考虑库容与订货批量约束的(R, Q) 策略优化

受订货批量和库容限制的购买商向单供应商采购单种产品,以其相邻两次订货间单位时间期望总成本最小为目标建立(R,Q)策略优化模型.针对均匀分布需求给出求解方法,结合算例从资源约束、成本参数及需求特征3个方面进行敏感性分析.将随机需求与资源约束下的安全库存与订货批量进行联合优化,克服已有(R,Q)策略研究将一定时期随机需求期望值默认为最优采购总量,并由此计算订货费、货物成本及缺货成本的不足,可为供应商的选择提供依据。     

Quasi-optimal integrated production, inventory and maintenance policies for a single-vendor single-buyer system with imperfect production process

In this paper we deal with the integrated supply chain management problem in the context of a single vendor-single buyer system for which the production unit is assumed to randomly shift from an in-control to an out-of-control state. At the end of each production cycle, a corrective or preventive maintenance action is performed, depending on the state of the production unit, and a new setup is carried out. Two different integrated production, shipment and maintenance strategies are proposed to satisfy the buyer’s demand at minimum total cost. The first one suggests that the buyer orders batches of size nQ and the vendor produces nQ and makes equal shipments of size Q. The second policy proposes that to satisfy the same ordered quantity, the vendor produces separately smaller batches of size Q, n times. The total integrated average cost per time unit corresponding to each strategy is considered as the performance criterion allowing choosing the best policy for any given situation.     

A supply chain contract with flexibility as a risk-sharing mechanism for demand forecasting

Demand forecasting is one of the main causes of the bullwhip effect in a supply chain. As a countermeasure for demand uncertainty as well as a risk-sharing mechanism for demand forecasting in a supply chain, this article studies a bilateral contract with order quantity flexibility. Under the contract, the buyer places orders in advance for the predetermined horizons and makes minimum purchase commitments. The supplier, in return, provides the buyer with the flexibility to adjust the order quantities later, according to the most updated demand information. To conduct comparative simulations, four-echelon supply chain models, that employ the contracts and different forecasting techniques under dynamic market demands, are developed. The simulation outcomes show that demand fluctuation can be effectively absorbed by the contract scheme, which enables better inventory management and customer service. Furthermore, it has been verified that the contract scheme under study plays a role as an effective coordination mechanism in a decentralised supply chain.     

Multi-period dynamic supply contracts with cancellation

This paper considers a class of multi-period dynamic supply contracts in which a buyer orders a product from a supplier in each period and the supplier allows the buyer to cancel a portion of an outstanding order with penalty during a planning horizon. We assume that both the buyer and the supplier have common knowledge. We first characterize the buyer's ordering and canceling policy that minimizes his expected cost during the planning horizon. We also characterize the supplier's optimal production policy under a very mild assumption on the costs of production and storage. Based on this structure, we then use simulation to show how the supplier chooses cancellation costs that minimize her expected cost during the planning horizon. Our simulation shows that both the buyer and the supplier would benefit from the contract.     

A mathematical model for order splitting in a multiple supplier single-item inventory system

In this paper we develop a mathematical model which considers multiple-supplier single-item inventory systems. The lead times of the suppliers and demand arrival rate are random variables. All shortages are backordered. Continuous review (s, Q) policy has been assumed. When the inventory level hits the reorder level, the total order is split among n suppliers. The problem is to determine the reorder level and order quantity for each supplier so that the expected total cost per time unit, including ordering cost, procurement cost, inventory holding cost and shortage cost is minimized. We also conduct extensive numerical experiments to show the advantages of our model compared to the relevant models in the literature. In addition, some managerial insights are observed.     

