An economic production lot size model in an imperfect production system

The paper investigates an EPL (Economic Production Lotsize) model in an imperfect production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘in-control’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective (imperfect), in ‘out-of-control’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.     

Cointegration analysis of brand and category sales: Stationarity and long‐run equilibrium in market shares

The present study uses modern time series methodology to understand long‐run equilibrium in markets and provides additional evidence of the frequent existence of stationary market shares for frequently purchased consumer products. Dekimpe and Hanssens, Marketing Science 1995; 14(2):G109–121 using a database of over 400 prior studies, found that 78 per cent of the market share series they studied were stationary, but that 68 per cent of the sales series were evolving. Our findings reconcile these results. A major contribution of this paper is its demonstration that the prior empirical evidence that a majority of sales series is in evolution is consistent with stationary market shares, if brand sales and category sales are cointegrated. To the extent that competitive activities have an effect on market share, an implication of our findings is that these activities may, in general, only have a temporary effect on market share. Finally, we distinguish, from a strategic perspective, between sales and share response at the primary‐demand level (category sales), selective‐demand level (brand sales) and relative‐position level (market share) and identify strategic scenarios depending upon their stable/evolving nature. Copyright © 2000 John Wiley & Sons, Ltd.     

Single firm product diffusion model for single-function and fusion products

The prosperity of multifunction products (also referred to as fusion products) has changed the landscape of the marketplace for several electronics products. To illustrate, as fusion products gain popularity in cellular phones and office machines, we observe that single-function products (e.g., stand-alone PDAs and stand-alone scanners) gradually disappear from the market as they are supplanted by fusion products. This paper presents a product diffusion model that captures the diffusion transition from two distinct single-function products into one fusion product. We investigate the optimal launch time of the fusion product under various conditions and conduct a numerical analysis to demonstrate the dynamics among the three products. Similar to previous multi-generation single product diffusion models, we find that the planning horizon, the products’ relative profit margin, and substitution effects are important to the launch time decision. However, there are several unique factors that warrant special consideration when a firm introduces a fusion product to the market: the firm’s competitive role, buyer consolidation of purchases to a multi-function product, the fusion technology and the age of current single-function products.     

Optimal pricing,EOL (end of life) warranty,and spare parts manufacturing strategy amid product transition

We study firm’s strategy to determine its product price and warranty period, and plan the spare parts manufacturing so as to maximize its profit and at the same time to fulfill its commitment to providing the customer with the key part continuously over the relevant decision time horizon, i.e., the product’s life cycle plus its EOL service (warranty) period. To examine the research question, we develop and solve a two-stage optimal control theory model. From the numerical analysis, we infer as follows. It is not always true that the longer the EOL warranty period, the better for the company’s profitability, implying there exists an optimal EOL warranty period that balances all the relevant forces like market demand and cost structures. The relationship between optimal EOL warranty period and failure rate (defect rate) is concave: when the defect rate is moderate, the company has to increase its EOL warranty period as the defect rate increases so as to compensate for the deteriorating quality; but, when the defect rate is beyond a threshold level, the company needs to curtail its EOL warranty commitment as the defect rate increases in order to avoid excessive cost to service the failed parts. By depicting key dynamics in this managerial problem, this paper sheds light on how to make decision for optimal pricing and warranty when the product life cycle is finite and the company is obliged to provide after-sales services to customers for an extended period of time after the current product is no longer produced.     

Quality and entry deterrence

We analyze the role of quality, which we define as an attribute of a product that increases consumers’ willingness to buy, as a competitive tool in a quality-price setting. We consider an incumbent’s entry-deterrence strategies using quality as a deterrent when faced by a potential entrant. We investigate settings motivating the incumbent to blockade the entrant (i.e., prevent entry without extra effort), deter the entrant (i.e., prevent entry with extra effort), or accommodate the entrant (i.e., allow the entry to take place). We identify conditions under which the incumbent may actually over-invest in quality to deter entrance. More interestingly, we also identify conditions under which the incumbent may decrease his quality investment to make it easier for the entrant to penetrate the market. Our model sheds light on entry scenarios of particular platform product markets such as the entry of Xbox to the video game console market.     

Research on competition diffusion of the multiple-advanced manufacturing mode in a cluster environment

This paper deals with competition diffusion of multiple-advanced manufacturing modes in a cluster environment, to reveal the competition diffusion rules of the advanced manufacturing mode. First, the influencing factors on advanced manufacturing mode diffusion in a cluster environment are analysed. Second, the diffusion properties and the diffusion mechanism are analysed, and the competition diffusion model of multiple-modes is established. Third, the model is analysed and the qualitative results are presented. Finally, the application of the diffusion model is exemplified and simulated (by matlab 7.1), producing results that are consistent with qualitative analysis that also verifies the correctness of the model. In addition, the influence of the cluster environment is discussed. The diffusion model helps enterprises understand the diffusion rules of the advanced manufacturing modes and provides a decision-making basis for enterprises and government.     

