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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. [ABSTRACT FROM AUTHOR]

Joint replenishment problems constitute an important class of models in inventory management. They exhibit aspects of possible coordination among multiple products to save costs. Their computational complexity had been open even if there are just two products that need to be synced. In "Integer factorization: Why two-item joint replenishment is hard," Schulz and Telha present a simple framework based on integer factorization to establish the computational hardness of two variants of the joint replenishment problem with two items. Whereas difficult to solve in practice and not believed to be solvable in polynomial time, integer factorization is not as difficult as NP-complete problems. The authors show that a similar technique can be used to show even the NP-completeness of one variant of the joint replenishment problem (again with just two items). Distribution networks with periodically repeating events often hold great promise to exploit economies of scale. Joint replenishment problems are fundamental in inventory management, manufacturing, and logistics and capture these effects. However, finding an efficient algorithm that optimally solves these models or showing that none may exist have long been open regardless of whether empty joint orders are possible or not. In either case, we show that finding optimal solutions to joint replenishment instances with just two items is at least as difficult as integer factorization. To the best of the authors' knowledge, this is the first time integer factorization is used to explain the computational hardness of any optimization problem. We can even prove that the two-item joint replenishment problem with possibly empty joint-ordering points is NP-complete under randomized reductions. This implies that even quantum computers may not be able to solve it efficiently. By relating the computational complexity of joint replenishment to cryptography, prime decomposition, and other aspects of prime numbers, a similar approach may help to establish the (integer-factorization) hardness of additional periodic problems in supply chain management and beyond, whose computational complexity has not been resolved yet. Funding: The first author gratefully acknowledges the support of the Alexander von Humboldt Foundation and the German Federal Ministry of Education and Research. The second author gratefully acknowledges the support of Agencia Nacional de Investigación y Desarrollo [Grant ANID/FONDECYT Iniciación 11200616] and Programa Regional STIC AMSUD [Grant 22-STIC-09]. [ABSTRACT FROM AUTHOR]

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 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. [ABSTRACT FROM AUTHOR]

A practical stochastic location-inventory-delivery problem with multi-item joint replenishment is studied. Unlike the conventional location-inventory model with a continuous-review (r, Q) inventory policy, the periodic-review inventory policy is adopted with multi-item joint replenishment under stochastic demand, and the coordinated delivery cost is considered. The proposed model considers the integrated optimization of strategic, tactical, and operational decisions by simultaneously determining (a) the number and location of distribution centers (DCs) to be opened, (b) the assignment of retailers to DCs, (c) the frequency and cycle interval of replenishment and delivery, and (d) the safety stock level for each item. An intelligent algorithm based on particle swarm optimization (PSO) and adaptive differential evolution (ADE) is proposed to address this complex problem. Numerical experiments verified the effectiveness of the proposed two-stage PSO-ADE algorithm. A sensitivity analysis is presented to reveal interesting insights that can guide managers in making reasonable decisions.

In this paper, we consider a combination of the joint replenishment problem (JRP) and single-machine scheduling with release dates. There is a single machine and one or more item types. Each job has a release date, a positive processing time, and it requires a subset of items. A job can be started at time t only if all the required item types were replenished between the release date of the job and time point t. The ordering of item types for distinct jobs can be combined. The objective is to minimize the total ordering cost plus a scheduling criterion, such as total weighted completion time or maximum flow time, where the cost of ordering a subset of items simultaneously is the sum of a joint ordering cost, and an additional item ordering cost for each item type in the subset. We provide several complexity results for the offline problem, and competitive analysis for online variants with min–sum and min–max criteria, respectively. [ABSTRACT FROM AUTHOR]

