Offsetting inventory replenishment cycles to minimize storage space

Boctor, Fayez F.

doi:10.1016/j.ejor.2009.07.035

Cited by 14 publications

(6 citation statements)

References 14 publications

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“…Studies of multi-cycle RSP with more than two items have been focused on the development of heuristics. These include genetic algorithms (Moon et al 2008, Yao and, a smoothing procedure utilizing a Boltzmann function , local search procedures (Croot and Huang 2013), a simulated annealing algorithm (Boctor 2010), hybrid heuristics (Boctor 2010, Russell andUrban 2016), and an evolutionary algorithm (Boctor and Bolduc 2015). None of these heuristics were shown to deliver a guaranteed approximation bound.…”

Section: Literature Reviewmentioning

confidence: 99%

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The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

Rao

2019

Operations Research

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The replenishment storage problem (RSP) is to minimize the storage capacity requirement for a deterministic demand, multi-item inventory system, where each item has a given reorder size and cycle length. We consider the discrete RSP, where reorders can only take place at an integer time unit within the cycle. Discrete RSP was shown to be NPhard for constant joint cycle length (the least common multiple of the length of all individual cycles). We show here that discrete RSP is weakly NP-hard for constant joint cycle length and prove that it is strongly NP-hard for nonconstant joint cycle length. For constant joint cycle-length discrete RSP, we further present a pseudopolynomial time algorithm that solves the problem optimally and the first known fully polynomial time approximation scheme (FPTAS) for the single-cycle RSP. The scheme is utilizing a new integer programming formulation of the problem that is introduced here. For the strongly NP-hard RSP with nonconstant joint cycle length, we provide a polynomial time approximation scheme (PTAS), which for any fixed , provides a linear time approximate solution. The continuous RSP, where reorders can take place at any time within a cycle, seems (with our results) to be easier than the respective discrete problem. We narrow the previously known complexity gap between the continuous and discrete versions of RSP for the multi-cycle RSP (with either constant or nonconstant cycle length) and the single-cycle RSP with constant cycle length and widen the gap for single-cycle RSP with nonconstant cycle length. For the multi-cycle case and constant joint cycle length, the complexity status of continuous RSP is open, whereas it is proved here that the discrete RSP is weakly NP-hard. Under our conjecture that the continuous RSP is easier than the discrete one, this implies that continuous RSP on multi-cycle and constant joint cycle length (currently of unknown complexity status) is at most weakly NP-hard.

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Section: Literature Reviewmentioning

confidence: 99%

“…The standard integer programming formulation is as follows. A straightforward formulation of RSP was used in previous studies, including Murthy et al (2003), Boctor (2010), and Russell and Urban (2016). Let the binary variables y ij be y ij 1 if item i is ordered at time j,…”

Section: Preliminaries and Integer Programming Formulationsmentioning

confidence: 99%

The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

Rao

2019

Operations Research

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“…The underlying idea in this stream of research is to stagger the timing of procurement of the various items so that they (roughly) complement each other vis-à-vis use of the available space or budget. For examples, see Boctor (2010) and references therein.…”

Section: Literature Reviewmentioning

confidence: 99%

Cheaper by the pallet? Multi-item procurement with standard batch sizes

2012

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This research was motivated by challenges facing inventory managers at a major retail chain in deciding how often to order each product and whether to use a standard batch size of a pallet, a half-pallet, or even less. The retailer offers thousands of different products, but the total demand for a typical product is only a few pallets per year. Manufacturers offer lower per unit prices for larger standard batch sizes, but larger order quantities increase inventory holding costs. The inventory managers are also concerned about how the ordering strategy might affect transportation costs and material handling costs at the warehouse.We develop a framework and solution strategy to determine the best shipment frequency, standard batch size (from a set of options), and an ordering plan for a set of products procured from a single supply location. To do so, the inventory holding and material handling costs incurred by a single product are derived for a given review interval and standard batch size. We incorporate the individual product costs into an optimization model to find, for a given transportation interval (with a limit on transport capacity for each shipment), the best procurement plan considering variable procurement, inventory, material handling, and excess transportation costs. With this, several transportation intervals can be compared and the best one selected. To the best of our knowledge, this work is the first to consider the effects of transportation capacity and standard batch sizes in a multi-item procurement problem with the goal of minimizing transportation, inventory, and material handling costs. larger standard batch sizes. On the other hand, larger order quantities increase inventory holding costs. If items were ordered in full pallet quantities, average inventory levels might amount to months of supply. Under such policies, it was difficult to improve inventory turnover.The inventory managers also had the perception that larger order quantities led to greater material handling costs. In view of this, we decided to include the most significant elements of the material handling costs in our model. We elaborate on these costs later in this article.The standard batch size also affects variable purchasing costs. Retailers typically negotiate prices with suppliers on the basis of annual sales volume and standard procurement quantities. If the retailer does not always order exactly the same quantity (e.g., sometimes half pallets and sometimes full pallets), the actual purchase costs may depend upon the mix of quantities. Quite often, the manufacturer's pricing is driven by volume and the minimum purchase quantity. As such, we initially assume that the retailer simply orders standard batch quantities (usually one at a time

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“…They provide an optimal solution procedure in a companion paper (Thomas and Hartley, 1983). Murthy et al (2003) and Boctor (2010) consider the problem of offsetting the replenishment cycles by integer multiples of some base period, and use the result that, if the integer multiples of two items are not relatively prime, it is possible to offset their cycles such that the peaks of their inventory cycles never coincide over an infinite time horizon. Murthy et al propose a heuristic for this framework, which is improved by Boctor.…”

Section: Introductionmentioning

confidence: 99%

Two-product storage-capacitated inventory systems: A technical note

Beemsterboer

Teunter²,

Riezebos

2016

International Journal of Production Economics

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This paper considers a two-product inventory model with limited storage capacity and constant demand rates. We aim at finding an ordering policy that minimizes the cost per time unit. In the literature, several solution methods have been developed for this problem, but these are limited to very restrictive classes of policies. We consider a much more general class where the order quantity of one of the products is allowed to vary. These policies are still cyclic and easy to implement. Closed-form expressions are derived for determining the optimal order quantities. It is shown that savings of up to 25% are possible compared to existing approaches.

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Offsetting inventory replenishment cycles to minimize storage space

Cited by 14 publications

References 14 publications

The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

The Replenishment Schedule to Minimize Peak Storage Problem: The Gap Between the Continuous and Discrete Versions of the Problem

Cheaper by the pallet? Multi-item procurement with standard batch sizes

Two-product storage-capacitated inventory systems: A technical note

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