Sequential market entries and competition modelling in multi-innovation diffusions

The diffusion of innovations for simultaneous processes cannot take into account and properly explain systematic perturbations due to competition-substitution effects if they are examined one by one. A first aspect in simultaneous competing diffusions is the distinction between simultaneous market entries (synchronic competition) and sequential entries (diachronic competition). In the latter case, the beginning of competition may upset the first entrant’s diffusion. A second important aspect in multiple competition is represented by the choice to model the word-of-mouth effect either at the category level (balanced model) or at the brand level, separating the within-brand effect from the cross-brand one (unbalanced model). In this paper, balanced models are studied, and we propose a model that allows for a change in the parameter values of the first entrant as soon as the second one enters the market. The resulting differential system has a closed-form solution that enables, through sales data, an empirical validation of the assumptions underlying the model structure, improving the forecasting accuracy. An application to pharmaceutical drug competition is discussed.     

Preferences for contractual forms in supply chains

The supply chain contracting literature has focused on incentive contracts designed to align supply chain members’ individual interests. A key finding of this literature is that members’ preferences for contractual forms are often at odds: the upstream supplier prefers relatively complex contracts that can coordinate the supply chain; however, the downstream retailer prefers a wholesale price-only contract because it leaves more surplus (than does a coordinating contract), which the retailer can capture. This paper addresses the following question: Under what circumstances do suppliers and retailers prefer the same contractual form? We study supply chain members’ preferences for contractual forms under three different competitive settings in which multiple supply chains compete to sell substitutable products in the same market. Our analysis suggests that both upstream and downstream sides of the supply chain may prefer the same “quantity discount” contract, which would eliminate the conflicts of interest that otherwise typify contracting situations. More interesting still is that both sides may also prefer the wholesale price-only contract; this finding provides a theoretical explanation for why that inefficient (but simple) contract is widely adopted in supply chain transactions.     

A market-driven transfer price for distributed products using mathematical programming

A distributed product has its manufacturing activities distributed among many locations. These locations could belong to one or more firms in a manufacturing network. Often, components needed to manufacture a distributed product move through different nodes in the network and sometimes across international borders. Hence, a transfer price is needed for the purpose of estimating duties and drawbacks. Being aware of the fact that transfer price can be used to manipulate taxable profits, many countries have instituted rules concerning transfer price estimation. For example, in the United Sates, the Internal Revenue Service (IRS) says that the right price is the market value. But for many components it is difficult to find a free market. Similar products may exist in the market but they may have different attributes. In such cases, it is important to be able to estimate the market-driven transfer price, given other similar products in the open market.We develop a method using a mathematical programming model and providing companies an opportunity to work proactively with the IRS in a cooperative manner in order to avoid costly audit and litigation. This way, companies avoid penalties and also gain certainty regarding tax liability. An example illustrating the method is presented.     

Product variety and channel structure strategy for a retailer-Stackelberg supply chain

Motivated by the observations that the direct sales channel is increasingly used for customized products and that retailers wield leadership, we develop in this paper a retailer-Stackelberg pricing model to investigate the product variety and channel structure strategies of manufacturer in a circular spatial market. To avoid channel conflict, we consider the commonly observed case where the indirect channel sells standard products whereas the direct channel offers custom products. Our analytical results indicate that if the reservation price in the indirect channel is sufficiently low, adding the direct channel raises the unit wholesale price and retail price in the indirect channel due to customization in the direct channel. Despite the fact that dual channels for the retailer may dominate the single indirect channel, we find that the motivation for the manufacturer to use dual channels decreases with the unit production cost, while increases with (i) the marginal cost of variety, (ii) the retailer’s marginal selling cost, and (iii) the customer’s fit cost. Interestingly, our equilibrium analysis demonstrates that it is more likely for the manufacturer to use dual channels under the retailer Stackelberg channel leadership scenario than under the manufacturer Stackelberg scenario if offering a greater variety is very expensive. When offering a greater variety is inexpensive, the decentralization of the indirect channel may invert the manufacturer’s channel structure decision. Furthermore, endogenization of product variety will also invert the channel structure decision if the standard product’s reservation price is sufficiently low.     

