Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints

In this paper, we study a duopolistic market of suppliers competing for the business of a retailer. The retailer sets the order cycle and quantities from each supplier to minimize its annual costs. Different from other studies in the literature, our work simultaneously considers the order size restriction and the benefit of order consolidation, and shows non-trivial pricing behaviour of the suppliers under different settings. Under asymmetric information setting, we formulate the pricing problem of the preferred supplier as a non-linear programming problem and use Karush–Kuhn–Tucker conditions to find the optimal solution. In general, unless the preferred supplier has high-order size limit, it prefers sharing the market with its competitor when retailer’s demand, benefit of order consolidation or fixed cost of ordering from the preferred supplier is high. We model the symmetric information setting as a two-agent non-zero sum pricing game and establish the equilibrium conditions. We show that a supplier might set a ‘threshold price’ to capture the entire market if its per unit fixed ordering cost is sufficiently small. Finally, we prove that there exists a joint-order Nash equilibrium only if the suppliers set identical prices low enough to make the retailer place full-size orders from both.     

Ex post demand information sharing between differentiated suppliers and a common retailer

We consider ex post demand information sharing in a two-echelon supply chain in which two suppliers sell differentiated products through a common retailer. We model three scenarios of information sharing to characterise the conditions under which information sharing may benefit or hurt different players: (1) no supplier is informed; (2) only one supplier is informed; and (3) both suppliers are informed. We find that the retailer may voluntarily share the low demand information when the product differentiation and demand magnitude satisfy certain conditions. In contrast, the retailer has no incentive to share the high demand information, even though this information benefits the suppliers. To achieve information sharing, we propose a side payment mechanism, which allows benefitted players to subsidise hurtful players. Finally, we extend our model by considering a situation where the suppliers have limited capacity and may invest to ramp up production capacity to satisfy a high demand.     

Mitigating supply disruption with a backup supplier under uncertain demand: competition vs. cooperation

In case of supply disruption following major disasters, many supply chains tend to break down due to stock-outs and take a long time to recover. However, by keeping emergency sources of supply, some supply chains continue to function smoothly even after a major disaster. In this work, using a game-theoretic-framework, we consider a two-suppliers-one-retailer supply chain with price-dependent stochastic demand in which suppliers are prone to disruption. To investigate the impact of supply disruption we consider two models: SC model, in which the retailer does not maintain any emergency sources of supply against any supply disruption, and SCB model, in which the retailer maintains a backup supplier to mitigate the impact of supply disruption. We mainly focus on the pricing strategies of the suppliers and the mitigating strategies of the retailer under supply and demand uncertainty. We address two coordinating mechanisms to enhance supply chain performance. Our results indicate that in the presence of supply disruption, even with lower probabilities, the retailer would always prefer to take the advantage of a backup supplier and the optimal reserve quantity increases with disruption probabilities. We further investigate the scenario in which the suppliers would always prefer to cooperate with each other.     

Joint pricing and inventory strategies in a supply chain subject to inventory inaccuracy

This paper focuses on pricing strategies, inventory policies for a supply chain when Radio Frequency Identification (RFID) technology is adopted to cope with inventory inaccuracy. The supply chain consists of one supplier and one retailer, in which the RFID tag price is shared between the supplier and the retailer. We present and compare the performance differences between a wholesale price contract and a consignment contract when the retailer is the Stackelberg leader and the supplier is the follower. Based on the optimal pricing and inventory decisions, an interesting observation of contract selection is that there are two critical values of inventory available rate such that when the inventory availability is less than the lower value, both the supplier and the retailer prefer a consignment contract; when the inventory availability is greater than the upper value, a wholesale price contract is their best choice; when the inventory availability is between the two values, the supplier prefers a wholesale price contract and the retailer prefers a consignment contract. Additionally, there exist threshold values of RFID tag price and sharing rate to determine the contract preference for the retailer. Furthermore, the profits of both the supplier and the retailer are independent of the RFID tag price sharing rate in a wholesale price contract, and the supplier has the incentive to invest in RFID tag cost in a consignment contract.     

Decentralized inventory control in a two-stage capacitated supply chain

This paper investigates a two-stage supply chain consisting of a capacitated supplier and a retailer that faces a stationary random demand. Both the supplier and the retailer employ base stock policies for inventory replenishment. All unsatisfied demand is backlogged and the customer backorder cost is shared between the supplier and the retailer. We investigate the determination of decentralized inventory decisions when the two parties optimize their individual inventory-related costs in a noncooperative manner. We explicitly characterize the Nash equilibrium inventory strategies and identify the causes of inefficiency in the decentralized operation. We then study a set of simple linear contracts to see whether these inefficiencies can be overcome. Finally, we investigate Stackelberg games where one of the parties is assumed to be dominating.     

