A stochastic and asymmetric-information framework for a dominant-manufacturer supply chain

Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at $p/unit. The retail-market demand volume varies with p according to a given demand curve. This basic system is commonly modeled as a manufacturer-Stackelberg ([mS]) game under a “deterministic and symmetric-information” (“det-sym-i”) framework. We first explain the logical flaws of this framework, which are (i) the dominant manufacturer-leader will have a lower profit than the retailer under an iso-elastic demand curve; (ii) in some situations the system’s “correct solution” can be hyper-sensitive to minute changes in the demand curve; (iii) applying volume discounting while keeping the original [mS] profit-maximizing objective leads to an implausible degenerate solution in which the manufacturer has dictatorial power over the channel. We then present an extension of the “stochastic and asymmetric-information” (“sto-asy-i”) framework proposed in Lau and Lau [Lau, A., Lau, H.-S., 2005. Some two-echelon supply-chain games: Improving from deterministic–symmetric-information to stochastic-asymmetric-information models. European Journal of Operational Research 161 (1), 203–223], coupled with the notion that a profit-maximizing dominant manufacturer may implement not only [mS] but also “[pm]”—i.e., using a manufacturer-imposed maximum retail price. We show that this new framework resolves all the logical flaws stated above. Along the way, we also present a procedure for the dominant manufacturer to design a profit-maximizing volume-discount scheme using stochastic and asymmetric demand information.     

Usefulness of resale price maintenance under different levels of sales-effort cost and system-parameter uncertainties

This paper on “resale price maintenance” (RPM) has three main parts:

(i)

Using a simple and parsimonious model, we show that even with only one retailer, a “supplier” or “manufacturer” (hereafter “Manu”) should impose minimum-RPM under some circumstances but maximum-RPM in others. These two sets of circumstances are defined by a very simple formula.     

How a dominant retailer might design a purchase contract for a newsvendor-type product with price-sensitive demand

A dominant retailer will purchase a newsvendor-type product from a manufacturer, who incurs a unit manufacturing cost k. The expected retail demand is a function of the unit retail price p. How should the retailer design her purchase contract? For this increasingly prevalent but inadequately studied scenario, we propose plausible adaptations of several contract formats that have been widely studied in the dominant-manufacturer context. For both symmetric-k and asymmetric-k-knowledge situations, we present performance results of these contracts. Our results then reveal that the performance of these contract formats under our scenario differs considerably from what one would surmise from the well-known results published for closely related scenarios. For example, the widely studied buyback and revenue-sharing formats turn out to be largely ineffective when implemented by a dominant retailer. In contrast, the two-part tariff format performs well relative to the theoretically optimal “menu of contracts.” Our results highlight the need to study purchase contract formats designed specifically for dominant-retailer newsvendor-product channels.     

Dollar vs. percentage markup pricing schemes under a dominant retailer

We investigate two very common pricing schemes for a Stackelberg-dominant retailer: percentage-markup and dollar-markup. We show that when a dominant retailer switches from dollar to percentage markup, the channel’s “overall pie” and the retailer’s “pie-piece” are both enlarged. In contrast, the manufacturer will be forced to levy a lower wholesale price, thus receiving a smaller pie-piece despite the larger pie. The preceding statements hold regardless of whether the demand is deterministic or stochastic. However, the effects of switching to percentage markup on the retail price and sales volume will depend not only on whether the demand is stochastic, but also on the assumed demand-curve shape and on whether demand stochasticity is “additive” or “multiplicative”. Besides presenting a comprehensive set of answers on the comparative performance of dollar- and percentagemarkups, our results also highlight the often overlooked importance of choosing between: (i) dollar- and percentage-markup; and (ii) the formats of the assumed stochasticity and demand curves.     

A comparison of different quantity discount pricing policies in a two-echelon channel with stochastic and asymmetric demand information

In this paper, we study quantity discount pricing policies in a channel of one manufacturer and one retailer. The paper assumes that the channel faces a stochastic price-sensitive demand but the retailer can privately observe the realization of an uncertain demand parameter. The problem is analyzed as a Stackelberg game in which the manufacturer declares quantity discount pricing schemes to the retailer and then the retailer follows by selecting the retail price and associated quantity. Proposed in the paper are four quantity-discount pricing policies: “regular quantity discount”; “fixed percentage discount”; “incremental volume discount” and “fixed marginal-profit-rate discount”. Optimal solutions are derived, and numerical examples are presented to illustrate the efficiency of each discount policy.     

