Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

A bounded dynamic programming approach to schedule operations in a cross docking platform

Cross docking is a logistic technique employed to reduce the inventory holding, order picking, transportation costs as well as the delivery time. Products arriving to the cross dock are unloaded from inbound trailers, possibly reconsolidated with other products arriving from different destinations and loaded into outbound trailers within less than 24 h. In this study, we consider a multiple receiving and shipping door cross dock environment. The objective is to find optimal (for reasonably small cross docks) or near optimal (for larger cross docking facilities) scheduling policies which minimizes the total costs related to the transshipment operations at the facility.     

A decision rule for coordination of inventory and transportation in a two-stage supply chain with alternative supply sources

This paper deals with a two-stage supply chain that consists of two distribution centers and two retailers. Each member of the supply chain uses a (Q,R) inventory policy, and incurs standard inventory holding and backlog costs, as well as ordering and transportation costs. The distribution centers replenish their inventory from an outside supplier, and the retailers replenish inventory from one of the two distribution centers. When a retailer is ready to replenish its inventory that retailer must decide whether it should replenish from the first or second distribution center. We develop a decision rule that minimizes the total expected cost associated with all outstanding orders at the time of order placement; the retailers then repeatedly use this decision rule as a heuristic. A simulation study which compares the proposed policy to three traditional ordering policies illustrates how the proposed policy performs under different conditions. The numerical analysis shows that, over a large set of scenarios, the proposed policy outperforms the other three policies on average.     

Stochastic models for the coordinated production and shipment problem in a supply chain

In this study, we consider the coordination of transportation and production policies between a single supplier and a single retailer in a stochastic environment. The supplier controls the production, holds inventory and ships the products to the retailer to satisfy the external demand. We model the system as a Markov decision process, and show that the optimal production and transportation decisions are complex and non-monotonic. Therefore, we analyze two widely-used shipment policies in the industry as well, namely time-based and quantity-based shipment policies in addition to a hybrid time-and-quantity based shipment policy. We numerically compare the performances of these policies with respect to the optimal policy and analyze the effects of the parameters in the system.     

A new heuristic to solve the one-warehouse N-retailer problem

We deal with a multi-echelon inventory system in which one warehouse supplies an item to multiple retailers. Customer demand arrives at each retailer at a constant rate. The retailers replenish their inventories from the warehouse that in turn orders from an outside supplier. It is assumed that shortages are not allowed and lead times are negligible. The goal is to determine replenishment policies that minimize the overall cost in the system. We develop a heuristic to compute efficient policies, which also can easily be used in a spreadsheet application. The main idea consists of finding a balance between the replenishment and the inventory holding costs at each installation. This new heuristic we compare with two other approaches proposed in the literature; the computational studies show that in most of the instances generated the new method provides lower costs.     

The evaluation of drop shipping option for e-commerce retailers

Many e-commerce retailers use drop shipping to satisfy demand. A retailer simply forwards customers' orders to the manufacturer who fills the orders directly to the customers and is paid a predetermined price by the retailer. Advantages of drop shipping include lower costs of holding inventory, materials handling, and obsolescence. Disadvantages of drop shipping include fragmented order delivery when a single customer order involves products from different manufacturers and longer delivery times. A mix of holding inventory and drop shipping is frequently optimal for e-retailers. In this paper, we design an optimal mix strategy which captures the advantages of drop shipping and avoids many of its shortcomings. We use two different optimization criterion, maximizing the expected profit and maximizing the probability of achieving a target profit. We provide results for uniform, exponential, and normal demand distributions. We illustrate the results with numerical examples.     

The benefit of VMI strategies in a stochastic multi-product serial two echelon system

We consider a multi-product serial two echelon inventory system with stochastic demand. Inventories at the downstream location are replenished periodically using an automatic ordering system. Under vendor managed inventory strategies the upstream stage is allowed to adapt these orders in order to benefit from economies of scale. We propose three different VMI strategies, aiming to reduce the order picking cost at the upstream location and the transportation costs resulting in reduced total supply chain costs. In a detailed numerical study the VMI strategies are compared with a retailer managed inventory strategy for two different demand models suitable for slow moving products. It is shown that if inventory holding costs are low, compared to handling and transportation costs, efficiencies at the warehouse are improved and total supply chain costs are reduced.     

