A supplier selection and order allocation problem with stochastic demands

We consider a system comprising a retailer and a set of candidate suppliers that operates within a finite planning horizon of multiple periods. The retailer replenishes its inventory from the suppliers and satisfies stochastic customer demands. At the beginning of each period, the retailer makes decisions on the replenishment quantity, supplier selection and order allocation among the selected suppliers. An optimisation problem is formulated to minimise the total expected system cost, which includes an outer level stochastic dynamic program for the optimal replenishment quantity and an inner level integer program for supplier selection and order allocation with a given replenishment quantity. For the inner level subproblem, we develop a polynomial algorithm to obtain optimal decisions. For the outer level subproblem, we propose an efficient heuristic for the system with integer-valued inventory, based on the structural properties of the system with real-valued inventory. We investigate the efficiency of the proposed solution approach, as well as the impact of parameters on the optimal replenishment decision with numerical experiments.     

季节性产品零售商的网络订单履行策略研究

以一个销售季节性产品的零售商为研究对象,该零售商拥有两个实体店,分别位于两个独立的地区,通过Drop-shipping方式接收网上的订单,以扩大销量。初始库存量是确定的,产品卖给网上顾客为零售商带来的收益要比卖给店内顾客的收益少（履行网上订单获得的收益是零售商与订单提供者共享）;因此,每当网上订单到达时,零售商需要在接收该订单、还是把产品留给能带来更高收益的未来的店内顾客间做决策;如果接收该订单,还要决策将由哪个实体店来履行订单效益更好;以最大化未来期望收益为目标,建立动态规划模型,并从实体店对单个产品期望收益的角度为这两个问题的决策提供依据;分别在两个实体店处于平等地位和其中一个实体店被确定为优先供应商两种不同的情况下,研究零售商决策结果的差异。     

The optimal integrated inventory policy with price-and-credit-linked demand under two-level trade credit

In this paper, we proposed a generalized, integrated, supplier–retailer inventory model using a trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M > N and M ? N are explored thoroughly. In addition, the demand rate is assumed to be a function of both retail price and the customers’ credit period. Consequently, this paper deals with the problem of determining the optimal retail price, economic order quantity, and the number of shipments from the supplier to the retailer in one production run for an integrated inventory system under both two-level trade credit and price-and-credit-linked demand rate. Algorithms are developed in order to determine the joint optimal policies. Numerical examples are presented to illustrate the proposed models, as well as sensitivity analysis of key parameters.     

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.     

Situation reactive approach to Vendor Managed Inventory problem

In this research, we deal with VMI (Vendor Managed Inventory) problem where one supplier is responsible for managing a retailer’s inventory under unstable customer demand situation. To cope with the nonstationary demand situation, we develop a retrospective action-reward learning model, a kind of reinforcement learning techniques, which is faster in learning than conventional action-reward learning and more suitable to apply to the control domain where rewards for actions vary over time. The learning model enables the inventory control to become situation reactive in the sense that replenishment quantity for the retailer is automatically adjusted at each period by adapting to the change in customer demand. The replenishment quantity is a function of compensation factor that has an effect of increasing or decreasing the replenishment amount. At each replenishment period, a cost-minimizing compensation factor value is chosen in the candidate set. A simulation based experiment gave us encouraging results for the new approach.     

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.     

Determinant on RFID technology investment for dominant retailer subject to inventory misplacement

Radio‐frequency identification (RFID) technology has been publicized as an effective way to solve the problem of inventory misplacement in academic research as well as in the user industries. In this paper, we consider a supply chain that consists of one supplier and one retailer where the retailer is the Stackelberg leader and makes the decisions first. The consignment contract is provided such that the supplier determines the order quantity, instead of the retailer. A Non‐RFID case, a supplier investing in RFID, and a retailer investing in RFID cases are analyzed and compared. By assuming an iso‐elastic demand function and the corresponding random factor follows uniform distribution, it is intriguing to find that both supplier and retailer have the incentive to take charge of the RFID tag cost, which is not revealed in previous research. Therefore, a case of joint investment in RFID technology is formulated to find out that there are upper and lower threshold values of RFID tag cost sharing rate; that is, if the tag cost sharing rate exceeds the upper value, it is beneficial for the supplier to invest in RFID; if the tag cost sharing rate is smaller than the lower value, it is beneficial for the retailer to invest in RFID; if the tag cost sharing rate is somewhere between these two values, both supplier and retailer are better‐off. Additionally, the end customer will be better‐off if the retailer invests in RFID.     