Inventory sharing via circular unidirectional chaining

This research studies the performance of circular unidirectional chaining – a “lean” configuration of lateral inventory sharing among retailers or warehouses – and compares its performance to that of no pooling and complete pooling in terms of expected costs and optimal order quantities. Each retailer faces uncertain demand, and we wish to minimize procurement, shortage and transshipment costs. In a circular unidirectional chain all retailers are connected in a closed loop, so that each retailer can cooperate with exactly two others as follows: receive units (if needed?available) from the left “neighbor” and send units (if needed?available) to the right, and a retailer who receives units from one neighbor is not allowed to send any units to its other neighbor. If the chain consists of at least three nodes and demands across nodes are i.i.d., its performance turns out to be independent of the number of nodes. The optimal stocking is therefore solved analytically. Analytical comparative statics with respect to cost parameters and demand distributions are provided. We also examine thoroughly the cases of uniform demand distribution (analytically) and normal demand distribution (numerically). In the uniform case with free transshipment, a unidirectional chain can save up to 1/3 of the expected cost of separate newsvendors caused by uncertainty. For three nodes, the advantage of complete pooling over unidirectional chaining does not exceed 19%.     

Dual role of price and myopia in a marketing channel

In this paper we study a dynamic two-player channel where the manufacturer controls the wholesale price and the investment in quality and the retailer chooses the retail price. We consider that the retail price affects both the demand and the perceived quality of the brand and that its variations contribute to the building of an internal reference price. One of the model’s distinctive features is that it accounts for the two meanings of price, i.e., its classical objective measure of the cost of acquiring a particular quantity of the product, and its subjective roles as an assessment of the quality of the product and an evaluation of gains or losses (deal vs. sacrifice) resulting from buying a “cheap” or an “expensive” product. This dual computation is done with respect to the internal reference price.     

Minmax regret location–allocation problem on a network under uncertainty

We consider a robust location–allocation problem with uncertainty in demand coefficients. Specifically, for each demand point, only an interval estimate of its demand is known and we consider the problem of determining where to locate a new service when a given fraction of these demand points must be served by the utility. The optimal solution of this problem is determined by the “minimax regret” location, i.e., the point that minimizes the worst-case loss in the objective function that may occur because a decision is made without knowing which state of nature will take place. For the case where the demand points are vertices of a network we show that the robust location–allocation problem can be solved in O(min{p, n − p}n³m) time, where n is the number of demand points, p (p < n) is the fixed number of demand points that must be served by the new service and m is the number of edges of the network.     

On channel coordination through revenue-sharing contracts with price and shelf-space dependent demand

This paper deals with the problem of coordinating a vertically separated channel under a consignment contract with revenue sharing. We consider the demand of the downstream player, e.g., the retailer, being price and shelf-space sensitive. Under such a setting, the retailer decides on the revenue-sharing percentage and the slotting fee. And the upstream player, e.g., the manufacturer, decides on the retail price and the size of shelf-space. For each item sold, the retailer deducts an agreed-upon percentage from the selling price and remits the balance to the manufacturer. We model the decision-making of the two firms as a Stackelberg game, and carry out equilibrium analysis for both the centralized and decentralized regimes of the channel, with and without cooperation. In addition, a profit sharing scheme through a two-part slotting allowance is proposed, which leads to Pareto improvements among channel participants. Our analysis reveals that the non-cooperative game tends to set a higher revenue-sharing percentage and lower slotting fee by the retailer, and a higher retail price and less display space by the manufacturer, which leads to a lower channel profit. The consistent bias can be perfectly rectified by the cooperative game through the proposed two-part contractual agreement.     

Some properties of buyback and other related schemes in a newsvendor-product supply chain with price-sensitive demand

A manufacturer wholesaling to a retailer a ‘newsvendor-type’ product such as a seasonal/fashion good or a perishable food item is considered here. It is known that such a manufacturer/retailer channel has difficulties in fully realizing the market's profit potential. We study a theoretical construct of such a channel and present practically useful results for a manufacturer trying to design more profitable pricing schemes. Specifically, we consider a ‘dominant’ manufacturer supplying a newsvendor-type product to a retailer. The retail market volume varies with the unit retail price according to a stochastic demand curve. We study the design and performance of ‘price-only’, ‘buyback’ and ‘manufacturer-imposed retail price’ schemes. All these schemes have been considered in earlier works. The first part of this paper studies some important but previously overlooked aspects of price-only and buyback schemes. We show that the performance of these schemes is strongly and somewhat counter-intuitively affected by the specific form of demand curve and of demand randomization. Thus, we identify hitherto neglected factors that must be carefully considered when designing pricing schemes for actual implementation. The second part of this paper demonstrates the practicality and merit of using buyback in conjunction with a manufacturer-imposed retail price—an arrangement overlooked in the literature because it is widely mistaken as illegal. Overall, the paper shows how a manufacturer can better realize the market's potential by: (i) modifying slightly the well-known buyback arrangement; and (ii) carefully modelling certain hitherto neglected aspects of the price/demand relationship—a conclusion quite contrary to what one might surmise from the current theoretical literature.     

