Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

Competitive Advertising Under Uncertainty: A Stochastic Differential Game Approach

We analyze optimal advertising spending in a duopolistic market where each firm's market share depends on its own and its competitor's advertising decisions, and is also subject to stochastic disturbances. We develop a differential game model of advertising in which the dynamic behavior is based on the Sethi stochastic advertising model and the Lanchester model of combat. Particularly important to note is the morphing of the sales decay term in the Sethi model into decay caused by competitive advertising and noncompetitive churn that acts to equalize market shares in the absence of advertising. We derive closed-loop Nash equilibria for symmetric as well as asymmetric competitors. For all cases, explicit solutions and comparative statics are presented.     

Allocation of flexible and indivisible resources with decision postponement and demand learning

We consider a firm that uses two perishable resources to satisfy two demand types. Resources are flexible such that each resource can be used to satisfy either demand type. Resources are also indivisible such that the entire resource must be allocated to the same demand type. This type of resource flexibility can be found in different applications such as movie theater complexes, cruise lines, and airlines. In our model, customers arrive according to independent Poisson processes, but the arrival rates are uncertain. Thus, the manager can learn about customer arrival rates from earlier demand figures and potentially increase the sales by postponing the resource allocation decision. We consider two settings, and derive the optimal resource allocation policy for one setting and develop a heuristic policy for the other. Our analysis provides managerial insights into the effectiveness of different resource allocation mechanisms for flexible and indivisible resources.     

A model for analyzing multi-channel distribution systems

To capture customers in different market segments, many firms distribute their products using multiple channels involving in-store, mail-order and electronic mediums. Nevertheless, the business literature is replete with examples where the management of multiple distribution channels becomes unwieldy. As a way to evaluate different distribution strategies arising from multiple channels, we develop a model of a general multi-channel distribution system subject to stochastic demand. Since the exact analysis of our model is intractable, we propose a decomposition scheme that enables us to develop a near-optimal distribution policy with minimum total expected distribution cost. We utilize our analysis of this multi-channel system in two specific applications arising from multi-channel distribution. The first application deals with a store-based retailer expanding into a direct sales channel. The retailer can fill the orders generated from this additional sales channel by using the existing stores or the existing depots. For this application, we evaluate the trade-off between these two options. The second application intends to find a cost-effective way to distribute products by utilizing the combined distribution system of two retailers after a potential merger-and-acquisition (M&A). For this application, we quantify the benefit of an M&A in terms of distribution efficiency.     

Stochastic optimal budget decision for advertising considering uncertain sales responses

Firms are faced with uncertain sales responses even though they advertise appropriately. To help marketing managers make optimal budget decisions in this situation, we develop a stochastic model, depicting the problem of advertising budget decision as a special Markov decision process where a new objective, maximizing expected market utility, is proposed. In the model we introduce a two-dimension state variable including accumulative sales, which vary randomly with advertising budget, and the predicted probability that an advertising campaign obtains a full sales response. We make an analysis of the model on the premise of growing infinite market potential, deriving the property of optimal policies and that of optimal value function. These results are successfully used to make advertising budget decisions for a private university in Xi’an, China.     

Modelling impact of advertising and optimizing advertising policy: an application in recreation

This paper deals with the problem of the desirable level of advertising expenditure, the optimal distribution of this expenditure in time and the allocation over the media: TV, radio and newspaper for a recreation park in the Netherlands.Although the model id developed for the specific situation of this park, in principle it can be applied in all situations where the interest is in short-term (day-by-day) effects of promotional activities on sales. Examples are: other situations in the recreation and leisure business, cultural events (theatre, cinema) and sales promotions (e.g. weekend offerings) for products in supermarkets.First a model was specified and estimated that relates number of visitors to advertising effort. It also takes into account non-advertising variables that effect the number of visitors.Then this model was used in a heuristic advertising planning procedure, which by means of incremental analysis, for a given budget level searches for the optimal allocation of the advertising budget over media and time.With this procedure, ways to readjust the advertising policy were found: by allocating the budget differently over media and time and by changing the overall budget level.Several recommendations were made to the management of the park, a number of which have already been implemented.     

Multistage multiproduct advertising budgeting

We propose and analyze an effective model for the Multistage Multiproduct Advertising Budgeting problem. This model optimizes the advertising investment for several products, by considering cross elasticities, different sales drivers and the whole planning horizon. We derive a simple procedure to compute the optimal advertising budget and its optimal allocation. The model was tested to plan a realistic advertising campaign. We observed that the multistage approach may significantly increase the advertising profit, compared to the successive application of the single stage approach.     

