Joint Replenishment Research Articles

Probabilistic Multi-Item Inventory Model for Chemicals in Regional Drinking Water Company

Inventory management of chemicals in The Regional Drinking Water Company (Perusahaan Daerah Air Minum, PDAM) is known to play an essential role in ensuring the smooth production of clean water and preventing shortages of chemicals that can affect production. At present, 2 primary models for multi-item inventory replenishment are under consideration by PDAM, namely individual and joint replenishment of items. Therefore, this study aims to evaluate the efficiency and effectiveness of individual and joint replenishment models based on uncertain demand with specific probability distribution. The results showed that a probabilistic inventory model (Q, r) with individual replenishment for chemicals in PDAM was recommended.

The Continuous-Time Joint Replenishment Problem: ϵ-Optimal Policies via Pairwise Alignment

The main contribution of this paper resides in developing a new algorithmic approach for addressing the continuous-time joint replenishment problem, termed [Formula: see text]-pairwise alignment. The latter mechanism, through which we synchronize multiple economic order quantity models, allows us to devise a purely combinatorial algorithm for efficiently approximating optimal policies within any degree of accuracy. As a result, our work constitutes the first quantitative improvement over power-of-2 policies, which have been state-of-the-art in this context since the mid-1980s. Moreover, in light of recent intractability results, by proposing an efficient polynomial-time approximation scheme for the joint replenishment problem, we resolve the long-standing open question regarding the computational complexity of this classical setting. This paper was accepted by Chung Piaw Teo, optimization. Funding: This work was supported by the Israel Science Foundation [Grant 1407/20].

A matheuristic for the joint replenishment problem with and without resource constraints

A matheuristic for the joint replenishment problem with and without resource constraints

Multi-retailer joint replenishment problem under different carbon regulation policies

ABSTRACT This paper considers a coalition of retailers who are engaged in a horizontal collaboration, pooling their orders for a single item from a mutually shared supplier. Simultaneously, it explores the impact of carbon cap and carbon tax policies on the coalition’s operations. A mathematical model for the carbon cap constrained joint replenishment problem (JRP) is developed along with a computationally efficient solution algorithm. An extensive numerical analysis is conducted to investigate the impact of the carbon cap on the operational and environmental performance of JRP solutions. Several managerial insights are obtained which shed some light on the trade-offs involved upon integrating environmental aspects. The numerical experiments illustrate that by making minor adjustments to their operational strategies, substantial reductions in carbon emissions are achievable. Furthermore, the computational experiments consistently demonstrate the superiority of the carbon cap policy over its carbon tax counterpart. This emphasises the potential for retailers to make environmentally responsible choices without significantly compromising their financial performance.

Multi-item stochastic inventory model for deteriorating items with power demand pattern under partial backlogging and joint replenishment

Multi-item stochastic inventory model for deteriorating items with power demand pattern under partial backlogging and joint replenishment

Managing Replenishment and Clearance of Perishables: Last-In, First-Out (LIFO) Issuing Policy and Age-Sensitive Demand

In supermarkets, customers choose the unit(s) they purchase, which leads to inventory being sold in a last-in, first-out (LIFO) order for perishable products. Furthermore, for such products, the demand for inventory may depend on its age since customers may choose to walk away if the freshest available inventory is too old for them. Despite the widespread occurrence of LIFO-based inventory systems, few studies have analyzed them. In this study, we contribute by developing insights on joint replenishment and clearance policy for a perishable product with a general, finite lifetime using a periodic review model such that the inventory is sold in a LIFO order and demand is age-dependent. The model seeks to optimize two decisions every period: how much of fresh inventory to order and how much of existing inventory to clear. A key objective of the model is to understand the effect of age-dependence of demand on the optimal replenishment and clearance policy. We find that the optimal clearance policy for all but the oldest inventory is a multiindex policy such that between any pair of adjacent indexes, either no inventory is cleared or all the inventory is cleared till the lower index. For the oldest inventory, we show that the optimal policy may have multiple forms depending on how sensitive demand is to inventory’s age. This is a notable result in inventory theory since parameters usually affect only the policy value(s) and not the policy structure. Since the optimal policy has a complex structure in general, which makes it difficult to compute, we develop an efficient heuristic to compute the replenishment and clearance quantities. The heuristic underperforms the optimal policy by [Formula: see text]0.92% on average.

Synthesis of Research on Joint Replenishment Problems and Cost Sharing

Among all existing inventory replenishment models, this research was dedicated to the Joint Replenishment Problem (JRP), which consists in the replenishment of multiple items simultaneously, aiming total cost reduction. Literature has presented several optimal and approximated solutions to this problem, with different applications and techniques, which results in a large quantity of solution proposals. Therefore, This paper organizes the related concepts and model studies of joint replenishment problem, and collects the solution algorithms of joint replenishment problem in different contexts, which provides reference for the research trend of joint replenishment afterwards. The cost sharing problem arising from the joint replenishment problem is also studied in the relevant literature to provide reference for the subsequent design of cost sharing rules.