Advertising coordination games of a manufacturer and a retailer while introducing a new product

Two kinds of vertical cooperative advertising program are considered in a distribution channel constituted by a manufacturer and a retailer, where the manufacturer pays part of the retailer’s advertising costs. In the first participation scheme, the manufacturer chooses his/her advertising participation rate in the retailer’s advertising effort and then each player determines the advertising effort that maximizes his/her profit. In the second scheme, the retailer chooses the manufacturer’s participation rate and then the manufacturer determines the advertising efforts of both players with the objective of maximizing the manufacturer’s profit. Each participation scheme corresponds to a special Stackelberg game: the manufacturer is the leader of the first, while the retailer is the leader of the second. The Stackelberg equilibrium advertising efforts and participation rate in both games are provided. Then the equilibrium strategies of the two players in the analyzed scenarios are compared with the Nash equilibrium in the competitive framework. Finally, the conditions which suggest a special kind of agreement to a player are analyzed. This work was supported by the Italian Ministry of University and Research and the University of Padua.     

Pricing and effort investment for a newsvendor-type product

We investigate a dominant retailer’s optimal joint strategy of pricing and timing of effort investment and analyze how it influences the decision of the manufacturer, the total supply chain profit, and the consumers’ payoff. We consider two pricing schemes of the retailer, namely, dollar markup and percentage markup, and two effort-investment sequences, namely, ex-ante and ex-post. A combination of four cases is analyzed. Our results show that: (1) under the same effort-decision sequence, a percentage-markup pricing scheme leads to higher expected profit for the retailer and the whole supply chain, but a lower expected profit for the manufacturer and a higher retail price for the consumers; (2) under the same markup-pricing strategy, the dominant retailer always prefers to postpone her effort decision until the manufacturer makes a commitment to wholesale price, since it can result in a Pareto-improvement for all the supply chain members. That is, the retailer’s and manufacturer’s expected profits are higher and the consumers pay a lower retail price; and (3) among the four joint strategies, the dominant retailer always prefers the joint strategy of percentage-markup plus ex-post effort decision. However, the dominated manufacturer always prefers the joint strategy of dollar-markup plus ex-post effort decision, which is also beneficial to the end consumers.     

On contracts for VMI program with continuous review (r, Q) policy

Based on continuous review (r, Q) policy, this paper deals with contracts for vendor managed inventory (VMI) program in a system comprising a single vendor and a single retailer. Two business scenarios that are popular in VMI program are “vendor with ownership” and “retailer with ownership”. Taking the system performance in centralized control as benchmark, we define a contract “perfect” if the contract can enable the system to be coordinated and can guarantee the program to be trusted. A revenue sharing contract is designed for vendor with ownership, and a franchising contract is designed for retailer with ownership. Without consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the other one is a perfect contract. With consideration of order policy and related costs at the vendor site, it is shown that one contract can perform satisfactorily and the performance of the other one depends on system parameters.     

Manufacturer's pricing strategy and return policy for a single-period commodity

This paper presents a model for designing the pricing and return-credit strategy for a monopolistic manufacturer of single-period commodities. That is, given the unit manufacturing cost and the unit retail sale price, the manufacturer determines: (i) the unit price C to be charged against the retailer; and (ii) the unit credit V to be given to the retailer for units returned. While the manufacturer is allowed to set C and V, the order quantity Q is set by the retailer in response to the manufacturer's C and V. Among the unexpected findings derived from our model are: (i) unless an external force supports the retailer, otherwise the manufacturer can usually design a (C,V)-scheme that gives himself the lion's share of the profit; (ii) depending on the risk attitudes of the manufacturer and the retailer, the optimal return policy can range from “no returns allowed” to “unlimited returns with full credit”; (iii) instead of losing his profit share to the retailer, a return-credits agreement can often be manipulated by a shrewd manufacturer to increase his profit.     

企业间信息共享的激励问题研究

本文考虑了一个零售商占主导地位但制造商具有市场需求信息优势的二级供应链系统;具体来说,制造商具有确定的市场需求信息,而零售商对市场需求信息仅仅有一个随机先验分布。本文讨论的问题是,当零售商设计采购合同时,制造商是否有意愿去改善零售商的需求信息？如果可能,是否零售商提供的合同越复杂越能激励制造商这么做呢？本文的研究结果表明,(i)制造商希望零售商需求估计的均值(即信息趋势)尽可能地低。但是对于需求估计的方差(即信息精度),则存在一个临界值,低于这个值时,制造商希望零售商需求的方差越大越好;高于这个值时,制造商希望零售商需求的方差越小越好,这意味着制造商在某种程度上愿意与零售商共享信息;(ii)复杂的合同并不能提供更多的激励去促使制造商共享信息。本文的结论意味着需要设计新的机制去促使制造商能够诚实地披露他的私有信息。     