To obtain higher profits, a third-party overseas warehouse increases the delivery frequency of goods by setting a holding cost rate that increases with the holding time. To reduce the cost incurred from using the third-party overseas warehouse, small cross-border e-commerce retailers form a coalition to jointly replenish the overseas warehouse. Based on cooperative game theory, this paper designs a cost allocation rule to allocate the total cost of a cooperative coalition. The cost allocation rule is proved to be in the core of the corresponding cooperative game, indicating that it satisfies individual rationality and coalition rationality. An (1 + ϵ) -approximate algorithm is presented to search for the optimal replenishment cycle under joint replenishment. Numerical experiments show that joint replenishment can help small cross-border e-commerce retailers to reduce costs, shorten replenishment cycles, and expedite commodity turnover. Having a greater number of retailers involved in joint replenishment would help to save more costs. The average saving cost rate after cooperation can be 58% when the fixed costs are very high. [ABSTRACT FROM AUTHOR]

In this paper, we consider the joint replenishment and delivery scheduling of the one‐warehouse, n$n$‐retailer system with stochastic demand. In this distribution system, items are first jointly replenished and therefore can share a major ordering cost. Then a coordinated delivery scheduling is adopted to arrange the delivery plan. The problem is formulated as a mixed integer nonlinear program. Subsequently, we introduce two algorithms to handle this complex problem: a Lipschitz optimization method and a modified RAND heuristic. Numerical experiments show that the proposed methods are quite efficient. Sensitivity analysis also shows some interesting findings in terms of management. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the problem of determining the optimal economic operating policy when a number of non-instantaneous deteriorating items are jointly replenished. We establish a multi-item joint replenishment model for non-instantaneous deteriorating items under constant demand rate allowing full backlogging. This problem is challenging, in particular, the cost function is a piecewise function with exponential parts, which makes the problem more complicated. To solve this problem, an approximation method is used to simplify the objective function and a bound-based heuristic algorithm is developed to solve the model. Numerical examples illustrate the effectiveness of the proposed method and the quality of the approximation. Experimental results on a real-life case study show that the proposed model can achieve substantial cost savings compared to the individual replenishment policy for non-instantaneous deteriorating items. Furthermore, sensitivity analysis of key parameters is carried out and the implications are discussed in detail. [ABSTRACT FROM PUBLISHER]

In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen.

Le Macaron French Pastries is based in Sarasota, Florida. Its central commissary specializes in baking macarons, a small, French-style pastry. It has more than 60 retail franchises throughout the United States, which order in large lots from the commissary. We developed a low-cost, user-friendly, and creative solution for the franchises to easily improve their orders to minimize costs and maintain product freshness. Implemented benefits include an 80% improvement in inventory at time of order, a 75% reduction in the number of orders, and an improvement in product freshness. [ABSTRACT FROM AUTHOR]

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.

This study investigates the multi-customer Joint Replenishment Problem with districting considerations and material handling capacity constraints (MJRPDC-MHCC). Solving MJRPDC-MHCC is important to the manager before signing a contract with a third-party logistics service provider since it obtains a logistics plan providing lotsizing and districting decisions. We propose a solution approach based on genetic algorithm (GA) as its framework and incorporate a heuristic that generates a feasible replenishment schedule for each districting setting. Following our numerical experiments, we observe that the average runtime of our approach grows in a cubic order with respect to both the number of customers and the number of items. Therefore, the proposed GA-based solution approach is recommended as a useful decision-support tool. [ABSTRACT FROM AUTHOR]

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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. [ABSTRACT FROM AUTHOR]

In this paper, impact of cost of substitution and joint replenishment on inventory decisions for joint substitutable and complementary items under asymmetrical substitution has been studied. The phenomenon of substitution is considered in a stock-out situation and when items become out of stock due to demand then unfulfilled demand is asymmetrically substituted by another item. We formulate the inventory model mathematically and derived optimal ordering quantities, optimal total costs and extreme value of substitution rate for all possible cases. Moreover, pseudo-convexity of the total inventory cost function is obtained and the solution procedure is provided. Numerical example and sensitivity analysis have been presented to validate the effectiveness of the inventory model and substantial improvement in total optimal inventory cost with substitution with respect to optimal total inventory cost without substitution is seen. [ABSTRACT FROM AUTHOR]

