Joint Replenishment Research Articles

Heuristic approaches for a two-echelon constrained joint replenishment and delivery problem

This paper addresses the optimization of the total cost for an inventory and distribution system which consists of a Distribution Center (DC), multiple retailers, and multiple items. The problem known as constrained 1-warehouse, N-Retailers, with multiple item inventory systems (C-OWNRMI), additionally considers budgetary and storage capacity constraints. The former limits the amount of inventory that can be held at any moment at the DC. Similarly, capacity constraints at retailers’ facilities restrict the number of items which may be delivered and stored at each retailer location. Although several authors have proposed various approaches for solving the problem in a multi-item scenario, they often consider only one item to be sold and delivered by each retailer. This study, in contrast, considers multiple items to be sold and delivered by all retailers. Further, herein, orders are placed in a coordinated manner. The main objective of this research was to identify cost-efficient solutions for the inventory system under study. With this goal, we proposed a hybrid mat-heuristic that combines the search strategy and mixed-integer programming. Furthermore, a memetic algorithm (MA) is introduced, which includes a local search operator that exploits certain mathematical properties derived from the problem. The results suggest that both approaches are appropriate for resolution of this problem. However, the hybrid method often leads to better quality solutions than those obtained with the memetic algorithm.

Inventory and fleet purchase decisions under a sustainable regulatory environment

ABSTRACTThis work studies the direct impacts of environmental policies on logistics practices. Specifically, the authors estimate the potential changes in inventory and fleet purchase decisions under a set of policies designed to improve the environmental efficiency of transport activities, through a reduction of overall transportation emissions; and requirements for a fleet mix to include zero and near-zero emission vehicle technologies, or, minimum vehicle type shares. The work introduces a constrained stochastic multi-objective joint replenishment problem (S-MJRP) to evaluate the policies while considering logistics costs and emissions as objectives. Moreover, the authors developed a solution algorithm and conducted empirical analyses. The results highlight the trade-off between capital investments in zero-emission vehicles and the logistics costs required to abide by the requirements of the mentioned regulatory policies. The results provide insights for both private and public stakeholders as they consider the logistics challenges and opportunities generated by these sustainability policies.

A joint replenishment supply model for multi-products grouped by several variables with random and time dependence demand

Purpose This paper aims to propose a supply model of periodic review with joint replenishment for multi-products grouped by several variables with random and time dependence demand. Design/methodology/approach The products are grouped by multivariate cluster analysis. The stochastic inventory model describes the random demand of each product, considering the temporal dependency through a generalized autoregressive moving average model. Stochastic programming for the total cost of inventory is obtained considering the expected value of the demand per unit of time. Findings The total costs for the products grouped with the proposed model are 6% lower than for the individual inventory policy. The expected shortage units decrease significantly in the proposed grouped model with temporary dependence. In addition, the proposal with temporary dependency has lower costs than when the independent and identically distributed demand is considered. Originality/value The proposed policy is exemplified with real-world data from a Chilean hospital, where the products (drugs) are segmented by grouping variables, forming clusters of drugs with homogeneous behavior within the groups and heterogeneous behavior between groups.

Bi-objective optimization of the joint replenishment problem in a two-echelon supply chain

In this research, a bi-objective optimisation model for the joint replenishment problem (JRP) of a supply chain comprised of a single supplier and multiple retailers is developed, in which the retailers are assumed to be members of a unique distribution company. The mathematical model minimises the supplier's as well as the retailers' cost subject to some constraints. The constraints are the required storage spaces for any retailer, for any product, and for all the products. The benefit of using the JRP policy is shown based on minimising total cost of supplier and retailers. Since the developed model of the problem is NP-hard, the multi-objective meta-heuristic optimisation algorithm of non-dominated sorting genetic algorithm-II (NSGA-II) is proposed to solve the problem. Besides, since no benchmark is available in the literature to verify and validate the results obtained, a non-dominated ranking genetic algorithm (NRGA) is suggested to solve the problem as well. For further validation, the Pareto fronts are compared to lower and upper bounds obtained using a genetic algorithm employed to solve two single-objective problems separately.