Contracting for vendor‐managed inventory with a time‐dependent stockout penalty

We examine vendor‐managed inventory contracts in a (Q, r) inventory system between a supplier and a retailer, in which a stockout penalty is charged to the supplier based on the length of the time period during which stockouts occur at the retailer. Linear and quadratic forms of the time‐dependent stockout penalty are considered. For the deterministic demand case, we find that the quadratic form of time‐dependent stockout penalty is equivalent to a proportional stockout penalty per unit short per unit time. For the stochastic demand case, we provide the exact cost expressions for the supplier and the retailer with a linear time‐dependent stockout penalty. We also discuss how the stochastic model can be extended to the case with a quadratic time‐dependent stockout penalty when there is at most one outstanding replenishment order at any point of time. We provide several interesting computational results.     

Optimal transfer,ordering and payment policies for joint supplier–buyer inventory model with price-sensitive trapezoidal demand and net credit

This study aims at formulating an integrated supplier–buyer inventory model when market demand is variable price-sensitive trapezoidal and the supplier offers a choice between discount in unit price and permissible delay period for settling the accounts due against the purchases made. This type of trade credit is termed as ‘net credit’. In this policy, if the buyer pays within offered time M₁, then the buyer is entitled for a cash discount; otherwise the full account must be settled by the time M₂; where M₂ > M₁ ? 0. The goal is to determine the optimal selling price, procurement quantity, number of transfers from the supplier to the buyer and payment time to maximise the joint profit per unit time. An algorithm is worked out to obtain the optimal solution. A numerical example is given to validate the proposed model. The managerial insights based on sensitivity analysis are deduced.     

Supply chain financing with advance selling under disruption

We study a financing problem in a supply chain (SC) consisting of one supplier and one buyer under supply disruption. The supplier could face a disruption at its end which could effectively reduce its yield in case of disruption, thereby resulting in supply yield uncertainty. The retailer can finance the supplier using advance selling that can help mitigate the impact of disruption. We model this problem as a Stackelberg game, where the supplier as the leader announces the wholesale price and the retailer responds by deciding its optimal order quantity given stochastic demand and an exogenous fixed retail price. The supplier then commences production and a disruption can happen with a known probability. We assume that under disruption the quantity delivered is a fraction of the initial quantity ordered by the retailer. The retailer loses any unmet demand. We analyze three different scenarios of the Stackelberg game, namely no advance selling with disruption, advance selling without disruption, and advance selling with disruption. Our results indicate that advance selling can be used to mitigate the impact of supply disruption and at the same time could lead to an increase in the overall SC profit.     

Bullwhip effect measure in a seasonal supply chain

In this study, the bullwhip effect in a seasonal supply chain was quantified by considering a two echelon supply chain which consists of one supplier and one retailer. The external demand occurring at the customer was assumed to follow a SARMA (1, 0) X (0, 1) _s scheme, a seasonal autoregressive-moving average process, while the retailer employed an base-stock policy to replenish their inventory. The demand forecast was performed with a SARMA (1, 0) X (0, 1) _s using the minimum mean-square error forecasting technique. In order to develop the bullwhip effect measure in a seasonal supply chain, the lead time demand forecast, forecast error, and the optimal inventory policy at the retailer were derived in sequence. The variance of order quantity based on these results was obtained. Then, various properties were derived by analyzing the bullwhip effect measure. Specifically, it was determined that the seasonal cycle plays an important role in bullwhip effect under a seasonal supply chain. The findings also point out that the replenishment lead time must be less than the seasonal cycle in order to reduce the bullwhip effect. Therefore, the lead time needs to be reduced through collaboration between the retailer and supplier.     

Production planning and backup sourcing strategy of a buyer-dominant supply chain with random yield and demand

This paper studies the backup sourcing strategy of the buyer and the production planning of the supplier in presence of both random yield and random demand. Since the production is susceptible to the randomness of yield beyond the control of the supplier, the buyer may access to a backup sourcing option for the finished items. We analyse the value of backup sourcing for both the decentralised and centralised channels. Backup sourcing strategy of the buyer may lower the supply chain's performance. We show that the order quantity of the buyer does not change the stocking factor of the supplier's input. Meanwhile, compared with the centralised operation, the decentralised operation is more dependent on the backup sourcing to reduce supply shortage of the contracting supplier. From the channel's perspective, an incentive scheme is developed to facilitate the coordination of both the buyer and the contracting supplier, we show that the proposed option contract can allow the supply chain members to share the respective risks involved in the production and selling processes. Finally, we also provide qualitative insights based on numerical examples of the centralised and decentralised solutions.     

