General Cost Structure Research Articles

Go Upscale? Quality Competition between National Brand and Store Brand

It is commonly assumed in private label literature that store brands are of lower quality than competing national brands. In this paper, we contest this notion by studying quality competition between a national- brand manufacturer and a store-brand retailer. The manufacturer sells its national-brand products through the retailer who produces a competing store brand at the same time. The two parties first invest in their brand qualities, after which the manufacture determines the wholesale price for the national brand and the retailer decides the retail prices for both brands. With a general quality-dependent cost structure, we explicitly characterize the equilibrium in both price and quality levels under various channel power structures. The results suggest that the store brand could possibly be of higher quality than the national brand even in absence of cost disparity; however, the store brand will charge a lower retail price whether its quality is superior to the national brand or not. Further, price competition and quality competition bear opposite implications on equilibrium solutions as well as profitability levels. Surprisingly, the manufacturer may benefit from a more costly production or quality investment scenario, while both the retailer and the supply chain will suffer from the same. The paper highlights the importance of accounting for quality decisions in the study of private label products.

Tactical supply chain planning under uncertainty with an application in the wind turbines industry

With today's rapidly changing global market place, it is essential to explicitly include uncertainty in supply chain planning models. In this paper, we develop a two-stage stochastic programming model for the comprehensive tactical planning of supply chains under demand and supply uncertainty. The model handles multi-period, multi-product, and multi-echelon supply chains. It incorporates backorder penalties with general cost structures. The considered supply uncertainty combines supplier random yield and stochastic lead times, and is thus the most general form of such uncertainty to date. We illustrate how our model directly applies to the planning of the supply chain of one of the world's biggest manufacturers of wind turbines. We illustrate theoretical and numerical results that show the impact of supplier uncertainty/unreliability on optimal procurement decisions. We also quantify the value of modeling uncertainty versus deterministic planning.

Fast Approximation Algorithms for the One-Warehouse Multi-Retailer Problem Under General Cost Structures and Capacity Constraints

We consider a well-studied multi-echelon (deterministic) inventory control problem, known in the literature as the one-warehouse multi-retailer (OWMR) problem. We propose a simple and fast 2-approximation algorithm for this NP-hard problem, by recombining the solutions of single-echelon relaxations at the warehouse and at the retailers. We then show that our approach remains valid under quite general assumptions on the cost structures and under capacity constraints at some retailers. In particular, we present the first approximation algorithms for the OWMR problem with nonlinear holding costs, truckload discount on procurement costs, or with capacity constraints at some retailers. In all cases, the procedure is purely combinatorial and can be implemented to run in low polynomial time.

Choosing a reliability inspection plan for interval censored data

ABSTRACTReliability test plans are important for producing precise and accurate assessment of reliability characteristics. This article explores different strategies for choosing between possible inspection plans for interval-censored data given a fixed testing timeframe and budget. A new general cost structure is proposed for guiding precise quantification of total cost in inspection test plan. Multiple summaries of reliability are considered and compared as the criteria for choosing the best plans using an easily adaptable method. Different cost structures and representative true underlying reliability curves demonstrate how to assess different strategies given the logistical constraints and nature of the problem. Results show several general patterns exist across a wide variety of scenarios. Given the fixed total cost, plans that inspect more units with less frequency based on equally spaced time points are favored due to the ease of implementation and consistent good performance across a large number of case study scenarios. Plans with inspection times chosen based on equally spaced probabilities offer improved reliability estimates for the shape of the distribution, mean lifetime, and failure time for a small fraction of population only for applications with high infant mortality rates. This article uses a Monte Carlo simulation-based approach in addition to the commonly used approach based on the asymptotic variance and offers comparison and recommendation for different applications with different objectives. In addition, the article outlines a variety of different reliability metrics to use as criteria for optimization, presents a general method for evaluating different alternatives, as well as provides case study results for different common scenarios.

Truncated SPRTs with application to multivariate normal data

ABSTRACTWe develop truncated sequential probability ratio test (SPRT) procedures for multivariate normal data. The framework includes a general cost structure and arbitrary mean and covariance structures. The truncated SPRT solutions have a practical and easy-to-use decision boundary representation. In the homogeneous case, a very fast recursive algorithm is presented for calculating the decision boundaries. Misclassification rates and expected sample size are investigated and the results are compared with a nonsequential procedure. A real-life data set on kidney dysfunction following heart surgery is used to illustrate the truncated SPRT procedure.