A Stochastic Joint Replenishment Problem with Dissimilar Items

ABSTRACTThe classical stochastic joint replenishment problem (SJRP) often assumes uncapacitated batch size, and identical items. However, real problems encountered relate to the truck , or the container which has limited capacity. When the shipping capacity is limited, and the items are dissimilar in size, the problem becomes more challenging. By defining a class of order‐up‐to policies, we formulate the SJRP of this kind as a combinatorial optimization problem. To solve the problem, a data structure and an algorithm are developed. Based on the algorithm, we also suggest several heuristics including the (U, S) policy—a generalization of the well‐known (Q, S) policy for dissimilar items. The numerical study shows the (U, S) policy is robust and efficient. It performs well, especially when the items become more dissimilar, in terms of shipping size and inventory velocity.

Optimal replenishment policy for multi-item probabilistic inventory model with all-units discount

In this paper, we develop a multi item inventory model for the retailer by considering all-units discount offered by the supplier. Demands in this model are assumed to be probabilistic following a Gamma distribution with certain values of shape and scale parameters. The aim of the model is to determine the optimal replenishment policy that minimize the total inventory cost. The total inventory cost was composed from the purchasing, ordering, handling or storing and shortage costs. All shortages are handled by backorder. We compare the individual and joint replenishment policies for the model and develop an algorithm to find the optimal replenishment policy. Numerical examples are given to give a better understanding of the model in comparing the individual and joint replenishment policies. We also perform sensitivity analysis by changing values of shape and scale parameters of the demand distribution to analyse the effects on the optimal solution.

Joint replenishment and carbon trading in fresh food supply chains

We investigate a fresh food supply chain comprising a large-scale supplier and multiple small-scale retailers under a carbon cap-and-trade policy. Retailers' joint replenishment and the carbon trading behavior of supply chain members are studied. We assume that three replenishment strategies are available for the supply chain: (1) separate replenishment; (2) joint replenishment: a leader-follower relationship among retailers; and (3) joint replenishment: the coalition of retailers. Under each strategy, a bargaining framework for supply chain members is set up to maximize their profits, where the price of the refrigerated transportation services provided by the supplier and the retail price of fresh food are optimized. The optimal decisions are analyzed to provide insights into logistics pricing and retail pricing strategies. Through comparing three replenishment strategies, we also identify the optimal replenishment strategies from the perspectives of the supplier, retailers and a carbon emission optimizer. Moreover, we investigate the role of the carbon cap-and-trade policy by comparing the cases with and without a carbon cap-and-trade policy. It is noteworthy that the goals of profit growth and emission reduction are simultaneously achieved under the carbon cap-and-trade policy.

Dual Sourcing and Joint Replenishment of Hospital Supplies

In response to increasing supply chain costs, hospitals are investing in new technology to improve inventory visibility and control at the point of use. This poses new inventory optimization opportunities and challenges for hospital management. The technology-enabled increased inventory visibility allows hospitals to implement more sophisticated inventory policies to reduce costs and improve availability. One such policy, implemented at a large Midwest hospital, is a dual-source hybrid inventory system that combines periodic and continuous order-placement epochs under a single-item setting, in which different items are treated independently. In this paper, we extend the dual-source hybrid policy to a two-item setting. We propose different joint replenishment policies that take advantage of increased inventory visibility to coordinate periodic and continuous replenishments across items. We develop a simulation-based search engine and test the benefits of these different policies under different parameter settings. We find that more benefits can be obtained using simple joint replenishment policies than are obtained using just the hybrid policy without coordinated replenishments.

The Dynamic-Demand Joint Replenishment Problem with Approximated Transportation Costs

In a vendor-managed inventory setting, a supplier determines the timing and size of replenishments for its customers. In the Dynamic-Demand Joint Replenishment Problem (DJRP), one assumes that the supplier pays a fixed fee for replenishing a customer which often occurs if the supplier outsources transportation. Hence, there is no incentive for the supplier to schedule replenishments for nearby customers in the same period. This results in higher transportation costs for the carrier, decreased vehicle utilization and increased future fees for the supplier. To lower costs for both parties, this paper extends the traditional DJRP to the DJRP with Approximated Transportation Costs (DJRP-AT) by taking transportation considerations into account. Since routing problems are difficult to solve and it is not necessary to know the sequence of the deliveries to the customers as these are outsourced, the transportation costs for a given set of customers are approximated using classical schemes. A solution approach for the DJRP-AT based on Branch-and-Cut-and-Price is validated using test instances from the literature. Results show improvements of 4% on average and up to 14.4% for individual instances compared with the DJRP. Moreover, when the DJRP-AT is compared with the DJRP on instances derived from a real-life case, similar savings are obtained. Comparing the DJRP-AT to an equivalent problem with actual routing costs, the solution values of the DJRP-AT are on average only 0.77% higher showing the value of the approximation.