Combined optimal price and optimal inventory replenishment policies when a sale results in increase in demand

When a supplier reduces the price of a product temporarily a buyer might place a large order and offer a sale on these units to its customers. In most cases a price discount results in an increase in demand. In this paper we relax the constant demand assumption made in most studies of inventory systems with price changes. We analyze the options available to a buyer and develop profit functions for different combinations of sales period and replenishment time and present optimal ordering policies. The paper also presents a procedure to include any relationship between price and demand to determine the combined optimal price and optimal order quantity.     

A quantity flexibility contract model for a system with heterogeneous suppliers

This paper focuses on a quantity flexibility contract through which two or more heterogeneous suppliers periodically deliver a single type of product to a buyer as promised in the contract. The buyer starts each period by informing each supplier of the order size for the period and the reservation quantity for all future periods within a planning horizon. The order size for the current period is finalized according to the amount previously reserved, although this amount can be increased or decreased by a predetermined percentage of the reservation amount.In this paper, a linear programming model including several key features of a quantity flexibility contract is developed from the buyer's perspective. A rolling-horizon implementation strategy is suggested for efficient implementation of the contract. Computational experiments demonstrate that the proposed method can be used to determine a cost effective solution for the buyer in a reasonable amount of time.     

Inventory control model for a supply chain system with multiple types of items and minimum order size requirements

This paper considers a replenishment problem for a single buyer who orders multiple types of items from two or more heterogeneous suppliers in order to sell to end customers. The buyer periodically orders each type of item from the suppliers according to a select inventory control policy. Processing the order, each supplier enforces the policy that an order from the buyer must meet a predetermined minimum order quantity (MOQ). Therefore, the buyer must decide how much to order from each supplier considering the current inventory level, demand forecast, and MOQ requirement. The buyer's problem is formulated as an integer programming model and an efficient implementation strategy is suggested to apply the model to real problems. Numerical experiments are performed to test the validity of the proposed model as well as the efficiency of the implementation strategy. The experimental results show that this model combined with the implementation method yields a considerable cost reduction compared to the most efficient policy currently available.     

Sourcing with random yields and stochastic demand: A newsvendor approach

We studied a supplier selection problem, where a buyer, while facing random demand, is to decide ordering quantities from a set of suppliers with different yields and prices. We provided the mathematical formulation for the buyer's profit maximization problem and proposed a solution method based on a combination of the active set method and the Newton search procedure. Our computational study shows that the proposed method can solve the problem efficiently, and is able to generate interesting and insightful results that lead us to various managerial implications.

Scope and purpose

In today's globally competitive environment, decision makers in supply chains face numerous challenges particularly regarding the selection of suppliers or outsourcing partners. To assist in this endeavor, we examined a double-layered supply chain where a buyer facing the end users has the option of selecting among a cohort of suppliers. The available suppliers may have different yield rates and unit costs. The buyer has to decide, given the stochastic nature of the problem's governing parameters, whether or not to order from each supplier, and if so how much. We developed a ‘newsvendor-style’ model for the problem, and proposed a solution algorithm for it. Numerical studies were performed to provide some insights for supplier selection and order quantity decisions.     

Coordinating orders in a two echelon supply chain with controllable lead time and ordering cost using the credit period

In this research, a coordination mechanism based on a credit period in a two echelon supply chain with one buyer and one supplier, is designed. The buyer is faced with uncertain demand by coping with normal distribution. Both lead time and ordering cost for receiving his order can be reduced at an added cost; in other words, they are controllable. The optimization models with and without integration are proposed. Then a way to coordinate orders in supply chain based on the credit period so that the total cost of supply chain would be minimized is designed. By using this mechanism we also discuss how the credit period is to be determined in order to achieve channel coordination and a win-win outcome. Finally, numerical examples are solved to illustrate the theoretical results and obtain the managerial insights.     