An empirical study on the Lanchester model of combat for competitive advertising decisions

This paper presents an empirical study on the Lanchester model of combat for competitive advertising decisions. Three issues are evaluated: (i) the specification of the market share response model; (ii) the effect of inflation on the estimation of the response model; and (iii) the performance of competitive strategies. It is shown that (a) the square root function that is used in previous studies is often inappropriate to characterize the market share response model; (b) market share variations are more responsive to current advertising expenditures; (c) closed-loop Nash equilibrium strategies are better competitive advertising strategies for firms to maximize profits than open-loop Nash equilibrium strategies; and (d), finally, general perfect equilibria Nash equilibrium strategies developed by Case are usually not good competitive advertising strategies for firms to maximize profits.     

The EU regulation on cross-border trade of electricity: A two-stage equilibrium model

The regulation on cross-border exchanges of electricity in the European Union is meant to enhance the trade of electricity between Member States, by facilitating access to the network and improving the management of congestion at the interconnections. This paper presents a computational model that embeds these two features. The problem is cast in the form of a two-stage equilibrium between regional Regulators. In the first stage, they decide on the allocation of their regional network costs between generators and customers. Either they maximise their regional welfare non-cooperatively (Nash equilibrium), or they centralise the decision as a super-regulator (leading to a cooperative equilibrium). In the second-stage equilibrium, the consequences of first-stage’s decisions are assessed by modelling the energy market as the result of imperfect competition equilibrium on competitive market, coupled with regulated pricing on the domestic less competitive markets. The “rules” that come out of the first-stage game largely influence the final equilibrium. We illustrate this on an extensive numerical example, showing that the model behaves properly and identifying policy issues worth of further investigations.     

Using recurrent neural networks with attention for detecting problematic slab shapes in steel rolling

The competitiveness in the manufacturing industry raises demands for using recent data analysis algorithms for manufacturing process development. Data-driven analysis enables extraction of novel knowledge from already existing sensors and data, which is necessary for advanced manufacturing process refinement involving aged machinery. Improved data analysis enables factories to stay competitive against newer factories, but without any hefty investment. In large manufacturing operations, the dependencies between data are highly complex and therefore very difficult to analyse manually. This paper applies a deep learning approach, using a recurrent neural network with long short term memory cells together with an attention mechanism to model the dependencies between the measured product shape, as measured before the most critical manufacturing operation, and the final product quality. Our approach predicts the ratio of flawed products already before the critical operation with an AUC-ROC score of 0.85, i.e., we can detect more than 80 % of all flawed products while having less than 25 % false positive predictions (false alarms). In contrast to previous deep learning approaches, our method shows how the recurrent neural network reasons about the input shape, using the attention mechanism to point out which parts of the product shape that have the highest influence on the predictions. Such information is crucial for both process developers, in order to understand and improve the process, and for process operators who can use the information to learn how to better trust the predictions and control the process.     

Improving reliability of a shared supplier with competition and spillovers

Supplier reliability is a key determinant of a manufacturer’s competitiveness. It reflects a supplier’s capability of order fulfillment, which can be measured by the percentage of order quantity delivered in a given time window. A perfectly reliable supplier delivers an amount equal to the order placed by its customer, while an unreliable supplier may deliver an amount less than the amount ordered. Therefore, when suppliers are unreliable, manufacturers often have incentives to help suppliers improve delivery reliability. Suppliers, however, often work with multiple manufacturers and the benefit of enhanced reliability may spill over to competing manufacturers. In this study, we explore how potential spillover influences manufacturers’ incentives to improve supplier’s reliability. We consider two manufacturers that compete with imperfectly substitutable products on Type I service level (i.e., in-stock probability). The manufacturers share a common supplier who, due to variations in production quality or yield, is unreliable. Manufacturers may exert efforts to improve the supplier’s reliability in the sense that the delivered quantity is stochastically larger after improvement. We develop a two-stage model that encompasses supplier improvement, uncertain supply and random demand in a competitive setting. In this complex model, we characterize the manufacturers’ equilibrium in-stock probability. Moreover, we characterize sufficient conditions for the existence of the equilibrium of the manufacturers’ improvement efforts. Finally, we numerically test the impact of market characteristics on the manufacturers’ equilibrium improvement efforts. We find that a manufacturer’s equilibrium improvement effort usually declines in market competition, market uncertainty or spillover effect, although its expected equilibrium profit typically increases in spillover effect.     

On a generalized Cournot oligopolistic competition game

We consider a model whereby players compete for a set of shared resources to produce and sell substitute products in the same market, which can be viewed as a generalization of the classical Cournot oligopolistic competition model, or, from a different angle, the Wardrop type routing model. In particular, we suppose that there are K players, who compete for the usage of resources as well as the sales of the end-products. Moreover, the unit costs of the shared resources and the selling prices of the products are assumed to be affine linear functions in the consumption/production quantities. We show that the price of anarchy in this case is lower bounded by 1/K, and this bound is essentially tight, which manifests the harsh nature of the competitive market for the producers.     