Allocation rules for joint replenishment and inventory sharing via transshipment

The product life cycle is getting shorter because of the acceleration of product upgrading. The mismatch between the demand of short life cycle product and inventory leads to high cost owing to demand uncertainty and forecast inaccuracy. In order to reduce cost, the paper considers several retailers jointly replenish inventory and share inventory via transshipment after demand have realized. Based on cooperative game theory, the paper designs cost allocation rule of joint replenishment and profit allocation rule of inventory sharing for retailers. And it prove that the cost allocation is core allocation when their holding cost are same and the profit allocation is value-preserve in the given condition of the paper. Finally, we analyze the effects of transshipment on replenishment activities in view of profit allocation rule and the paper presents an example which shows that the coalition can benefit from transshipment by regulating their inventory level if the holding cost of retailers vary widely and the cost of transshipment is low.

Joint replenishment model of both-ways and one-way substitution among products in fixed time horizon

A general joint replenishment model (JRM) has been developed for two substitutable products with different demand structures depending on their prices and availabilities over the time cycle. When both products are available, the demand of a substitute product deceases against its own price and increases with the other's price. When one product is out of stock, a portion of demand of the stock-out product goes to the available product. The model is formulated to determine the optimal order quantities and total profits for different scenarios are determined using the classical optimisation method and parametric study. The optimal criteria for maximum profit is outlined and the model is illustrated numerically. Some sensitivity analyses with different substitution ratios are performed and some interesting conclusions have been derived.

Joint replenishment model of both-ways and one-way substitution among products in fixed time horizon

A general joint replenishment model (JRM) has been developed for two substitutable products with different demand structures depending on their prices and availabilities over the time cycle. When both products are available, the demand of a substitute product deceases against its own price and increases with the other's price. When one product is out of stock, a portion of demand of the stock-out product goes to the available product. The model is formulated to determine the optimal order quantities and total profits for different scenarios are determined using the classical optimisation method and parametric study. The optimal criteria for maximum profit is outlined and the model is illustrated numerically. Some sensitivity analyses with different substitution ratios are performed and some interesting conclusions have been derived.

Modelling and optimising the multi-item stochastic joint replenishment problem with uncertain lead-time and controllable major ordering cost

In this paper, we extend the existing stochastic joint replenishment model to a more realistic condition by considering uncertainties in lead-time and effective investment to reduce the major ordering cost. The aim is to determine the optimal strict cyclic replenishment policy and the optimal major ordering cost simultaneously to minimise the total cost. The objective cost function is approximated by expressing one element of the cost function as a Taylor series expansion. A bounds-based heuristic algorithm is then developed to solve the proposed model. The performance of the algorithm and the quality of the approximation are examined by computational experiments. The results of the models without considering uncertainty and ordering cost reduction are presented to illustrate the effectiveness of the proposed model. Experimentation and analysis of results demonstrate that the standard deviation of lead-time has a significant effect on the system. [Received: 21 December, 2016; Revised: 29 July 2017; Revised: 29 December 2017; Revised: 30 September 2018; Revised: 17 November 2018; Accepted: 26 January 2019]

变质率呈Weibull分布的易腐品联合补货优化

变质率呈Weibull分布的易腐品联合补货优化

The Periodic Joint Replenishment Problem Is Strongly 𝒩𝒫-Hard

In this paper, we study the long-standing open question regarding the computational complexity of one of the core problems in supply chains management, the periodic joint replenishment problem. This problem has received a lot of attention over the years, and many heuristic and approximation algorithms have been suggested. However, in spite of the vast effort, the complexity of the problem remains unresolved. In this paper, we provide a proof that the problem is indeed strongly 𝒩𝒫-hard.