Order timing strategies in a single-supplier,multi-retailer system

The timing of retailer order placement is an important factor in supply chain performance in systems with uncertain end-customer demands. Retailers often prefer short order lead times, which permits the resolution of demand uncertainty prior to order placement, and reduces the risks associated with excess inventory. Suppliers, in contrast, prefer long lead times, in order to match supply output with retailer demand. These conflicting preferences create tension between a supplier and retailers regarding order timing preferences. This paper considers order timing preferences within a strategic framework involving a supplier and one of its retailers in a multiple-retailer system. We identify and explore several mechanisms a supplier can use within this framework to induce early retailer order placement and improve expected cost performance.     

Benefits of retailer–supplier partnership initiatives under time-varying demand: a comparative analytical study

This paper aims to help supply chain managers to determine the value of retailer–supplier partnership initiatives beyond information sharing (IS) according to their specific business environment under time-varying demand conditions. For this purpose, we use integer linear programming models to quantify the benefits that can be accrued by a retailer, a supplier and system as a whole from shift in inventory ownership and shift in decision-making power with that of IS. The results of a detailed numerical study pertaining to static time horizon reveal that the shift in inventory ownership provides system-wide cost benefits in specific settings. Particularly, when it induces the retailer to order larger quantities and the supplier also prefers such orders due to significantly high setup and shipment costs. We observe that the relative benefits of shift in decision-making power are always higher than the shift in inventory ownership under all the conditions. The value of the shift in decision-making power is greater than IS particularly when the variability of underlying demand is low and time-dependent variation in production cost is high. However, when the shipment cost is negligible and order issuing efficiency of the supplier is low, the cost benefits of shift in decision-making power beyond IS are not significant.     

Risk, risk aversion and the optimal time to produce

This paper studies the order-fulfillment process of a supplier producing a customized capital good. When they decide at what time to begin production, suppliers in these industries typically face the following dilemma. On the one hand, their customers expect them to be responsive and the time that they are prepared to wait for the product is much shorter than the time needed to produce and deliver it. On the other hand, it is risky for the suppliers to start production before the customers confirm their orders due to inventory holding costs and the possibility of order cancellation. We offer a model to help understand this dilemma and investigate the comparative statics effects of lead time, lead time uncertainty and the risk aversion of the supplier. Relative to existing work, our model has two novel components: demand distribution updating and the supplier's risk attitude. Previous empirical studies reveal that the supplier is very conservative when commencing the order fulfillment. The studies attribute this to high holding and cancellation costs relative to the delay cost. Our model provides two alternative explanations. First, other than costs, when the supplier starts to produce depends also on how the distribution of the demand arrival time is updated as time progresses. Second, although the effect of increasing risk aversion of the supplier on the optimal time to produce is ambiguous, we show that it plays a major role in the decision and thus it alone may have caused the supplier to be conservative.     

寄售合同的设计与拍卖研究

分析了零售商面对多个供应商竞争有限销售渠道资源时的供应商选择策略以及收益分配机制.供应商的产能成本参数为供应商的私有信息,产能成本参数独立同分布.供应商以寄售模式销售某产品,负责产品的补货,零售商仅承担产品库存管理费用.为识别产能成本最低的供应商,零售商将分享总销售收益的比例设计为供应商产能成本的函数,并将包含此函数的寄售合同当作物品在多个供应商间进行拍卖.供应商对此寄售机会进行估价,并以自己的估价进行竞标,竞标价最高的供应商将提前支付一笔进场费给零售商,从而赢得此寄售机会.这种寄售合同拍卖机制能够同时解决供应商选择与确定理想的分享收益比例的问题,对实践中采用的进场费的确定问题给出了解释.最后通过数值算例分析了相关参数对零售商以及获胜供应商的期望收益的影响.     

Horizontal cooperation and information sharing between suppliers in the manufacturer–supplier triad

In this paper, we analyse a collusion and information-sharing problem between two suppliers in a manufacturer–supplier triad. The manufacturer treats one supplier as a strategic supplier and the other as a backup. While the strategic supplier offers modules of good quality but longer lead times, the backup supplier offers modules with inferior quality but shorter lead times. If there are urgent orders, the manufacturer must turn to the backup supplier. However, it is difficult for the manufacturer to estimate whether the urgent supplier has put extra effort into their production. We formulate this problem by assuming that the urgent supplier has either low or high production costs. To take advantage of the competition between two suppliers, the manufacturer can design a contract menu that defines total payment and lead times, under which both suppliers may be worse off. Meanwhile, it is possible for the suppliers to tacitly form a coalition, and to even share the private cost information. We study this problem by formulating it as a three-stage game. Furthermore, we investigate the variation of profits for each part of the supply chain. We find that the manufacturer is worse off when suppliers cooperate or share private information. Both suppliers, however, can benefit from cooperation and information sharing.     

