Suman Mallik

Coordinating Supply Chains with Competition: Capacity Allocation in Semiconductor Manufacturing

Abstract This paper, motivated by the experiences of a major US-based semiconductor manufacturer, presents an integrated model of incentive problems arising in forecasting and capacity allocation. Our model involves multiple product managers and multiple manufacturing managers who forecast the means of their respective demand and capacity distributions. A central coordinator is responsible for allocating capacities to product lines. When these distributions are unknown to the central coordinator and capacity is scarce, the managers misrepresent their forecasts. A product manager inflates his forecast to gain a greater allocation of the capacity; a manufacturing manager deflates his forecast to cover for the uncertainties in production. We propose a game theoretic model and design a mechanism (a bonus scheme for all managers and an allocation rule to allocate realized capacity to the product managers) that elicits truthful reporting by all managers. The results herein show that the structure of the truth-eliciting bonus schemes is rather simple with easily calculable parameters. We also show that large classes of allocation rules, including the current allocation practice of the firm, are manipulable. A bonus is often required for elicitation of truthful information. We synthesize the implications of our results for the practitioners.

Inventory competition and allocation in a multi-channel distribution system

Abstract Consider a supply chain involving one manufacturer and one independent retailer. The manufacturer distributes her product to the end consumer through the independent retailer as well as through her direct channel. Each of the two channels faces a stochastic demand. If one channel is out of stock, a fraction of the unsatisfied customers visit the other channel, which induces inventory competition between the channels. Under the scenario described above, will the manufacturer ever undercut the retailer’s order when the capacity is infinite? What are the equilibria of the game? How does a capacity constraint affect the equilibrium outcome? What is the optimal inventory allocation strategy for the manufacturer? Using a game theoretic model we seek answers to the above questions. Both the capacitated and the infinite capacity games are considered. We establish the necessary condition for a manufacturer to undercut a retailer’s order and show that a manufacturer may deny the retailer of inventory even when the capacity is ample. We show that there can be an equilibrium in the capacitated game where a manufacturer might not use the entire capacity and still deny a retailer inventory. We also show that a mild capacity constraint may make both parties better off and thereby increase the total supply chain profit. We develop a simple yet practical contract called the reverse revenue sharing contract and show that along with a fixed franchise fee this contract can coordinates our decentralized supply chain.

Scheduling Commercial Videotapes in Broadcast Television

This paper, motivated by the experiences of a major U.S.-based broadcast television network, presents algorithms and heuristics to schedule commercial videotapes. Major advertisers purchase several slots to air commercials during a given time period on a broadcast network. We study the problem of scheduling advertisers commercials in the slots it purchased when the same commercial is to be aired multiple times. Under such a situation, the advertisers typically want the airings of a commercial to be as evenly spaced as possible. Thus, our objective is to schedule a set of commercials in a set of available slots such that multiple airings of the same commercial are as evenly spaced as possible. A natural formulation of this problem is a mixed-integer program that can be solved using third-party solvers. We also develop a branch-and-bound algorithm based on a problem-specific bounding scheme. Both approaches fail to solve larger problem instances within a reasonable time frame. We present an alternative mixed-integer program that lends itself to an efficient solution. For solving even larger problems, we present multiple heuristics.

Optimal temporal product introduction strategies under valuation changes and learning

Consider a firm facing two consumer segments with differing valuations for quality. The demand is stationary and known, and consumers make repeat purchase. However, once a premium product is introduced, the valuations of the consumers change in the next period. The firm derives a cost savings due to learning effect in the second period, the magnitude of which depends on the volume in the first period. Under such a situation, should a firm introduce a premium product before a basic product or vice-versa? Should it introduce two products simultaneously? What should it then do in the second period? Should it introduce a single product into the market first and expand its product offering later? Using a two-period stylized model we seek to answer these questions. We characterize the optimal product introduction strategy for the firm. We show how the firms choice is influenced by cost savings and valuation changes. The managerial implications of the model are also discussed.