Joint replenishment decision considering shortages, partial demand substitution, and defective items

Abstract A shortage may occur because of the insufficient production capacity or possible damages of items in transit, and the shortage can be partially fulfilled with substitutable items. In this study, a joint replenishment problem (JRP) with the shortage and partial demand substitution is investigated by developing a mixed integer nonlinear programming model. Several real-world constraints, such as budget, transportation capacity, and shipment requirement constraints are incorporated in the proposed model. Three heuristic algorithms, namely two-dimensional genetic algorithm I, two-dimensional genetic algorithm II, and differential evolution, are proposed, and numerical examples are provided to demonstrate the applicability of the proposed model in a real-world setting. The performance of the heuristic algorithms is investigated with the help of extensive computational experiments. The results show that differential evolution performs best in term of the minimum total cost among three heuristics. Sensitivity analyses are conducted to provide managerial insights. The results indicate that partial demand substitution policy can effectively decrease the total expected cost, but defective items will exponentially increase the total expect cost. The major ordering cost, budget, and truck capacity also affect the system.

Application of the joint replenishment problem in a collaborative Inventory approach to define resupply plans in urban goods distribution contexts

This article presents an application of the joint replenishment problem (JRP) as the basis for proposing a collaborative inventory model with joint orders, in which multiple customers share the required information to define their supply plans. This information is consolidated by the supplier and it is responsible for carrying out the collaborative joint replenishment process. The application of the model allows generating a replenishment process that reduces costs compared to carrying out the individual plans for each customers and also generates a reduction in the number of trips required, which is a positive contribution to urban goods distribution processes.

A stochastic joint replenishment problem considering transportation and warehouse constraints with gainsharing by Shapley Value allocation

The purpose of this paper is to introduce a heuristic approach that uses a capacitated inventory model as means for identifying a collaborative agreement between different buyers jointly replenishing multiple items from multiple vendors, thus attaining economies of scale while reducing by sharing fixed procurement and operational costs. The proposed approach is denominated Stochastic Collaborative Joint Replenishment Problem (S-CJRP) and consists of two stages. The first stage determines a cost-efficient replenishment frequency for each collaborating company in all possible coalition arrangements. To accomplish the former, an extension of the known Joint Replenishment Problem (JRP) considering real-life capacity constraints, such as stochastic demand assuming normal distribution, finite storage and transport, is solved via genetic algorithms delivering a suitable coalition. In a second stage, the Shapley Value function is established to assess and allocate the potential gains achieved by colluding in the first stage, determining a fair share distribution among players that increases the viability of such coalition. Several scenarios from a simulated numerical study illustrate average cost savings of 32.3%. 28.2% and 32.7% for 3, 4 and 5 players, respectively, considering up to 30 items for the proposed collaboration, in all cases consistently exhibiting cost reduction and increasing the proposal feasibility.

Modeling and solving a bi-objective joint replenishment-location problem under incremental discount: MOHSA and NSGA-II

In this paper, the joint replenishment-location problem of some distribution centers (DCs) with a centralized decision maker who is responsible for ordering and dispatching shipments of a single product is modeled. The warehouse spaces of the DCs are limited and the product is sold under an incremental discount policy. The model seeks to minimize the total cost of the supply chain under the joint replenishment policy along with minimizing the cost of locating the DCs in potential sites as the first objective. The second objective is to minimize the warehouse space of all DCs using the revisable approach. As the proposed model is a bi-objective integer non-linear optimization problem (NP-Hard) and cannot be solved by an exact method in a reasonable computational time, a multi-objective harmony search algorithm is developed to solve it. Since there is no benchmark available in the literature, the non-dominated sorting genetic algorithm II is utilized as well to validate the results obtained. As the performance of a meta-heuristic algorithm is largely influenced by the choice of its parameters, the response surface methodology is employed to tune the parameters. Several numerical illustrations are provided at the end to not only demonstrate the application of the proposed methodology, but also to analyze and compare the performances of the two solution algorithms in terms of several multi-objective measures.

Optimal Ordering Quantity for Substitutable Products Under Quantity Discount with Cost of Substitution

Three aspects of inventory control, quantity discount, product substitution and cost of substitution that affect retail inventory decisions are discussed in this paper. With these parameters, we developed an inventory model for which demand is satisfied by using two mutually substitutable products where when a product is out of stock, demand for it is met by the other product and any part of demand not met due to unavailability of the other product is lost. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted product. The demands are assumed to be deterministic and constant and quantity discount is offered by the distributor/supplier to the retailer and retailer use cost of substitution for substituted product under joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. Extensive numerical experimentation and sensitivity analysis is carried out for the improvement in the optimal total cost with substitution as compared to the case without substitution to draw insights into the behaviour of the model.