It is a widespread financial practice in procurement management for a supplier aiming to attract customers to offer trade credits when customers make inquiries about the sold products. In this paper, we examine the joint replenishment problem considering trade credits (JRP-TC) under the power-of-two (PoT) policy. We formulate a mathematical model and conduct an analysis that reveals insights into the properties of the optimal objective function. From there, we propose an effective search algorithm that obtains the global optimal solution for the JRP-TC under the PoT policy. Our complexity analysis shows that the JRP-TC and the conventional joint replenishment problem under the PoT policy are pseudo-polynomial time solvable. [ABSTRACT FROM AUTHOR]

This paper presents tight mathematical programming formulations for the dynamic demand joint replenishment problem (DJRP). Experimental studies using general-purpose software document the improved computational efficiency of the new formulations versus the earlier models of Boctor et al. (Boctor, F.F., Laporte, G. and Renaud, J., Models and algorithms for the dynamic-demand joint replenishment problem. Int. J. Prod. Res. , 2004, 42, 2667–2678.) and Robinson and Gao (Robinson, E.P. and Gao, L., A dual-ascent procedure for multi-product dynamic demand coordinated replenishment with backlogging. Manag. Sci. , 1996, 42, 1556–1564.). The findings encourage the development of specialized algorithms for their solution. The paper also evaluates the performance of the perturbation and dual-ascent heuristics for solving DJRP finding the perturbation heuristic is superior at relatively low set-up cost ratios and high joint set-up cost levels, while the dual-ascent heuristic strongly dominates at relatively high set-up cost ratios and low joint set-up costs. Considering that both heuristics are computationally efficient, the best application strategy is to solve the problem with both heuristics and implement the best found solution. [ABSTRACT FROM AUTHOR]

The joint replenishment problem determines order quantities and the grouping of products replenished from the same supplier. The objective is to minimize the ordering and holding cost of the purchasing firm. The problem is frequently solved assuming products with constant unit cost. An efficient algorithm for solving the joint replenishment problem for products that may be experiencing unit cost increase or decrease is developed. The proposed algorithm is tested on a sample of randomly generated problems containing up to 25 items and it is shown that it identifies the global optimal solutions for most of these problems. For the worst case where the algorithm fails to identify the global optimal solution, the solution it provides had a total cost 0.007% above the global minimum. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. • Four response strategy influences for coping with defective items are examined. • Both random imperfect items and stochastic demands are considered. • An adaptive mutation probability and opposition-based learning are considered. • Numerical experiments are designed and extensively performed. • Insights are obtained through experiments on different scale cases. [ABSTRACT FROM AUTHOR]

In today’s fast-paced and competitive market place, organizations need every edge available to them to ensure success in planning and managing inventory of items with demand uncertainty. In such an effort, cost effective methods in determining optimal replenishment policies are paramount. In this paper, a mathematical model is proposed that optimize inventory replenishment policies of a periodic review inventory system under stochastic demand; with particular focus on malaria drugs in Ugandan pharmacies. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for drugs that treat malaria. Using weekly equal intervals, the decisions of whether or not to replenish additional units of drugs were made using discrete time Markov chains and dynamic programming over a finite period planning horizon. Empirical data was collected from two pharmacies in Uganda. The customer transactions of drugs were taken on a weekly basis; where data collected was analyzed and tested to establish the optimal replenishment policy and inventory costs of drugs. Results from the study indicated the existence of an optimal state-dependent replenishment policy and inventory costs of drugs at the respective pharmacies.

This paper deals with the problem arising from a supply chain with a single supplier and multiple retailers which do joint replenishment by using EOQ model. The aim of this paper is to investigate a joint replenishment interval-valued EOQ model without shortage among the retailers whose demands are intervals, the obtained retailers' order quantities and the coalitions' inventory costs are intervals as well. In order to allocate the interval-valued inventory costs, we propose an interval-valued proportional surplus division for a special subclass of interval-valued inventory cost allocation cooperative games. By adding the coalition size monotonicity-like conditions, a simplified and an effective method is developed to obtain the lower and upper bounds of the proposed interval-valued proportional surplus division via utilizing the lower and upper bounds of the interval-valued inventory costs of coalitions, respectively. The applicability and effectiveness of the proposed method are demonstrated with a real numerical example. This paper may provide theory and method support for solving complex inventory cost allocation problems. [ABSTRACT FROM AUTHOR]