单供应商面对具有多个销售点的零售商时的VMI模型研究

在供应商管理用户库存（VMI）环境中,当面临的具体条件不同时,供应商和零售商的利润分配是不同的,论述了当一个供应商面对具有多个销售点的零售商时的VMI模型,此时供应商负责库存决策,他可以在各个销售点之间转运（Transshipment）库存.建立了供应商和零售商的一个Stackelberg博弈,零售商作为领导者是通过决定销售价格来体现的.结果显示最终供应商和零售商可以达到一个子博弈精练纳什均衡,零售商在该模式下获得了很大的利润份额.给出了一个算例计算了均衡时的库存量和销售价格.     

Blockchain adoption or contingent sourcing? Advancing food supply chain resilience in the post-pandemic era

In the post-pandemic era, food supply chains and firms therein are facing unprecedented severe challenges, because once infection is detected, numerous products must be recalled or abandoned, and both suppliers and retailers in the supply chain suffer enormous loss. To survive under the pandemic, retailers have adopted different sourcing strategies, such as contingent sourcing, which, in turn, affect the upstream suppliers and hence the resilience of the whole supply chain. With the rapid development of digital technologies, retailers nowadays can utilize blockchain as a reliable and efficient way to reduce product risk and hence advance the resilience of food supply chains by improving product traceability and inspection accuracy, and making sourcing transparent. In this paper, we develop a game-theoretic model to investigate the interrelation between the retailer’s decisions on blockchain adoption and sourcing strategies. We consider that a retailer originally orders from a risky supplier while conducting an imperfect inspection to detect infected products before selling. The retailer may speculatively keep on ordering from the risky supplier or adopt contingent sourcing by ordering from an alternative safe supplier. The retailer also has an option to implement blockchain to improve the inspection accuracy and product traceability. We derive the optimal retail prices under different sourcing strategies with and without blockchain adoption and then analyze the incentives for sourcing strategy and blockchain adoption. Then, we identify the conditions of an all-win situation for food retailer, supplier, supply chain resilience, and consumers with/without government subsidy. Finally, we extend to consider the situation that some consumers have health-safety concerns and preferences for blockchain adoption.     

The economic lot and delivery scheduling problem: models for nested schedules

We investigate the problem of simultaneously determining schedules for the production of several assembly components at a captive supplier and delivery of those components to the customer. We consider situations in which production economies of scale in the form of setup costs and/or setup times make it desirable for the supplier to produce in batches that are larger than the desired order quantity of the customer. The objective is to minimize the average cost per unit time of transportation, inventory at both the customer and the supplier, and, where applicable, setup costs.

We develop a heuristic solution procedure and a lower bounding approach for this problem. We also report experimental results that indicate that the heuristic provides solutions close to the lower bound in most instances. Our results provide a means to answer the often-asked question of whether just-in-time suppliers are (or should be) asked to hold inventory for their customers, and the question of how much setup costs and setup times need to be reduced so that the suppliers no longer need to hold that inventory.     

The implication of vendor inventory liability period in a decentralised assembly system

This paper investigates a decentralised assembly system that consists of one manufacturer and multiple suppliers who produce the complementary components. In a single selling season, the manufacturer initially sets a vendor inventory liability period (VILP) to control the suppliers’ delivery times, and the suppliers simultaneously determine when to deliver their components. Given the firms’ equilibrium strategies, we find that it is not wise for the manufacturer to set an overly long VILP, since having no inventory is not always beneficial to the manufacturer. A supplier may choose to postpone his delivery when the length of the VILP increases or the other suppliers’ deliveries are delayed, and either of these conditions is detrimental to the supplier’s profitability. We also examine the impact of VILP under different situations and find that having VILPs customised for different suppliers can reduce the manufacturer’s cost as well as improve the supply chain’s overall efficiency.     

Theory of constraints based mafia offer for supply chains of deteriorating products

Mafia offer is an unbelievably good offer that a company makes to its customers; the attractiveness of the offer makes it impossible for the customers to decline the offer and difficult for the competitors to match it [Cox, James, III, and John Schleier. 2010. Theory of Constraints Handbook. McGraw-Hill]. This study analyses the performance of one such offer that a producer of deteriorating items can make to its customers in the supply chain, such as retailers and distributors. The results from the analytical model show that the mafia offer increases the profits of both the producer and the retailer in a deteriorating items' supply chain. The efficacy of the proposed offer is tested for multiple combinations of ordering cost, wholesale price, and the retailer's cash constraints. The experimental results suggest that the producer would be able to increase its profits by more than 60%, for a given level of retailer's profits, owing to the mafia offer. The availability of the existing items offered by the retailer will increase significantly, despite a reduction in the retailer's inventory levels. The offer will result in an average increase of over 56% in the variety of items held by the retailer. The producer will also be able to command significantly higher margins (more than 44%) from the retailer for the existing items without adversely affecting the retailer's profitability.     