Coordinating a three-level supply chain with delay in payments and a discounted interest rate

Both researchers and practitioners recognize the importance of the interactions between financial and inventory decisions in the development of cost effective supply chains. Moreover, achieving effective coordination among the supply chain players has become a pertinent research issue. This paper considers a three-level supply chain, consisting of a capital-constrained supplier, a retailer, and a financial intermediary (bank), coordinating their decisions to minimize the total supply chain costs. Specifically, we consider a retailer managing its cash through the supplier’s bank, in return for permissible delay in payments from the supplier. The bank, benefiting from increasing its cash holdings with the retailer’s cash deposits, offers the supplier a discount on its borrowing rate. We show that the proposed coordination mechanism achieves significant cost reduction, by up to 26.2%, when compared to the non-coordinated model. We also find that, with coordination, the retailer orders in larger quantities than its economic order quantity, and that a higher return on cash for the retailer leads to a higher order quantity. Furthermore, we empirically validate our proposed coordination mechanism, by showing that banks, retailers, and suppliers have much to gain through collaboration. Thus, using COMPUSTAT datasets for the years 1950 through 2012, we determine the most important factors that affect the behavior of the retailers and suppliers in granting and receiving trade credit. Our results indicate that engaging into such a coordination mechanism is a win–win situation to all parties involved.     

The consignment stock of inventories in coordinated model with generalized policy

In this paper, coordination between a single vendor (or manufacturer) and a buyer (or retailer) via the delivery schedule in a production and distribution system is presented. A continuous deterministic model with centralized decision process is developed. To satisfy the buyer’s demands, the product is delivered in discrete batches from the vendor’s stock to the buyer’s stock and all shipments are realized instantaneously. A more general type of consignment stock (CS) policies for the vendor–buyer integrated production–distribution model is analyzed. Our model does not require equal in size shipments. The inventory patterns and the cost structure of production distribution cycles (PDC) are described in different scenarios. A comparative study of the results shows that the generalized CS policies perform better. Considering CS-policies Braglia and Zavanella (2003) ask about a possibility of cost reduction by delaying a number of late deliveries. Unfortunately, a negative answer was given by Zanoni and Grubbström (2004). We verify this problem to obtain a positive answer in more general setting. A solution procedure is developed to find optimal generalized CS-policy for the problems with nonequal and equal in size deliveries. Optimal solutions are found and illustrated with numerical examples.     

On conflict and cooperation in a two-echelon inventory model for deteriorating items

Four scenarios are proposed concerning cooperative behavior for inventory policies between suppliers and retailers: no information is shared; the supplier is dominant during negotiations with retailers; the retailer is dominant during negotiations with suppliers; and the supplier and retailer cooperate. Unlike other studies, we consider deteriorating items and permit completed backorders, with a fixed service rate, in the models for these four scenarios. We explore the optimality of these models and present a procedure to find the optimal solution. Numerical examples are provided to illustrate the procedure, which are also used for sensitivity analysis. The results show that the cooperation scenario with information sharing is the best way to reach a win–win position. However, some compensation programs might be required to persuade suppliers or retailers to cooperate when one of them faces a loss of profits in a cooperative scenario.     

An integrated approach for logistic and vendor managed inventory in supply chain

In this paper, a quaternary policy system towards integrated logistics and inventory aspect of the supply chain has been proposed. A system of multi retailers and distributors, with each distributor following a unique policy, will be analysed. The first policy is continuous time replenishment policy where the retailers’ inventory is replenished in every time interval. In the next three policies, inventory of the retailers will be replenished by some definite policy factors. The vendor managed inventory (VMI) system is used for updating the inventory of the retailers. An order-up-to policy (q, Q) is used for updating the inventory of distributors. Total erstwhile demands to the retailer will be used to determine the amount of inventory acclivity. Furthermore, the distributors will be sending the delivery vehicles to few fellow retailers who are shortlisted according to the policy, followed by the retailers and associated distributors. On the basis of random demand that the retailers are facing from end customers and the total demand that has incurred in the supply chain, products are unloaded to the selected retailers from the delivery vehicle. The path of the delivery vehicle is retrieved by dynamic ant colony optimization. In addition, a framework has been developed to measure the end-customer satisfaction level and total supply chain cost incorporating the inventory holding cost, ordering cost and the transportation cost. The framework has been numerically moulded with different settings to compare the performance of the quadruplet policies.     