Managing on-air ad inventory in broadcast television

An analytical model for managing on-air ad inventory in broadcast television is presented. The ad inventory in this industry is priced based on rating points or the number of viewers that watch a commercial. The rating points during a broadcast year are sold through two distinct processes: the upfront market which occurs before the broadcast season, and the scatter market which occurs during the broadcast season. A firm needs to allocate its total rating points inventory to these two markets before knowing either the performance rating of its shows or the scatter market price, both of which are random. Broadcast networks offer ratings (performance) guarantees on the inventory that is sold on the upfront market while such guarantees are seldom offered in the scatter market. An optimization model is proposed that allows the networks to manage their rating points inventory. The model explicitly incorporates the performance uncertainty of the television shows as well as the revenue uncertainty of the scatter market. We derive conditions for feasibility of the problem and characterize the optimal amount of rating points to sell on the upfront market. Our model explains the current practice of selling around 60–80% of the total rating points for the season during the upfront market and analyzes other common strategies used by broadcast companies. In addition to providing key managerial insights, this work introduces quantitative methodologies to television networks planning their upfront market activities.

Contracting over multiple parameters: Capacity allocation in semiconductor manufacturing

Abstract This paper is a generalization of Mallik and Harker [Mallik, S., Harker, P.T., 2004. Coordinating supply chains with competition: Capacity allocation in semiconductor manufacturing. European Journal of Operational Research 159, 330–347] that presented an integrated model of incentive problems arising in forecasting and capacity allocation. In that model, multiple product managers and multiple manufacturing managers forecast the means of their respective demand and capacity distributions, and a central coordinator allocates capacities based on these forecasts. A mechanism that elicits truthful information from the managers was the main contribution of that paper. The objective of this paper is to generalize our previous results to multiple statistics reporting. This work assumes that the central coordinator can ask the managers to report multiple statistics (mean and variance, for example) about their respective distributions. We propose a game theoretic model and design a mechanism (a bonus scheme and an allocation rule) that elicits truthful reporting of all statistics by all managers. It turns out that the structure of the optimal bonus schemes are rather simple with easily calculable parameters. We also show that a large class of allocation rules are manipulable. A bonus is often required for elicitation of truthful information. We compare our results of multiple statistics reporting with those from Mallik and Harker (2004). We also characterize under what conditions the reporting of the extra information is of limited use.

Bundling of Vertically Differentiated Products in a Supply Chain

We consider a supply chain consisting of a single manufacturer and a single retailer. The manufacturer produces a basic and a premium product. If desired, a bundle of the two products might also be produced at a unit bundling cost. We allow either the manufacturer or the retailer to produce the bundle from the component products. All products, however, must be sold exclusively through the retailer. Using game theoretic models, we compare and contrast the equilibrium outcomes under retailer bundling and manufacturer bundling scenarios. We show that under manufacturer bundling, the manufacturer never offers the full product line composed of the basic product, the premium product, and the bundle, at equilibrium; while the same does not hold under retailer bundling. We show that total supply chain profit under retailer bundling weakly dominates that under manufacturer bundling and characterize the region in the parameter space where this domination is strict. We explore an extension where there is a capacity constraint in producing one or both of the component products and characterize the equilibrium outcomes. We show that unlike the infinite capacity case, offering the full product line is an equilibrium outcome under manufacturer bundling when the capacity of the premium good is limited.

Quality signaling through warranty & brand reputation

When product quality is unobservable to consumers, a manufacturer can convey quality information using signals such as warranty and brand reputation. The purpose of this paper is to study the interaction between warranty, brand reputation, and product quality, and to examine alternative quality-signaling strategies. We model a monopolist who conveys unobservable product quality through signals of warranty and brand reputation. Heterogeneous consumers perceive the signals, form quality beliefs, and make purchase decisions. Consumers also update brand reputation perceptions after product consumptions. Under this framework, we study the monopolists optimal decisions of price, warranty, and quality in a one-period model.