Managing Fashion Goods Inventories: Dynamic Recourse for Retailers with Outlet Stores

The proliferation of both online and bricks and mortar outlet stores underscores the observation that secondary markets are readily accessible to retailers of short-life-cycle products. These secondary markets provide recourse channels for retailers to sell excess inventory of out-of-favor items at reduced prices when overstocking occurs in a primary market. We study the problem of determining when a retailer should terminate its primary selling season by selling remaining inventory on a secondary market. The retailer has a single opportunity to procure prior to a primary selling season consisting of multiple periods. Demand in each period is random, but correlated. At the end of each period, any remaining inventory incurs a holding cost. Then, based upon the current level of inventory and the cumulative demand-to-date, the retailer decides either to terminate the primary selling season by selling all or part of the remaining inventory on a secondary market, or to extend the current primary selling season by another period. We develop structural properties of the optimal policy for determining when to terminate the primary selling season, and we develop corresponding implications for procurement.     

Component Inventory Costs in an Assembly Problem with Uncertain Supplier Lead-Times

We present a generic study of inventory costs in a factory stockroom that supplies component parts to an assembly line. Specifically, we are concerned with the increase in component inventories due to uncertainty in supplier lead-times, and the fact that several different components must be present before assembly can begin. It is assumed that the suppliers of the various components are independent, that the suppliers' operations are in statistical equilibrium, and that the same amount of each type of component is demanded by the assembly line each time a new assembly cycle is scheduled to begin. We use, as a measure of inventory cost, the expected time for which an order of components must be held in the stockroom from the time it is delivered until the time it is consumed by the assembly line. Our work reveals the effects of supplier lead-time variability, the number of different types of components, and their desired service levels, on the inventory cost. In addition, under the assumptions that inventory holding costs and the cost of delaying assembly are linear in time, we study optimal ordering policies and present an interesting characterization that is independent of the supplier lead-time distributions.     

Supply chain coordination under trade credit and retailer effort

In this paper, we study the role of trade credit in coordinating a Capital Constrained Supply Chain in the presence of retailer Effort (CCSCE), essentially because of the impact of its related default risks on the relationship between the chain’s members. We consider a CCSCE consisting of a supplier and a retailer where the retailer may exert costly promotional efforts to increase the market demand but has limited capital and no access to bank financing due to low credit rating. Conversely, the supplier has adequate funds to offer trade credit to the retailer without borrowing from external channels. We then examine whether the existing coordination contracts can still coordinate the CCSCE under trade credit. Our result shows that these contracts can achieve coordination of the supply chain when the interest rate of trade credit is competitively priced. Nevertheless, this position cannot always be reached. That’s why we propose a generalised contract based on risk compensation to coordinate the CCSCE. Using our proposed coordinating contract, the supplier perfectly coordinates the retailer’s decisions for the largest joint profit, and arbitrarily allocates the maximised joint profit among supply chain members. Finally, the numerical study allows to verify this finding. From managerial insights, our results provide the supply chain managers with novel insights on how to combine trade credit with the existing coordination contracts in order to improve the profitability of the entire supply chain as well as the individual member.     

Supply chain management using put option contracts with information asymmetry

We study the problem of hedging demand uncertainty in a supply chain consisting of a risk-neutral supplier and a risk-averse retailer under a buyback contract. We use semi-variance of the possible profit values as a measure of the retailer’s risk attitude. We first study the setting where the supplier can observe the risk type of the retailer and find that in this case the supplier can design a buyback contract that extracts the maximum profit for the supplier. When the retailer’s type is unobservable, a new contract needs to be designed (the ‘option buyback contract’) and we show that in this case the retailers will self-select and chose an order quantity that maximises the total supply chain profit. Through numerical computations, we analyse the dynamics between the benefits of hedging risk, information rent and the retailer’s type, and outline cases when, depending on the shape of the reservation utilities of the retailers, it is too costly for the supplier to manage risk. In conclusion, our results show that whereas semi-variance has appealing properties as a measure of risk, its use introduces analytical challenges that can only be overcome through numerical computation.     

Inventory competition and incentives to back-order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers' back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors' customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players.