Amy Hing Ling Lau

Some two-echelon supply-chain games: Improving from deterministic-symmetric-information to stochastic-asymmetric-information models

Abstract Many supply-chain and inventory models use the following two-echelon symmetric-information and deterministic gaming structure: a “manufacturer” wholesales a product to a “retailer,” who in turn retails it to the consumer. The retail market demand varies with the retail price according to a deterministic “demand function” that is known to both the manufacturer and the retailer. It is then assumed that the “players” (the manufacturer and the retailer) arrive at their pricing and batch-size decisions through a Stackelberg game or a “fixed markup percentage” game. The first part of this paper reveals many implausible effects of demand-curve forms on the behavior of these gaming models. However, we do not merely conclude that two-echelon gaming results obtained via assuming one convenient demand-curve form can often become invalid under other demand-curve forms. More importantly, we argue in the second part of the paper that the various implausible effects revealed here suggest a different but more fundamental conclusion: the assumed non-cooperative games are themselves flawed, because “gaming” is meaningless and logically circular in a deterministic-and-symmetrical-information system. We then present an introductory illustration on how the introduction of stochasticity and information- a symmetry leads to more plausible two-echelon supply-chain gaming models. Together, the two parts demonstrate the necessity and practicality of using a stochastic-and-asymmetric-information instead of the prevalent deterministic-symmetric-information approach in many supply-chain models.

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.

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

Abstract Consider a dominant manufacturer wholesaling a product to a retailer, who in turn retails it to the consumers at

Pricing and volume discounting for a dominant retailer with uncertain manufacturing cost information

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. Using our sto-asy-i framework to resolve the logical flaws of the det-sym-i framework also reveals two noteworthy points: (i) the attractiveness of the perfectly legal but overlooked channel-coordination mechanism [pm]; and (ii) volume discounting as a means for the dominant manufacturer to benefit from information known only to the retailer.

When should a manufacturer share truthful manufacturing cost information with a dominant retailer

Abstract A product costs the manufacturer c /unit to produce; the retailer sells it at p /unit to the consumers. The retail-market demand volume V varies with p according to a given demand curve D p . How would or should the “players” (i.e., the manufacturer and the retailer) set their prices? In contrast to many studies that assume a dominant manufacturer implementing the “manufacturer-Stackelberg” (“[mS]”) game, this paper examines how a dominant retailer should operate when his knowledge of c is imperfect. We first derive optimal decisions (some of them counter-intuitive) for the dominant retailer when he is restricted to choosing between [rS] (retailer-Stackelberg) and [mS]. Second, we propose a “reverse quantity discount” scheme that the dominant retailer (i.e., the downstream player) can offer to the manufacturer (note that the standard discount scheme is offered by the upstream player). We show that this discounting scheme is quite effective compared to the considerably more complicated though nevertheless theoretically optimal “menu of contracts.” We also reveal a largely overlooked function of discounting; i.e., discounting enables an “ignorant” but dominant player to usurp the earnings attributable to the knowledge of the dominated player. Finally, we also show that discounting works well when the demand curve is linear, but becomes ineffective when the demand curve is iso-elastic – a result echoing the conclusions of some earlier related works.

Considering asymmetrical manufacturing cost information in a two-echelon system that uses price-only contracts

Consider a dominated manufacturer (Manu) supplying a dominant retailer (Reta). Manu knows the products unit manufacturing cost (m) deterministically, whereas Reta knows it only in the form of an a priori subjective distribution . Reta may implement any one of four contract formats: price-only; franchise fee; two-part tariffs; and menu of contracts ([MC]). This paper presents two groups of results. The first-group consists of procedures for Reta to compute optimal parameters for each of these contract formats. These first-group results are then used to study: (i) the conditions under which Manu is interested in sharing his m-information and thus improving Retas -perception; and (ii) how such information sharing conditions are affected by the contract formats. We find that: (i) Manu benefits from reducing Retas uncertainty on her -perception only when the products profitability is quite small; (ii) over a wide range of plausible conditions Manu benefits from a poorer quality of Retas a priori -perception, regardless of what contract format Reta uses; (iii) the range of conditions under which Manu benefits from a poorer quality of Retas m-perception is not altered or narrowed by Retas use of a more sophisticated contract format (such as [MC]), even though such channel coordinating contracts increase channel efficiency and Retas profit. In short, current methods cannot motivate Manu to share m-information honestly, hence Reta should not trust the m-information provided by Manu. These results reveal an overlooked aspect amidst the popular bigger pie notion of supply chain cooperation and emphasize the need to develop arrangements that can truly motivate honest information sharing.

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

Consider a basic “price-only” supply chain interaction in which the “players” are a manufacturer and a retailer. The manufacturer sets the wholesale price (

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

w/unit) of a product she supplies to a retailer, who in turn sets the retail price (

Designing a quantity discount scheme for a newsvendor-type product with numerous heterogeneous retailers

p/unit) at which he sells to the consumers. The products demand curve is a function of p. The players select to play one of several non-cooperative games such as the manufacturer-Stackelberg game. How should the players set their prices w and p? Most existing studies assume information symmetry i.e., the cost and market parameters are known equally and perfectly to both players. In reality, the retailers knowledge of the manufacturing cost c is often controlled by the manufacturer. This paper considers explicitly the asymmetry of knowledge in c. This approach reveals interesting and surprising deviations from earlier symmetrical-c-knowledge results. Moreover, the approach also ameliorates some of the internal inconsistencies within the symmetric-information framework. We also show how the effect of knowledge asymmetry varies with the shape of the demand curve and with the degree of relative dominance between the players. We find that under a linear demand curve a manufacturer should overstate c, which is an intuitively expected result. However, under an iso-elastic demand curve she benefits herself and the entire system by understating c, which is counter-intuitive. Also, under asymmetric c-knowledge, the simultaneous decision (or “vertical Nash”) game becomes non-viable under a linear demand curve, but the game becomes quite viable and desirable under an iso-elastic demand curve.

Dollar vs. percentage markup pricing schemes under a dominant retailer

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 markets 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 markets 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.