Production and availability policies through the Markov Decision Process and myopic methods for contractual and selective orders

In this paper, we consider a supply chain with one manufacturer, one retailer, and some online customers. In addition to supplying the retailer, manufacturers may selectively take orders from individuals online. Through the Markov Decision Process, we explore the optimal production and availability policy for a manufacturer to determine whether to produce one more unit of products and whether to indicate “in stock” or “out of stock” on website. We measure the benefits and influences of adding online customers with and without the retailer’s inventory information sharing. We also simulate the production and availability policy via a myopic method, which can be implemented easily in the real world. Prediction of simple switching functions for the production and availability is proposed. We find the information sharing, production capacity and unit profit from online orders are the primary factors influencing manufacturer profits and optimal policy. The manufacturer might reserve 50% production capacity for contractual orders from the retailer and devote the remaining capacity to selective orders from spontaneous online customers.     

Three revenue-sharing variants: their significant performance differences under system-parameter uncertainties

In the widely studied ‘revenue sharing’ (hereafter [RS]) contract format, the manufacturer of a product not only charges the retailer a unit wholesale price w, but also requires the retailer to share part of the product's revenue (ie, the unit retail price p) with him. For a product with price-dependent demand, it is well known that if a dominant manufacturer knows the system parameters deterministically, then [RS] gives him the perfect power of simultaneously coordinating the channel and allocating profit arbitrarily. Unfortunately, [RS]'s power deteriorates as the manufacturer's knowledge of the system parameters becomes increasingly uncertain. This paper shows that this deterioration can be substantially reduced by using slightly modified versions of [RS]; these modifications roughly amount to sharing a retailer's gross profit instead of revenue. In other words, this paper presents simple modifications to the classical [RS], leading to contract formats that perform substantially better under system-parameter uncertainty.     

Topological games and continuity of group operations

We consider a topological game GΠ involving two players α and β and show that, for a paratopological group, the absence of a winning strategy for player β implies the group is a topological one. We provide a large class of topological spaces X for which the absence of a winning strategy for player β is equivalent to the requirement that X is a Baire space. This allows to extend the class of paratopological or semitopological groups for which one can prove that they are, actually, topological groups.Conditions of the type “existence of a winning strategy for the player α” or “absence of a winning strategy for the player β” are frequently used in mathematics. Though convenient and satisfactory for theoretical considerations, such conditions do not reveal much about the internal structure of the topological space where they hold. We show that the existence of a winning strategy for any of the players in all games of Banach-Mazur type can be expressed in terms of “saturated sieves” of open sets.     

A real-time decision rule for an inventory system with committed service time and emergency orders

In this paper, we study the inventory system of an online retailer with compound Poisson demand. The retailer normally replenishes its inventory according to a continuous review (nQ, R) policy with a constant lead time. Usually demands that cannot be satisfied immediately are backordered. We also assume that the customers will accept a reasonable waiting time after they have placed their orders because of the purchasing convenience of the online system. This means that a sufficiently short waiting time incurs no shortage costs. We call this allowed waiting time “committed service time”. After this committed service time, if the retailer is still in shortage, the customer demand must either be satisfied with an emergency supply that takes no time (which is financially equivalent to a lost sale) or continue to be backordered with a time-dependent backorder cost. The committed service time gives an online retailer a buffer period to handle excess demands. Based on real-time information concerning the outstanding orders of an online retailer and the waiting times of its customers, we provide a decision rule for emergency orders that minimizes the expected costs under the assumption that no further emergency orders will occur. This decision rule is then used repeatedly as a heuristic. Numerical examples are presented to illustrate the model, together with a discussion of the conditions under which the real-time decision rule provides considerable cost savings compared to traditional systems.     

Profit criteria involving risk in price setting of virtual products

This work deals with pricing of “virtual” products, i.e., products that a retailer can supply after demand has been realized. Such products allow the retailer to avoid holding costs and ensure timely fulfillment of demand with no risk of shortage. Demand is commonly price-dependent and uncertain, and we seek to maximize each of three criteria: expected profit, the likelihood of achieving a profit target, and the profit for a given percentile. Simultaneous multiple criteria are also explored. Two forms of demand uncertainty are considered in the analysis: the multiplicative form, where, due to stochastic dominance, all the investigated profit criteria—and, in fact, any utility function of the profit—can be optimized simultaneously; and the additive form, where stochastic dominance cannot occur. Under the multiplicative form of demand, the property of stochastic dominance is shown to hold in a two-echelon supply chain (comprising both the supplier and the retailer) and in a centralized system.