lot size restriction instead of specifying a fixed set-up costs, which are difficult to determine for individual product lines (Porras and Dekker, 2006). In such a way, the managers strive to achieve economies of scale (Zhou et al, 2007) and guarantee full utilization of resources (Constantino, 1998).…”