Optimizing upgrade and imperfect preventive maintenance in failure-prone second-hand systems

Upgrade operations are improvement actions that can be carried out on recovered end-of-life systems to rejuvenate them and make them fit for subsequent lifecycles. These operations are costly but improve the reliability of these second-hand systems and consequently can reduce their maintenance costs. In this paper, a mathematical model for the joint determination of the optimal acquisition age, upgrade level, and imperfect preventive maintenance strategy is developed for a second-hand system. The system is acquired and upgraded, if necessary, before being put into operation and preventively maintained each time its reliability reaches a minimum required reliability threshold. Preventive maintenance actions are imperfect and modeled using the hybrid hazard rate approach. Optimality conditions are derived and discussed for general cost structures of the acquisition and upgrade actions. A test case is provided to illustrate the validity of the proposed approach. Numerical experiments and sensitivity analysis are also conducted to investigate the interactions between the upgrade level decisions, the optimal maintenance policy decisions and the total costs incurred during the lifetimes of these refreshed second- hand systems.

Optimality of (s, S) policies in EOQ models with general cost structures

The classical economic-order-quantity (EOQ) model is at the heart of supply chain optimization and the theory of inventories. We study an extension of the original EOQ model that permits a minimal set of assumptions on the ordering/procurement and holding/backorder costs and establish necessary and sufficient conditions for the existence of an optimal policy of the (s, S) type. Our work lends theoretical credibility to the practice of using (s, S) policies for virtually any cost structure of practical interest. Our proof is constructive and elementary, in the sense that it is based on first principles that do not rely on advanced mathematical machinery. We also prove that an optimal policy, not necessarily of the (s, S) type, always exists within our general EOQ framework.

Strategic Intellectual Property Sharing: Competition on an Open Technology Platform Under Network Effects

In this paper, we explore the strategic decision of an incumbent to open a proprietary technology platform to allow same-side co-opetition in a market characterized by network effects. We propose a game-theoretic model that analytically conceptualizes the interplay among the degree of same-side platform openness, the absorptive capacity of the entrant, and the intensity of network effects. Our analysis uncovers interesting new results. First, when entrant product quality is exogenous, under very strong network effects, the incumbent closes the technology. Moreover, we discuss various interesting open-platform co-opetition outcomes that arise under a fully covered market. When the entrant chooses the quality level and the incumbent is strategic in its platform opening decision, we find that intense network effects make new players shun the market, so intellectual property (IP) sharing is not possible in equilibrium. When the network effects are of intermediate intensity, the incumbent opens the technology to the entrants who have a sufficiently high absorptive capacity, calibrating the amount of sharing to the entrant’s absorptive capacity level to ensure that the duopoly setting is mutually beneficial. Our key findings and insights are robust to several model extensions, including scenarios when the incumbent is uncertain of the entrant’s absorptive capacity, or when the entrant incurs a general non-linear development cost structure. We also compare and contrast bounded versus unbounded market scenarios. We further explore the ability of the incumbent to engineer the strength of network effects in the market and uncover non-trivial alternating-monotonicity patterns for the optimal intensity of network effects with respect to the entrant’s absorptive capacity. We also show that a model with exogenous network effects could drastically underestimate the range of entrants’ absorptive capacity values for which the incumbent should open its platform, causing the latter to miss valuable co-opetition opportunities. We also discuss various managerial implications of our theoretical framework.The online appendix is available at https://doi.org/10.1287/isre.2017.0756 .

Cost effective campaigning in social networks

Campaigners are increasingly using online social networking platforms for promoting products, ideas and information. A popular method of promoting a product or even an idea is incentivizing individuals to evangelize the idea vigorously by providing them with referral rewards in the form of discounts, cash backs, or social recognition. Due to budget constraints on scarce resources such as money and manpower, it may not be possible to provide incentives for the entire population, and hence incentives need to be allocated judiciously to appropriate individuals for ensuring the highest possible outreach size. We aim to do the same by formulating and solving an optimization problem using percolation theory. In particular, we compute the set of individuals that are provided incentives for minimizing the expected cost while ensuring a given outreach size. We also solve the problem of computing the set of individuals to be incentivized for maximizing the outreach size for given cost budget. The optimization problem turns out to be non trivial; it involves quantities that need to be computed by numerically solving a fixed point equation. Our primary contribution is, that for a fairly general cost structure, we show that the optimization problems can be solved by solving a simple linear program. We believe that our approach of using percolation theory to formulate an optimization problem is the first of its kind.