竞争市场下考虑再制造产品售后服务的供应链运营策略

在同时生产新产品和再制造产品的原始制造企业(企业1)与生产具有替代性产品的企业(企业2)构成竞争关系下的供应链系统中,探讨供应链在不同售后服务策略下供应链的运营策略,分析在竞争市场下供应链定价策略和再制造产品的售后服务对定价策略及供应链中各企业利润的影响。揭示再制造产品售后服务对定价策略和供应链各企业最优利润的影响。得到如下主要研究结论:(1)当制造企业为再制造产品提供售后服务时,再制造产品销售量增加,新产品和竞争替代产品销售量降低;有趣的是新产品和再制造产品的市场零售价格同时增加,竞争替代产品的市场零售价格降低。(2)制造企业为再制造产品提供售后服务时的利润总是大于没有售后服务时的利润,且不受单位产品生产成本影响。同时当单位产品生产成本较高时,制造企业为再制造产品提供售后服务策略会带来竞争对手企业利润增加。这些结论对具有再制造产品供应链如何提供再制造产品售后服务具有一定指导作用和管理启示。     

A generalized ordering and recovery policy for reusable items

This paper deals with a joint EOQ and EPQ model in which a stationary demand is satisfied by recovered products as well as newly purchased products. It is assumed that a fixed proportion of the used products are collected from customers and later recovered for reuse. We generalize the (P, R) policy in the literature by treating the sequence of orders for newly purchasing products and setups for recovery process within a cycle as a decision variable. Through example problems we illustrate the validity of the model and solution procedure developed.     

Analytical and managerial implications of integrating product substitutability in the joint pricing and procurement problem

This paper studies the analytical and managerial implications of product substitutability on the joint pricing and procurement decisions. We consider a single-period model with two products: an existing product and an improved new product that can substitute the demand for the existing product in case of a shortage. Demand for each product follows a general distribution with an expected value that is a linear function of the price of the new product. While the price of the existing product is determined by the market, it is necessary to determine the new product’s price and the procurement quantities of both products so as to maximize the profits. We analytically show that the expected profit function is unimodal and in the existence of substitution: the expected total profit is higher; the optimal price and the safety stock of the new product are higher; and the optimal safety stock of the existing product is less. Using these properties an efficient algorithm is developed. We also provide a numerical analysis to demonstrate that considering substitution in advance could increase the profitability by 58% and the new product price by 5% while decreasing the total procurement quantity by 15%.     

Capacity augmentation of a supply chain for a short lifecycle product: A system dynamics framework

For an innovative product characterized by short product lifecycle and high demand uncertainty, investment in capacity buildup has to be done cautiously. Otherwise either the product’s market diffusion is impeded or the manufacturer is left with unutilized capacity. Using the right information for making capacity augmentation decisions is critical in facing this challenge. In this paper, we propose a method for identifying critical information flows using the system dynamics model of a two-echelon supply chain. The fundamental premise of system dynamics methodology is that (system) structure determines (its) behavior. Using loop dominance analysis method we study the feedback loop structure of the supply chain system. The outcome is a set of dominant loops that determine the dynamics of capacity growth. It is revealed that the delivery delay information has little effect while the loop that connects retail sales with production order affects the dynamics significantly. Modifying this loop yields appropriate capacity augmentation decisions resulting in higher performance. What-if analyses bring out effects of modifying other structural elements. In conclusion, we claim that the information feedback based methodology is general enough to be useful in designing decision support systems for capacity augmentation. The limitations of the model are also discussed and possible extensions identified.     

A singular control model with application to the goodwill problem

We consider a stochastic system whose uncontrolled state dynamics are modelled by a general one-dimensional Itô diffusion. The control effort that can be applied to this system takes the form that is associated with the so-called monotone follower problem of singular stochastic control. The control problem that we address aims at maximising a performance criterion that rewards high values of the utility derived from the system’s controlled state but penalises any expenditure of control effort. This problem has been motivated by applications such as the so-called goodwill problem in which the system’s state is used to represent the image that a product has in a market, while control expenditure is associated with raising the product’s image, e.g., through advertising. We obtain the solution to the optimisation problem that we consider in a closed analytic form under rather general assumptions. Also, our analysis establishes a number of results that are concerned with analytic as well as probabilistic expressions for the first derivative of the solution to a second-order linear non-homogeneous ordinary differential equation. These results have independent interest and can potentially be of use to the solution of other one-dimensional stochastic control problems.