In today's fast-paced and competitive market place, organizations need every edge available to them to ensure success in planning and managing the inventory of items with demand uncertainty. In such an effort, cost effective methods in determining optimal replenishment policies are paramount. In this paper, a mathematical model that optimizes inventory replenishment policies of a periodic review inventory system under stochastic demand is proposed, with particular focus on malaria drugs in Ugandan pharmacies. Adopting a Markov decision process approach, the states of a Markov chain represent possible states of demand for drugs that treat malaria. Using weekly equal intervals, the decisions in terms of whether or not to replenish additional units of drugs were made using discrete time Markov chains and dynamic programming over a finite period planning horizon. Empirical data was collected from two pharmacies in Uganda. The customer transactions of drugs were taken on a weekly basis, where the data collected was analyzed and tested to establish the optimal replenishment policy and inventory costs of drugs. Results from the study indicated the existence of an optimal state-dependent replenishment policy and inventory costs of drugs at the respective pharmacies. [ABSTRACT FROM AUTHOR]

Most often, we observe that certain spare parts are used together for various maintenance activities of equipment. If spare parts are used frequently in a group, then there exists some hidden dependency among these parts. Sometimes the entire maintenance work cannot be accomplished due to the shortage of a single spare in the group. These parts are termed here as associated spare items. These parts can be determined by frequent itemsets mining. In this paper, the groups of spare parts are found out through hierarchical clustering method using support and weighted support of the data mining measure. A methodology is proposed to incorporate both support and weighted support values for computing an overall cost of replenishment for joint replenishment policy for the associated spares. Finally, a case study is presented to illustrate the validation of our model and compared the results among the group with normal support and group with weighted support. [ABSTRACT FROM AUTHOR]

In recent years, joint replenishment and delivery problem (JRD) has been examined extensively in the context of replenishment and inventory control. However, as an extension of joint replenishment problem, the JRD is more complex and difficult to optimize with an exact algorithm. In this study, lower and upper bounds of JRD are obtained approximately but quickly using a novel bounding procedure. Then, a variable neighborhood search (VNS) with the bounding method is developed to solve the JRD. Computational examples show that the bounding procedure can effectively and efficiently determine satisfactory bounds, which are helpful for the proposed VNS. Results of randomly generated examples further indicate that the hybrid VNS performs better than the best known heuristic and metaheuristic for JRD in terms of accuracy. [ABSTRACT FROM AUTHOR]

We consider the infinite-horizon multiple retailer joint replenishment problem with first-order interaction. In this model, the joint setup cost incurred by a group of retailers placing an order simultaneously consists of a group-independent major setup cost and retailer-specific minor setup costs. The goal is to determine an inventory replenishment policy that minimizes the long-run average system-wide cost. In this paper, we adopt a noncooperative approach to study the joint replenishment game. We consider the allocation rule in which the major setup cost is split equally among the retailers who place an order together, and each retailer pays his own holding and minor setup costs. Given the preannounced allocation rule, each retailer determines his replenishment policy to minimize his own cost anticipating the other retailers' strategy. We show that a payoff dominant Nash equilibrium exists, and quantify the efficiency loss of the noncooperative outcome relative to the social optimum. Although the worst-case ratio between the best decentralized outcome and the social optimum is O((ln n)1/2), where n is the number of retailers, numerical results suggest that the best equilibrium is near optimal. The online appendix is available at . [ABSTRACT FROM AUTHOR]

In this paper we develop an inventory model, to determine the optimal ordering quantities, for a set of two substitutable deteriorating items. In this inventory model the inventory level of both items depleted due to demands and deterioration and when an item is out of stock, its demands are partially fulfilled by the other item and all unsatisfied demand is lost. Each substituted item incurs a cost of substitution and the demands and deterioration is considered to be deterministic and constant. Items are order jointly in each ordering cycle, to take the advantages of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. We provide an extensive numerical and sensitivity analysis to illustrate the effect of different parameter on the model. The key observation on the basis of numerical analysis, there is substantial improvement in the optimal total cost of the inventory model with substitution over without substitution. [ABSTRACT FROM AUTHOR]