Mathematical modeling and Bayesian estimation for error-prone retail shelf audits

Prevalent execution errors such as out-of-stock, inventory record inaccuracy, and product misplacement jeopardize retail performance by causing low on-shelf availability, which discourages not only retailers who have lost sales but also manufacturers who have worked hard to deliver goods into retail stores. Thus, external service companies are hired by manufacturers to conduct manual inspection regularly. Motivated by the practical need of shelf audit service providers, we use a general cost structure to develop a decision support model for periodic inspection. Some qualitative insights about the intricate relationships among inspection efficacy, cost factors, failure rate of shelf inventory integrity, and optimal decisions are derived from analytics assuming risk-neutrality. From simulation experiments we also find that managers' risk preferences have non-trivial impacts on optimal decisions. Based on a total cost standpoint high-quality inspection is predominantly preferred regardless of the level of risk aversion. Finally, we propose a Bayesian statistical model and a Markov chain Monte Carlo approach to estimate model parameters such that managers can make empirically informed decisions. Our major contribution lies in developing a mathematical model that is practically applicable and proposing a Bayesian estimation approach to rationalize unobservable model parameters, which are influential to optimal decisions but often arbitrarily assumed by decision makers.

On the political geometry of international unions: A coalition-theoretic approach

This paper examines the endogenous strategic considerations in simultaneously creating, enlarging, and deepening an international union of countries within a framework of variable geometry. I introduce a coalition-theoretic model to examine the equilibrium relationship between union size and scope. What is the equilibrium (stable) size and scope of an international union and how do these variables interact? When should we expect countries to take advantage of more flexible modes of integration and how does that possibility affect the pace and depth of integration? In tackling these questions, I characterize the various policy areas of cooperation with respect to their cross-country and cross-policy spillovers, their efficiency scales, the heterogeneity of preferences, and the general cost structure. I then go on to show that the enlargement of a union and the widening of its policy scope are two symbiotic and mutually reinforcing dynamic processes under certain conditions. This is an exciting research puzzle given that extant game-theoretic predictions have been at odds with the empirical reality of European integration.

Optimal sourcing from alternative capacitated suppliers with general cost structures

Most manufacturers or retailers must procure items or services necessary for their businesses, in an environment that typically includes a number of competing suppliers with varying cost structures, price schemes, and capacities. In this paper, we consider the sourcing problem in which the buyer determines the sources that should be utilized and to what extent, in turn, dictating the total quantity available for the buyer to sell/utilize, subject to stochastic demand/requirement. Our approach advocates not to determine the quantity to be sourced a priori. We allow for capacitated sources and any cost structure in which fixed costs and quantity discounts are special cases. Some simpler versions of this problem are shown to be NP-hard in the literature. By proving that the order of the sources is irrelevant for the optimal solution, we devise a dynamic programming model with pseudo-polynomial complexity to solve the multiple supplier sourcing problem to optimality. We propose two extensions: one limits the number of suppliers, and the other allows multi-period sourcing.

Reformulating Environmentally Constrained Traffic Equilibrium via a Smooth Gap Function

Various government laws have recently been enacted to alleviate the environmental deterioration of transportation systems. Environmental constraint is a valid means to explicitly reflect various environmental protection requirements imposed by the government. In this paper, we examine the environmentally constrained traffic equilibrium problem (EC-TEP), which is a fundamental tool for modeling and evaluating environmental protection requirements. Specifically, we provide an equivalent reformulation for the EC-TEP. The proposed reformulation adapts the concept of gap function to simultaneously reformulate the nonlinear complementarity conditions associated with the generalized user equilibrium conditions, environmental constraints, and conservation constraints as an equivalent unconstrained optimization problem. This gap function reformulation has two desirable features: (1) it can handle a general environmental constraint structure (linear or nonlinear; link-based or area-based) and a general link and route cost structure, enhancing the modeling adaptability and flexibility; (2) it is smooth and unconstrained, permitting a number of existing efficient algorithms for its solution. A gradient-based solution algorithm with a self-regulated averaging stepsize scheme is customized to solve the reformulated unconstrained optimization problem. Numerical examples are also provided to demonstrate the modeling flexibility of the proposed EC-TEP reformulation.

Controlled Sensing for Sequential Multihypothesis Testing with Controlled Markovian Observations and Non-Uniform Control Cost

A new model for controlled sensing for multihypothesis testing is proposed and studied in the sequential setting. This new model, termed a controlled Markovian observation model, exhibits a more complicated memory structure in the controlled observations than existing models. In addition, instead of penalizing just the delay until the final decision time as in standard sequential hypothesis testing problems, a much more general cost structure is considered that entails accumulating the total control cost with respect to an arbitrary control cost function. An asymptotically optimal test is proposed for this new model and is shown to satisfy an optimality condition formulated in terms of decision-making risk. It is shown that the optimal causal control policy for the controlled sensing problem is self-tuning, in the sense of maximizing an inherent “inferential” reward simultaneously under every hypothesis, with the maximal value being the best possible corresponding to the case where the true hypothesis is known at the outset. Another test is also proposed to meet distinctly predefined constraints on the various decision risks nonasymptotically, while retaining asymptotic optimality.