The value of information sharing in a supply chain with a seasonal demand process

This paper considers a two echelon seasonal supply chain model that consists of one supplier and one retailer, with the assumption that external demand from the customer follows a seasonal autoregressive moving average (SARMA) process, including marketing actions that cannot be deduced from the other parameters of the demand process. In our model, the supplier and the retailer employ order-up-to policy to replenish their inventory. In order to evaluate the value of information sharing in a two echelon seasonal supply chain, three levels of information sharing proposed by Yu, Yan, and Cheng (2002) are used. The results for optimal inventory policies under these three levels of information sharing are derived. We show that the seasonal effect has an important impact on optimal inventory policies of the supplier under the three levels of information sharing. Our findings also demonstrate that the replenishment of lead time must be less than the seasonal period in order to benefit from information sharing. Thus, this result provides managers with managerial insights to improve supply chain performance through information sharing integration partnerships.     

Analysis of Admission and Inventory Control Policies for Production Networks

Problems of inventory control and customer admission control are considered for a manufacturing system that produces one product to meet random demand. Four admission policies are investigated: lost sales, complete backordering, randomized admission, and partial backordering. These policies are combined with an integral inventory control policy, which releases raw items only when an incoming order is accepted and keeps the inventory position (total inventory minus outstanding orders) constant. The objective is to determine the inventory level and the maximum number of backorders, as well as the admission probability that maximize the mean profit rate of the system. The system is modeled as a closed queueing network and its performance is computed analytically. The optimal parameters for each policy are found using exhaustive search and convex analysis. Numerical results show that managing inventory levels and sales jointly through partial backordering achieves higher profit than other control policies.     

Three level partial trade credit with promotional cost sharing

In this paper, an economic ordered quantity (EOQ) model, specifically for a newly launched product has been developed with selling price, customers’ credit period and customers’ credit amount induced demand under three levels of partial trade credit policy, where a supplier, a wholesaler and a retailer offer some credit periods on some fraction of the total purchased amount to the wholesaler, the retailer and the customer respectively. Also, here it is assumed that the retailer obtained a quantity discount from the wholesaler on purchased units above a certain level. In addition, the wholesaler and the retailer both enjoy freight charge discount according to the ordered quantity. Retailer introduces a promotional cost to increase the base demand of the item. Objective of this investigation is to maximize the profit of the retailer as well as the wholesaler. It is established that if the wholesaler contributes some portion of the promotional cost then individual profits as well as the joint profit increases. Due to the uncertainty and vagueness of different inventory costs, the proposed model is also discussed in fuzzy and rough environments. Combining the features of particle swarm optimization (PSO) and simulated annealing (SA) a hybrid algorithm named Particle Swarm-Simulated Annealing (PSSA) is developed to find the most appropriate strategies for the proposed model. Efficiency of this algorithm is tested and compared with PSO and genetic algorithm (GA) for a set of benchmark test problems. The model is illustrated with numerical examples and some managerial insights are outlined.     

An integrated multi-stage supply chain inventory model under an infinite planning horizon and continuous price decrease

This paper studies an integrated inventory model in a supply chain that involves procurement, production and delivery activities. The model is studied in an environment where products experience continuous price decrease and planning is performed in an infinite time horizon. In this model, a manufacturing facility purchases a fixed-quantity of raw materials from an outside supplier, processes the materials, and delivers a fixed-quantity of finished products to a customer periodically. In order to take advantage of the decreasing price trend, customers demand frequent deliveries of small lots of finished products, and this inventory management strategy has been used by many successful companies in technology-related industries. Therefore, the ultimate intention of this research is to study and model the inventory system for high-tech companies whose products are experiencing continuous price decrease. This model is used to determine an optimal economic lot size model for raw material procurement, production setup and finished goods delivering under an infinite planning horizon. Two efficient algorithms are developed in this paper to solve this nonlinear model and the test results consistently indicate that ordering of raw materials and delivery of finished goods should be frequent in small lots for low ordering and shipment costs. Finally an operational schedule is provided to show the implementation procedure of the model.     