In this paper, we study an inventory system for two substitutable deteriorating items where when an item is out of stock, the demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. The level of inventory of both items deplete due to combined effect of demand fulfilment and deterioration. The rates of demand and deterioration are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle so as to take advantage of joint replenishment. The problem is formulated and a solution procedure is developed to determine the optimal ordering quantities that minimize the total inventory cost. An extensive numerical analysis is carried out to illustrate the parameters of the model. The results indicate that there is substantial improvement in the optimal total cost of the inventory system with substitution over the case without substitution. [ABSTRACT FROM AUTHOR]

An inventory system of two mutually substitutable items has been studied where an item is out of stock, demand for it is met by the other item and any part of demand not met due to unavailability of the other item is lost. In the event of substitution, there is an additional cost of substitution involved for each unit of the substituted item. The demands are assumed to be deterministic and constant. Items are ordered jointly in each ordering cycle, in order to take advantage of joint replenishment. The problem is formulated and a solution procedure is suggested to determine the optimal ordering quantities that minimize the total inventory cost. The critical value of the substitution rate is defined to help in deciding the optimal value of decision parameters. Extensive numerical experimentation is carried out, which shows that prior knowledge of the critical value of the substitution rate helps to minimize the total inventory cost. 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. [ABSTRACT FROM AUTHOR]

In B2C E-Commerce operations, multiple quantity discount offers are commonly practiced in the multi-item replenishment environment. In this paper, a novel joint replenishment model ( JRP ) is presented considering two quantity discounts, all-unit quantity discount, incremental quantity discount, simultaneously. A novel swarms search technique, locust swarms algorithm ( LS ) is introduced and redesigned to solve the novel formulated JRP model. Numerical experiments and parameter sensitivity analyses reveal that LS is an effective and efficient algorithm for solving the proposed model in terms of solution quality and searching stableness comparing to some other meta-heuristic algorithms, such as GA, DE and PSO . Moreover, management insights such as the mutual effects of multiple quantity discounts to the total cost, and the role of multiple quantity discounts to different stakeholders in replenishment are outlined. [ABSTRACT FROM AUTHOR]

We extend the classical economic order quantity model to address the joint replenishment of multiple products under substitution. The proposed model optimizes ordering quantities for each product under substitution effects with the objective of minimizing the total cost associated with the setup, holding, and shortage of products, while partially meeting demand. First, the special case of three substitutable products is examined in detail. Then, a nonlinear mathematical programming formulation is presented as a general-purpose solution approach for any number of substitutable products. The convexity of the model is discussed. We find that the objective function to be convex in the important special case of products having equal unit holding costs, which typically holds for substitutable products in practice. Sensitivity analysis is conducted in order to determine the impact of cost parameters variations on the ordering policy. We focus on identifying conditions that favor substitution among products. We find that allowing substitution among products is an effective vehicle for cost cutting in supply chain settings involving high fixed costs, low holding costs, and low shortage costs. [ABSTRACT FROM AUTHOR]

In this paper, a novel joint replenishment and synthetical delivery (JRD) model is proposed to improve the coordination of replenishment and delivery processes. Traditional, in a warehouse centralized supply chain, orders from online customers are usually delivered independently after multiple items have been jointly replenished. To decrease the outbound delivery cost, a new delivery strategy considering synthetical dispatched orders, orders and customers matching, and customer visiting sequence is proposed. Three new beta-heuristic algorithms, namely, quantum evolution algorithm (QEA), differential evolution algorithm (DE) and quantum differential evolution algorithm (QDE), are utilized to solve the proposed JRD. The most important parts of each algorithm (initialization, reproduction and mutation, and selection) are redesigned according to the structure of the decision variables. Numerical experiments are conducted to find the best parameter settings and potential searching abilities of each algorithm. Finally, experimental results show the superiorities of the proposed DE and QDE in terms of searching speed, accuracy, and robustness. [ABSTRACT FROM AUTHOR]