Integration of sales, inventory, and transportation resource planning by dynamic-demand joint replenishment problem with time-varying costs

This paper addresses the joint replenishment problem in the context of sales and operations planning. Unlike traditional ones that assume static demands, unit costs, and transportation capacity, we consider dynamic-deterministic demands from sales plans and time-varying unit costs and transportation capacity to deal with the recent logistics conditions. We then introduce the capacitated dynamic-demand joint replenishment problem with time-varying costs. To efficiently solve this problem, a three-phase approach is proposed: (1) simplifying the problem and determining ideal inventory quantities using mixed integer linear programming, (2) estimating policy variables for each item using the covariance matrix adaptation evolution strategy, and (3) updating the ideal inventory quantities based on evaluated shortages until all demands are satisfied. Our method outperforms conventional approaches with at least 12 times faster solution runtimes in tests with up to 100 items. We also obtain the insight that the cost-efficient replenishment plan changes according to the increase rate of the unit transportation cost.

Integrated multi-product, multi-level supply chain inventory model with joint replenishment and loss sharing

Integrated multi-product, multi-level supply chain inventory model with joint replenishment and loss sharing

An optimal integrated inventory management for vendor-buyer with substitutable deteriorating product under joint replenishment and cost of substitution

An optimal integrated inventory management for vendor-buyer with substitutable deteriorating product under joint replenishment and cost of substitution

Integrated Multi-Product, Multi-Level Supply Chain Inventory Model with Joint Replenishment and Loss Sharing

Integrated Multi-Product, Multi-Level Supply Chain Inventory Model with Joint Replenishment and Loss Sharing

Incorporating transportation costs into the single and multiple items newsvendor problems.

The efficiency and responsiveness of supply chains are vitally dependent on inventory replenishment and transportation decisions. In this paper, we study a supply chain consisting of a single retailer ordering seasonal products within the newsvendor framework. The primary objective of the paper is to investigate the retailer's decision-making process, aimed at determining the optimal replenishment quantities and selecting the appropriate mix and size of the truck fleet. Initially, we formulate a mathematical model where the retailer exclusively manages a limited fleet of its own trucks for inbound transportation of a single seasonal product. In this context, we determine a lower breakeven point for the fixed transportation cost than what has been previously proposed in the literature. Subsequently, we examine a commonly encountered transportation scenario where the retailer has the opportunity to expand its fleet size by leasing trucks from the external market. The outcomes of the numerical example indicates that the flexibility resulting from the utilization of different types of trucks can lead to reduced overall costs. We also address the practical transportation problem of efficiently shipping various seasonal products solely with the retailer's own trucks. For this complex problem, we propose an optimal solution procedure based on Lagrangian method. We show that the joint replenishment of multiple products results in cost savings and enhances utilization of the trucks' capacities.

Modeling and Solving the Joint Replenishment Problem with Cross-Selling Effects Considering One Shared Minor Item

In this paper, we provide a model to handle multiple replenishment cycles and the cross-selling of multiple major items with one minor item, while allowing partial late delivery. The optimization analytic expression of the model is finally obtained by utilizing the convexity of cost function for F and using the first-order conditions in optimization theory. Numerical examples and sensitivity analysis demonstrate the effectiveness of the model and algorithm, which offers a competent solution for practical applications.

A decision making framework for joint replenishment and delivery scheduling problems under mixed uncertainty

Concerning the essence of risk, a joint replenishment and delivery scheduling problem with fuzzy cost-related parameters and random number of imperfect quality items is developed to make it suitable for the inherent uncertainties of procurement-shipment process. The mathematical modelling-based decision system is formulated as a chance-constrained programming with the idea of embedding decision makers’ risk tolerance. Following this notion, the model is translated into an equivalent non-linear counterpart and a neighbourhood heuristic search is designed based on the properties of the cost function. We introduce an integrated cross-entropy algorithm, incorporating the heuristic in the cross-entropy framework, to solve it. The numerical results demonstrate that ICE is quite effective in comparison to state-of-the-art algorithms. Our framework is helpful for decision makers to determine economically acceptable performance objectives in the presence of uncertain issues, and thus to build resilience in supply chain.