Pricing games of mixed conventional and e-commerce distribution channels

In this paper, a distribution system is studied, in which a supplier sells a common product through conventional (physical retailer) and e-commerce (e-tailers) channels. We examine two types of Stackelberg pricing games and one type of Nash pricing game in this dual-channel distribution system. We also analyze the effects of several key factors (i.e., the supplier’s pricing mode, game schemes, and efficiency of e-channel in relation to acceptance of channels) on the resulting prices as well as the profits for the supplier and the retailer, respectively. This paper is an effort to examine modeling competition in the multiple-channel environment from a pricing viewpoint. We find that channel acceptance plays a critical role in influencing equilibrium prices and profits in the dual-channel distribution system. When the customer acceptance of one channel exceeds a certain threshold, this channel cannibalizes all retail sales and dominates the distribution system. The supplier can make more profits by adopting a differential pricing strategy; on the contrary, the retailer prefers uniform pricing. Numerical analysis indicates that both the supplier and the retailer are worse off in the Nash game than in the Stackelberg games. The supplier prefers an e-channel with higher efficiency, whereas the physical retailer has to maintain higher channel acceptance to maintain its position in the distribution system.     

Using robust optimization for distribution and inventory planning for a large pulp producer

Södra Cell is a world leading producer of pulp and has a large distribution network for its pulp products. This network includes production mills in Sweden and Norway, terminals in European harbours and inland locations, and many customers. The company uses several transport modes including long chartered vessels, spot vessels, trains, barges and trucks. The company uses a supplier managed inventory with a large proportion of its customers. This makes the logistic planning including transportation and inventory critical, as Södra Cell has direct responsibility of their customers’ inventories. However, there is still some uncertainty regarding customer demand and Södra Cell has traditionally used a safety stock inventory approach to handle this. In this paper, we introduce a robust optimization approach to handle the uncertainty and to establish a distribution plan, together with related inventory management. With this approach there is no need for explicit safety stock levels. This is instead taken into account directly through the robust solution. In the proposed model, we can use practical characterization and historical information on the uncertainty. An important result with this is that we can avoid solutions that are too conservative and costly as in standard robust models. A large case study from Södra Cell is used to validate the proposed approach against the traditional approach with safety stock. The analysis is based on simulations and it shows that the robust approach is more cost efficient and can be used as a basis in a decision support system.     

Two-echelon competitive integrated supply chain model with price and credit period dependent demand

This study considers a two-echelon competitive supply chain consisting of two rivaling retailers and one common supplier with trade credit policy. The retailers hope that they can enhance their market demand by offering a credit period to the customers and the supplier also offers a credit period to the retailers. We assume that the market demand of the products of one retailer depends not only on their own market price and offering a credit period to the customers, but also on the market price and offering a credit period of the other retailer. The supplier supplies the product with a common wholesale price and offers the same credit period to the retailers. We study the model under a centralised (integrated) case and a decentralised (Vertical Nash) case and compare them numerically. Finally, we investigate the model by the collected numerical data.     

A tabu search procedure for coordinating production,inventory and distribution routing problems

This paper addresses the problem of optimally coordinating a production‐distribution system over a multi‐period finite horizon, where a facility production produces several items that are distributed to a set of customers by a fleet of homogeneous vehicles. The demand for each item at each customer is known over the horizon. The production planning determines how much to produce of each item in every period, while the distribution planning defines when customers should be visited, the amount of each item that should be delivered to customers and the vehicle routes. The objective is to minimize the sum of production and inventory costs at the facility, inventory costs at the customers and distribution costs. We also consider a related problem of inventory routing, where a supplier receives or produces known quantities of items in each period and has to solve the distribution problem. We propose a tabu search procedure for solving such problems, and this approach is compared with vendor managed policies proposed in the literature, in which the facility knows the inventory levels of the customers and determines the replenishment policies.     