The value of postponing online fulfillment decisions in multi-channel retail/e-tail organizations

Many retail/e-tail organizations assign responsibilities for online sales immediately and to the closest fulfillment location that has available stock. Unfortunately there is little research on the value of using such policies in retail/e-tail companies. To fill this gap, this paper examines two aspects of the online fulfillment assignment decision that differ from current practice. We propose that online sales should be accumulated before they are assigned to a fulfillment site and that more inventory position information should be leveraged into the fulfillment decision. Specifically, we develop and evaluate a “quasi-dynamic” allocation policy that assigns accumulated online sales to fulfillment locations based on expected inventory, shipping, and customer wait costs. Computational results show that our policy can reduce costs (i.e., holding, backorder, transportation cost) at the fulfillment locations by as much as 23% on average over a commonly used transportation cost policy. In addition, postponing the allocation decision and allowing sales to accumulate can reduce inventory costs at the fulfillment sites by 14% over common practice of instantaneously assigning online sales responsibilities. The magnitude of the benefit depends critically on the number of allocations made each period and the fraction of total sales coming from the online channel. Although postponement delays receipt of online sales, our findings suggest that explicitly incorporating customer service in the allocation decision can improve product availability at little or no additional cost.     

Pricing and inventory management in a system with multiple competing retailers under (r, Q) policies

We consider a multi-retailer system operated on an infinite horizon, in which each retailer faces stochastic demand following a Poisson process and adopts a continuous-review (r, Q) policy for replenishing inventory to satisfy customer demand. The system involves decisions of pricing and inventory management with the goal of maximizing profit, which equals the sales revenue minus the purchase and inventory costs. Taking Cournot competition into account, models are formulated to optimize simultaneously the expected sales volumes and (r, Q) policies of all retailers. An efficient approach is proposed to calculate the approximate inventory cost. Based on this approach, solution methods for centralized and decentralized scenarios are developed. A great number of numerical computations are provided to evaluate the efficiency of the solution methods, and their performance in the two scenarios. Moreover, system performance under sequential decisions (first pricing and then inventory management) is also investigated.     

考虑单位车辆运力的运输-库存随机需求决策模型

针对提前期和客户需求不确定的生产、运输和库存协调控制问题, 基于整车直达运输策略, 从优化系统物流成本角度, 建立了在决策中明确体现单位车辆运力影响的运输-库存系统协调模型, 设计了求解模型的优化搜索机制并从数学上证明了其有效性. 最后, 进一步对单位车辆运力进行敏感性分析并得出以下结论: 在其他条件不变时, 单位车辆的运力会影响系统决策结果, 该运力既不是越大越好, 也不是越小越好, 而是某个适中值.

     

A joint model for cash and inventory management for a retailer under delay in payments

As retail companies continue to navigate through the economy downturn, it becomes critical to find innovative cost reduction methods. Cash management is a cost-intensive process for retailers, who are currently focusing on effective cash management, such as deciding on the maximum cash level to keep in their business accounts and how much to borrow to finance inventories and pay suppliers. In this paper, we consider the problem of finding the optimal operational (how much to order and when to pay the supplier) and financial decisions (maximum cash level and loan amount) by integrating the cash management and inventory lot sizing problems. We consider a supplier offering a retailer an interest-free credit period for settling the payment. Beyond this period, the supplier charges interest on the outstanding balance. Whenever the cash exceeds a certain limit, it will be invested in purchasing financial securities. At the time when the retailer pays the supplier for the received order, cash is withdrawn from the account, incuring various financial costs. If the cash level becomes zero or not sufficient, the retailer obtains an asset-based loan at interest. We model this problem as a nonlinear program and propose a solution procedure for finding the optimal solution. We perform a numerical study to analyze the impact of optimal cash management on the inventory decisions. The results indicate that the optimal order quantity decreases as the retailer’s return on cash increases. We compare our model to a model that ignores financial considerations of cash management, and show numerically that our model lowers the retailer’s cost. Also, we illustrate the effect of changing various model parameters on the optimal solution and obtain managerial insights.     