Analisis Pengendalian Persediaan Bahan Baku Serbuk Warna dengan Pendekatan Periodic Review Joint Replenishment untuk Sistem Persediaan Stokastik di PT XYZ

PT XYZ is a manufacturing company engaged in the manufacture of extruded aluminum profile products. The problem experienced by PT XYZ is that the company often orders several types of color powder raw materials separately even though they come from the same supplier. This causes more frequent orders to be made. The company also sometimes experiences shortages and excess stock of color powder raw materials which can cause swelling of the company's inven-tory costs. The purpose of this study is to determine the optimal inventory control of color pow-der raw materials to minimize the company's total inventory costs. This research was conducted using a probabilistic model approach with the periodic review joint replenishment method. This method is carried out with a periodic review (p) model, ordering raw materials will be carried out in combination every certain time interval. The calculation results obtained the minimum total inventory cost is with the Periodic Review Joint Replenishment method of Rp 19.519.552.589,- compared to the company method of Rp 19.670.799.095,-. Thus, a savings of Rp 151.246.506 is obtained, or a savings percentage of 0.8%. Forecasting for the period November 2023 - October 2024, the value of the order time interval is obtained every 15 working days with the inven-tory level of each raw material is for white powder of 22.336 kg, brown powder of 12.413 kg, black powder of 8.290 kg, and milk white powder of 1.882 kg with a total inventory cost of color powder raw materials of Rp 19.559.415.435.

OBRUN algorithm for the capacity-constrained joint replenishment and delivery problem with trade credits

OBRUN algorithm for the capacity-constrained joint replenishment and delivery problem with trade credits

A decomposition and coordination method for optimising (Q, S ) policies in a two-echelon distribution system with joint replenishment

A continuous-review, two-echelon distribution system with one central distribution centre (CDC) and multiple regional distribution centres (RDCs) is studied. The CDC jointly replenishes its inventories of multiple items from an external supplier, while each RDC replenishes its inventories of the items from the CDC. Each RDC faces a Poisson demand for each item, and the inventories of each stock in the system are controlled by a (Q, S ) policy. Under this policy, an order is placed by a stock whenever its aggregate demand since the last order reaches a given quantity, and the inventory position of each item is raised up to its order-up-to level after the order placement. The objective is to optimise these (Q, S ) policies so that the expected total cost of this system is minimised. We propose a decomposition and coordination method for this optimisation after deriving analytically the cost function of the system. Our extensive numerical experiments demonstrate the effectiveness of the proposed method. Furthermore, a parameter sensitivity analysis is conducted to analyse the impacts of some key system parameters on the performance of the method, and managerial insights are provided for optimising distribution systems with joint replenishment and real applications of the method.

Response strategies for coping with imperfect items of a joint replenishment model with the adaptive bare-bone differential evolution

In joint replenishment problem with random number of imperfect items (IJRP), it is a great challenge for managers to correctly ascertain the number of imperfect items and take the right response strategy to make rectifications simultaneously. In this paper, the effectiveness of four common response strategies, i.e., scrap, all-unit quantity discount, rework & repair, and buy replacements for coping with imperfect items are investigated based on IJRP for the first time, respectively. Considering the NP-hard nature of the classical JRP and its extensions, as well as enhancing the explorable performance in crossing scale-levels of IJRP models and exploitable performance in diversifying the solution population of bare-bones differential evolutionary (BBDE), a meta-heuristic algorithm named as the adaptive BBDE (ABBDE) is designed by introducing an problem scale related adaptive recombination probability and a generalized opposition-based learning (OBL). Through numerical experiments, it has been found that (1) The adaptive improvements of ABBDE have been verified through obtaining the lower best-found total cost (TC), the lowest mean value, and the smallest standard error comparing to that of genetic evolution algorithm (GA), particle swarm optimization (PSO), differential evolution (DE), bare-bones PSO (BBPSO), BBDE. (2) Parameter sensitivity analyses indicate that the scale of yearly demand, lead-time, and significance of uncertainty have significant impacts on system cost, whilst the parameters pertinent to specific response strategy are main factors causing system cost disturbance. (3) Management insights and limitations on adoption of a right response strategy and the practical usage of ABBDE are obtained.

Multi-tank joint replenishment problem with overlapping time windows in refined oil distribution

Multi-tank joint replenishment problem with overlapping time windows in refined oil distribution

An online joint replenishment problem combined with single machine scheduling

This paper considers a combination of the joint replenishment problem with single machine scheduling. There is a single resource, which is required by all the unit-time jobs, and a job can be started at time point t on the machine if and only if the machine does not process another job at t, and the resource is replenished between its release date and t. Each replenishment has a cost, which is independent of the amount replenished. The objective is to minimize the total replenishment cost plus the maximum flow time of the jobs. We consider the online variant of the problem, where the jobs are released over time, and once a job is inserted into the schedule, its starting time cannot be changed. We propose a deterministic 2-competitive online algorithm for the general input. Moreover, we show that for a certain class of inputs (so-called p-bounded input), the competitive ratio of the algorithm tends to sqrt{2} as the number of jobs tends to infinity. We also derive several lower bounds for the best competitive ratio of any deterministic online algorithm under various assumptions.