A numerical solution for a two-stage production and inventory system with random demand arrivals

This paper is about the study of a production lot sizing problem consisting of customers, one retailer, and one manufacturer. Demand from customers arrives randomly at a retailer one unit at a time. The retailer replenishes inventory from the manufacturer upon receiving a customer's order after its inventory depleted to zero. The manufacturer's production rate is assumed to be a finite constant. A production cycle starts when the manufacturer's inventory falls to or below zero and stops when its on-hand inventory reaches its optimal level. During the uptime in a production cycle, inventory is being built while randomly arriving orders from retailer are being fulfilled. The order arrival times from customers are independently and identically distributed, hence the inventory processes at both the manufacturer and the retailer become a renewal process that is difficult to solve analytically for a general distribution of order arrival time. Therefore, a numerical approach is used in developing a search procedure to obtain the optimal solution to the problem. Employing such a numerical approach, we also investigate how optimal solutions in different cases will change over the spectrum of some key parameters of the problem.     

Backup agreements with penalty scheme under supply disruptions

This article considers a supply chain for a single product involving one retailer and two independent suppliers, when the main supplier might fail to supply the products, the backup supplier can always supply the products at a higher price. The retailer could use the backup supplier as a regular provider or a stand-by source by reserving some products at the supplier. A backup agreement with penalty scheme is constructed between the retailer and the backup supplier to mitigate the supply disruptions and the demand uncertainty. The expected profit functions and the optimal decisions of the two players are derived through a sequential optimisation process. Then, the sensitivity of two players’ expected profits to various input factors is examined through numerical examples. The impacts of the disruption probability and the demand uncertainty on the backup agreement are also investigated, which could provide guideline for how to use each sourcing method.     

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.     

An integrated retail space allocation and lot sizing models under vendor managed inventory and consignment stock arrangements

In this paper, we develop integrated retail shelf space allocation and inventory models for a single item with a stock dependent demand. The integrated models are developed for a supply chain operating under vendor-managed inventory (VMI) and consignment stock (CS) agreement. More precisely, the supplier is responsible for initiating orders on behalf of the retailer and decides about the size of each order, the quantity to be displayed on the shelves, and the reorder point. In addition, the supplier owns the stock at the retailer’s premises until it is sold. We develop mathematical models to assess the benefits accrued by both parties as a result of the adoption of VMI–CS partnership. Results from the numerical experimental study show that such partnership is more attractive to all supply chain members when the retailer provides a flexible display capacity. Moreover, the supplier can use his/her selling price and the maximum allocated shelf space as negotiation means to benefit from the partnership.     

Optimization of cost and service level in the presence of supply chain disruption risks: Single vs. multiple sourcing

The coordinated supplier selection and customer order scheduling in the presence of supply chain disruption risks is studied for single and multiple sourcing strategies. Given a set of customer orders for products, the decision maker needs to select a single supplier or a subset of suppliers for purchasing parts required to complete the customer orders, and schedule the orders over the planning horizon, to mitigate the impact of disruption risks. The suppliers are located in different geographic regions and the supplies are subject to different types of disruptions: to random local disruptions of each supplier individually, to random regional disruptions of all suppliers in the same region simultaneously and to random global disruptions of all suppliers simultaneously. For any combination of suppliers hit by different types of disruptions, a formula for calculating the corresponding disruption probability is developed. The obtained combinatorial stochastic optimization problem is formulated as a mixed integer program with conditional value-at-risk as a risk measure. The problem objective is either to minimize expected worst-case cost or to maximize expected worst-case customer service level, i.e., the expected worst-case fraction of customer orders filled on or before their due dates. The risk-averse solutions that optimize worst-case performance of a supply chain under disruptions risks are compared for the two sourcing strategies and the two objective functions. Numerical examples and computational results are presented and some managerial insights on the choice between the two sourcing strategies are reported.