Scheduling tamping operations on railway tracks using mixed integer linear programming

A mixed integer linear programming model for the problem of scheduling tamping operations on ballasted tracks is presented and analyzed. The model improves a previously proposed one by introducing disaggregated constraints yielding in a model with stronger lower bound from the continuous relaxation of the binary variables. A more general cost structure is proposed; a structure having the possibility of including setup costs for the tamping operations. The problem considered is shown to be NP-hard. A numerical study is performed to evaluate the performance of the model compared to two simple policies for constructing maintenance schedules. The computational results show that the maintenance costs can be reduced by up to 10 % as compared with the best policy investigated.

Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure

We consider the task assignment problem to heterogeneous parallel servers with switching delay, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient task assignment (dispatching) policies that minimize the long-run average cost. To evaluate our starting policy, we first analyze a single work-conserving M/G/1 queue with a switching delay and derive a value function with respect to a general cost structure. Our costs include energy related switching and processing costs, as well as general performance-related costs, such as costs associated with both means and variability of waiting time and sojourn time. The efficiency of our dispatching policies is illustrated with numerical examples.

Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices

In this study, we analyze the replenishment decision of a buyer with the objective of maximizing total expected profits. The buyer faces stepwise freight costs in inbound transportation and a hybrid wholesale price schedule given by a combination of all-units discounts with economies and diseconomies of scale. This general cost structure enables the model and the proposed solution to be also used for the supplier selection of a buyer under the single sourcing assumption. We show that the buyer's replenishment problem reduces to finding and comparing the solutions of the following two subproblems: (i) a replenishment problem involving wholesale prices given by an all-units discount schedule with economies of scale and a lower bound on the replenishment quantity, and (ii) a replenishment problem involving wholesale prices given by an all-units discount schedule with diseconomies of scale and an upper bound on the replenishment quantity. We propose solution methods for these two subproblems, each of which stands alone as practical problems, and utilize these methods to optimally solve the buyer's replenishment problem.

The Economics of the Long Tail

Abstract Anderson (2006) argues that e-commerce and other new technologies improve efficiency by encouraging the entry of new producers and innovations, creating a “long tail” of niche products while reducing the market share of previously popular products. We study the strategic interaction between hits and niches in their pricing, entry, and innovation decisions using a model of competition under product differentiation and generalized cost structure. In contrast to the popular view, we show that improvements in information and communication technology can lead to either the long tail effect or an opposite “superstar” effect (Rosen, 1981), depending on (a) how the structure (not simply the level) of producer costs changes, and (b) how disparate are consumer preferences. These two factors also determine whether there is excessive or insufficient product diversity. Post-entry product and technology innovation incentives may be inefficient in the long tail market structure because producers can soften price competition by engaging in excessive product differentiation and adopting technologies with high variable costs. These results have implications for various competition-related policies.

Hospital Competition and Quality with Regulated Prices*

AbstractWe analyse the effect of competition on quality in hospital markets with regulated prices, considering the effect of both introducing competition (monopoly versus competition) and increasing competition through either lower transportation costs (increased substitutability) or a higher number of hospitals. With semi‐altruistic providers and a fairly general cost structure, we show that the relationship between competition and quality is generally ambiguous. In contrast to the received body of theoretical literature, this is consistent with, and potentially explains, the mixed empirical evidence.

Bin packing with general cost structures

Following the work of Anily et al., we consider a variant of bin packing called bin packing with general cost structures (GCBP) and design an asymptotic fully polynomial time approximation scheme (AFPTAS) for this problem. In the classic bin packing problem, a set of one-dimensional items is to be assigned to subsets of total size at most 1, that is, to be packed into unit sized bins. However, in GCBP, the cost of a bin is not 1 as in classic bin packing, but it is a non-decreasing and concave function of the number of items packed in it, where the cost of an empty bin is zero. The construction of the AFPTAS requires novel techniques for dealing with small items, which are developed in this work. In addition, we develop a fast approximation algorithm which acts identically for all non-decreasing and concave functions, and has an asymptotic approximation ratio of 1.5 for all functions simultaneously.