Construct the stable vendor managed inventory partnership through a profit-sharing approach

In real life, the vendor managed inventory (VMI) model is not always a stable supply chain partnership. This paper proposes a cooperative game based profit-sharing method to stabilize the VMI partnership. Specifically, in a B2C setting, we consider a VMI program including a manufacturer and multiple online retailers. The manufacturer provides the finished product at the equal wholesale price to multiple online retailers. The online retailers face the same customer demand information. We offer the model to compute the increased profits generated by information sharing for total possible VMI coalitions. Using the solution concept of Shapley value, the profit-sharing scheme is produced to fairly divide the total increased profits among the VMI members. We find that under a fair allocation scheme, the higher inventory cost of one VMI member increases the surplus of the other members. Furthermore, the manufacturer is glad to increase the size of VMI coalition, whereas, the retailers are delighted to limit the size of the alliance. Finally, the manufacturer can select the appropriate retailer to boost its surplus, which has no effect on the surplus of the other retailers. The numerical examples indicate that the grand coalition is stable under the proposed allocation scheme.     

A computational study for common network design in multi-commodity supply chains

In this paper, we study a supply chain network design problem which consists of one external supplier, a set of potential distribution centers, and a set of retailers, each of which is faced with uncertain demands for multiple commodities. The demand of each retailer is fulfilled by a single distribution center for all commodities. The goal is to minimize the system-wide cost including location, transportation, and inventory costs. We propose a general nonlinear integer programming model for the problem and present a cutting plane approach based on polymatroid inequalities to solve the model. Randomly generated instances for two special cases of our model, i.e., the single-sourcing UPL&TAP and the single-sourcing multi-commodity location-inventory model, are provided to test our algorithm. Computational results show that the proposed algorithm can solve moderate-sized problem instances efficiently.     

Integrated Inventory Control and Facility Location Decisions in a Multi-Echelon Supply Chain Network with Hubs

This paper develops mathematical models to coordinate facility location and inventory control for a four-echelon supply chain network consisting of multiple suppliers, warehouses, hubs and retailers. The hubs help in reducing transportation costs by consolidating products from multiple warehouses and directing the larger shipments to the retailer. The integrated models studied in this paper simultaneously determines three types of decisions: (i) facility location—the number and location of warehouses and hubs, (ii) allocation—assignment of suppliers to located warehouses and retailers to located warehouses via the location hubs, and (iii) inventory control decisions at each located warehouse. The goal is to minimize the facility location, transportation and the inventory costs. A mixed integer nonlinear programming formulation is first presented. The nonlinear integer programming formulation is then transformed into a conic mixed integer program and a novel and compact conic mixed integer programming formulation. Computational runs are conducted using commercial solvers to compare the performance of the different formulations. The compact conic mixed integer programming formulation was found to significantly outperform the other formulations by achieving significant computational savings. The results demonstrate that large scale instances of certain multi-echelon supply chain network design problems can be solved using commercial solvers through intelligent reformulation of the model.     

贸易信用下考虑零售商违约风险的供应链协调问题研究

本文研究延迟支付和提前支付同时存在下的供应链协调问题。考虑由一个供应商和一个零售商构成的二级供应链,市场需求随机,延迟支付下零售商会增加订购数量,但由于其违约风险的存在,供应商会降低其交付量,最终导致供应商交付量小于零售商订购量,降低供应链收益。要求零售商提前支付部分货款则可以有效避免零售商的违约问题,通过建立延迟支付和提前支付同时存在下的零售商收益模型和供应商的收益模型,给出了零售商的最优订购量决策和供应商的最优交付量决策,通过调整延迟支付期限和提前支付比例,使得二者相等,并等于供应链整体收益最大化下的生产数量,实现供应链协调。最后通过数值算例分析了相关参数的敏感性等问题。     

Analysing the effectiveness of vendor-managed inventory in a single-warehouse,multiple-retailer system

This paper considers a two-stage supply chain, consisting of a single warehouse and multiple retailers facing deterministic demands, under a vendor-managed inventory (VMI) policy. It presents a two-phase optimisation approach for coordinating the shipments in this VMI system. The first phase uses direct shipping from the supplier to all retailers to minimise the overall inventory costs. Then, in the second phase, the retailers are clustered using a construction heuristic in order to optimise the transportation costs while satisfying some additional restrictions. The improvement of the system's performance through coordinated VMI replenishments against the system with direct shipping only is shown and discussed in the comparative analysis section.