Coordinated ordering decisions for products with short lifecycle and variable selling price

The supplier–buyer coordination is an important policy in the supply chain management. The buyer in the two-echelon inventory system with regular selling season has to face the uncertainty of customer demand, supplier’s delivery time and variable price change. At the same time, the supplier has to consider the inventory holding and delay cost. The objective of this study is to develop an integrated supply chain strategy for products with short lifecycle and variable selling price to entice cooperation. The strategy must provide a win–win situation for both the supplier and the buyer. A numerical case example, sensitivity analysis and compensation mechanism are given to illustrate the model.     

A revised sales rebate contract with effort‐dependent demand: a channel coordination approach

In this paper, simultaneous coordination of order quantity and sales effort (SE) decisions in a supplier/retailer system with stochastic effort‐dependent demand is investigated. The main aim of the proposed model is to attain an optimal balance that results in a Pareto‐efficient solution for both channel members. A revised sales rebate (RSR) contract is developed to achieve channel coordination. In addition to the usual incentive approach of sales rebate schemes, a punitive approach is designed for the new proposed contract as a stockout penalty. Furthermore, some numerical experiments are examined to analyze the performance of the presented model under three decision‐making scenarios (i.e., decentralized, centralized, and RSR). Additionally, some in‐depth sensitivity analyses are conducted to examine the behavior of the supply chain performance under alteration of different parameters. The results show that the proposed RSR contract leads to channel coordination, while both channel members experience a Pareto improving situation. Moreover, it is proved that the RSR contract has significant potential on neutralizing adverse impacts of demand fluctuations on channel performance indicators.     

Dynamic Pricing for Time-Limited Goods in a Supplier-Driven Electronic Marketplace

Existing e-commerce systems employ a pull model of marketing where buyers, possibly through agents, search the e-market for suppliers offering the product of their choice. In contrast, the push model where suppliers agents approach buyers with their products, has been relatively less investigated. Push strategies are particularly appropriate for commodities that have a short shelf-life and, therefore, an elastic demand curve, allowing suppliers to exploit unexpected supply. The speed and low cost of e-commerce makes it particularly suited to the push paradigm. In this paper, we consider time-limited goods in a supplier driven marketplace that employs the push model of marketing. When constrained by a strict deadline to sell the good, the supplier uses a mobile sales agent that visits every buyer and estimates the short run demand curve of the good. At every buyer, the sales agent also employs a heuristic technique called the Maximum Returns Algorithm to recalculate the price of the good, so that the supplier can obtain the best possible gross returns from trading with the buyers. On the other hand, when the deadline to sell is not stringent, the sales agent negotiates the exchange at a point that improves both the buyers utility and the suppliers profit, as compared to the exchange point without negotiation.This research has been supported by QAD Inc. through the California Micro Program, Grants 97-122 and 98-107 and by the DARPA/ONR Grant N66001-00-1-8931.     

An analysis of contract form for supply chains with quality improvement

This study examines different contract forms for the supply chain with quality improvement decision and retailer price decision. We consider three types of quality improvement: cost consuming, cost identical, and cost saving, which correspond to the cases in which quality improvement leads to an increment, no change, and a decrease in production cost, respectively. We compare the performance of two types of quality contracts: (1) pay‐before‐performance contract, under which the supplier receives monetary support from the buyer before exerting quality improvement effort; and (2) pay‐after‐performance contract, under which the supplier receives monetary compensation based on the outcome of effort. We find that the performance of each contract depends on the types of quality improvement. Further, the pay‐after‐performance contract leads to close‐to‐perfect contract efficiency and dominates the pay‐before‐performance contract from the supplier's perspective in most cases. However, this result does not apply in two extended cases: when there are multiple competing suppliers, the pay‐before‐performance contract can dominate the pay‐after‐performance contract if quality improvement is cost consuming; and when the buyer can exert sales effort, neither contract can achieve close‐to‐perfect efficiency in most cases.     

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.