Jian-Cai Wang

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

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.

A stochastic model of a reconfigurable manufacturing system Part 2: Optimal configurations

Various products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) manages to satisfy customers, with each family corresponding to one configuration of the RMS. Then, the products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system possesses the reconfigurable function for different families. In the design period of a RMS, there may exist several feasible configurations for each family. Then, an important issue in a RMS is the optimal configurations for the families. Based on a stochastic model, an optimization problem stemmed from the issue is formulated. Two algorithms are devised to solve the optimization problem. Numerical examples are presented for evaluating the efficiency of the algorithms.

A stochastic model of a reconfigurable manufacturing system Part 3: Optimal selection policy

Products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) satisfies customer requirements by ensuring that each family corresponds to one configuration of the RMS. Products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system is reconfigurable for different families. To utilize the RMS, a selection policy that is an action rule is needed, by which the manufacturer selects a family to produce ordered products belonging to the selected family. Thus, an important issue for an RMS is the optimal selection policy. Based on a stochastic model, an optimization problem stemmed from the issue is formulated. Two solution procedures are devised to solve the optimization problem. Numerical examples are presented for evaluating the efficiency of the algorithms.

A stochastic model of a reconfigurable manufacturing system - Part 4: Performance measure

Various products required by customers are classified into several product families, each of which is a set of similar products. A reconfigurable manufacturing system (RMS) manages to satisfy customers, with each family corresponding to one configuration of the RMS. Then, the products belonging to the same family will be produced by the RMS under the corresponding configuration. The manufacturing system possesses the reconfigurable function for different families. A performance measure is defined as service levels for the families. A semi-Markov process is formulated for obtaining the performance measure. When a larger fluctuation in the market happens, the manufacturer can adjust the system to improve the performance measure. An optimization of a reassigning problem is discussed, which reassigns the maximum numbers of orders to the families. Two solution approaches are proposed to solve the problem. Numerical examples are given for illustrating the methodologies.

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 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.

Markup pricing strategies between a dominant retailer and competitive manufacturers

Markup pricing contracts have been widely employed in many industries. Under such contracts, a retailer charges a retail margin over the wholesale price levied by the supplier to guarantee her financial prudence. In a setting where two competitive manufacturers sell substitutable products through a common dominant retailer, we investigate and compare performance of two different markup arrangements, namely, percentage and dollar, under the deterministic and stochastic demand situations, respectively. We find that, no matter what the demand characteristic is, when the retailer switches from dollar to percentage markup, the retailer makes a higher profit while the manufacturers suffer, because the switching forces manufacturers charge lower wholesale prices and thus leads to lower retail prices. Moreover, under the deterministic demand situation, the switching brings about a larger order quantity and a higher channel profit. Under the stochastic demand situation, however, the effect of the switching on order quantity and channel profit depends on manufacturer differentiation and retailer efficiency: order quantity (channel profit) becomes smaller (lower), as manufacturer differentiation becomes weaker or retailer efficiency becomes higher. And, the demand uncertainty intensifies the effect.

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

Abstract This paper presents a practical approach for designing a quantity-discount (“qd”) scheme for a manufacturer who supplies a newsvendor-type product to a large number of heterogeneous retailers. The main components of our approach are: (i) an information structure for handling a large number of heterogeneous retailers with changing identities; and (ii) expected-profit expressions for any given qd scheme. We show that these expected-profit expressions can be easily optimized to produce attractive qd schemes; also, these schemes are shown to be quite robust against errors in parameter estimation. As a significant by-product, our multi-retailer scenario provides a more meaningful framework for designing manufacturer-perspective qd schemes, since we also show in this paper that a single-retailer scenario leads to a degenerate problem.

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.

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.

Defending and improving the ‘slotting fee’: how it can benefit all the stakeholders dealing with a newsvendor product with price and effort-dependent demand

Abstract‘Slotting fee’ (hereafter ‘SF’) is an upfront fee a ‘supplier’ is required to pay a retailer in order to have his product sold on the retailers shelves. It is becoming increasingly common, but also widely reviled. This paper considers a newsvendor product whose expected demand is dependent on retail price and sales effort. The question we pose is: given that the Stackelberg-dominant retailer has to choose a pricing contract with which she transacts with the supplier, how would the supply-chain stakeholders fare when the retailer implements SF instead of another practical pricing contract? We show that, contradicting its negative public image, SF empowers the dominant retailer to specify contract terms that will benefit all the stakeholder-groups. That is, the suppliers and the retailers profits are higher, the production workers are asked to produce more, and the consumers pay a lower retail price. We also propose a new ‘composite’ contract format that incorporates both the SF and ‘buyback’ features. This composite format empowers the retailer to provide even greater benefits to the supply-chains stakeholders.