汇率的就业传导渠道及其效应测算——基于中国制造业面板数据的实证研究

文章研究了汇率的就业传导渠道,及其行业异质性。本文基于传统的生产函数理论,通过建模和理论分析得出:汇率影响就业的传导渠道主要有出口需求、资源配置和效率的三渠道。并基于中国制造业30个行业的2003年至2009年的面板数据,运用残差替代法和面板平滑机制转换回归,测算出各传导渠道在汇率影响就业过程中所起到的作用,结果表明:在整个传导机制中,出口需求对就业的作用较强,效率渠道和资源配置作用相对较弱;人民币升值对就业的总体效应为负效应,且传导机制中各渠道均具不同程度不同特征的行业异质性。     

National and store brand advertising strategies

As the propensity of premium store brands (SBs) increases, retailers must consider different ways to drive sales besides promotional strategies. With this in mind, we consider a national brand (NB) and a (premium) SB co-existing in a market. Each brand has to decide the amount to invest in advertising its product and the prices to charge its customers, which can be determined separately or in unison. When either advertising expenditures or pricing decisions are set, each brand must keep in mind that the advertising efforts and revenue may spillover between the two brands, customers who intend to purchase the NB may end up purchasing the SB and vice versa. We derive an analytical model of the situations described and characterize equilibrium advertising decisions. We find that the characteristics of a premium SB may depend on which marketing/promoting instrument (advertising or pricing) is the primary method for driving demand; and in some situations an NB may be better off to not advertise at all and instead let the premium SB carry out all of the advertising.     

Coordinating advertising and pricing in a manufacturer–retailer channel

Cooperative advertising is a practice that a manufacturer pays retailers a portion of the local advertising cost in order to induce sales. Cooperative advertising plays a significant role in marketing programs of channel members. Nevertheless, most studies to date on cooperative advertising have assumed that the market demand is only influenced by advertising expenditures but not by retail price. This paper addresses channel coordination by seeking optimal cooperative advertising strategies and equilibrium pricing in a two-member distribution channel. We establish and compare two models: a non-cooperative, leader–follower game and a cooperative game. We develop propositions and insights from the comparison of these models. The cooperative model achieves better coordination by generating higher channel-wide profits than the non-cooperative model with these features: (a) the retailer price is lower to consumers; and (b) the advertising efforts are higher for all channel members. We identify the feasible solutions to a bargaining problem where the channel members can determine how to divide the extra profits.     

Optimal resource allocation across related channels

In this paper, we consider resource allocation strategies of a limited resource across two related channels in a multi-period setting. We study a stochastic control problem where the objective is to determine the optimal limited resource allocation policy across two related channels and optimal transshipment policy between these two channels. We characterize some structural results of the optimal resource allocation policy and show that it is determined by three monotone curves.     

Contract type and decision right of sales promotion in supply chain management with a capital constrained retailer

From the practices of Chinese consumer electronics market, we find there are two key issues in supply chain management: The first issue is the contract type of either wholesale price contracts or consignment contracts with revenue sharing, and the second issue is the decision right of sales promotion (such as advertising, on-site shopping assistance, rebates, and post-sales service) owned by either manufacturers or retailers. We model a supply chain with one manufacturer and one retailer who has limited capital and faces deterministic demand depending on retail price and sales promotion. The two issues interact with each other. We show that only the combination (called as chain business mode) of a consignment contract with the manufacturer’s right of sales promotion or a wholesale price contract with the retailer’s right of sales promotion is better for both members. Moreover, the latter chain business mode is realized only when the retailer has more power in the chain and has enough capital, otherwise the former one is realized. But which one is preferred by customers? We find that the former is preferred by customers who mainly enjoy low price, while the latter is preferred by those who enjoy high sales promotion level.     

Optimal advertising pulsation policies: a dynamic programming approach

This study formulates and solves an advertising pulsation problem for a monopolistic firm using dynamic programming (DP). The firm aims at maximising profit through an optimal allocation of the advertising budget in terms of rectangular pulses over a finite planning horizon. Aggregate sales response to the advertising effort is assumed to be governed by a modified version of the Vidale–Wolfe model in continuous time proposed by Little. Using a numerical example in which a planning horizon of one year is divided into one, two through ten equal time periods, computing routines are developed to solve 150 DP problems. Computational results show among other findings that the performance yielded by the DP policy dominates the uniform advertising policy (constant spending) for a concave advertising response function and the advertising pulsing policy (turning advertising on and off) for a linear or convex response function.     

New product advertising in dynamic oligopolies

The success of the introduction of a new product in a market is very sensitive to the marketing decision variables adopted by the firm. In the present paper we are concerned with the question of new product advertising in a heterogeneous oligopoly market consisting of N firms. A dynamic game is formulated to model strategic as well as sales interactions in such a market. Optimal advertising strategies are identified as open-loop Nash solutions.The comments of two anonymous referees are appreciated. The first author wishes to acknowledge support from NSERC (Grant No. OGP0037342).     

Integrated multi-site aggregate production-pricing planning in a two-echelon supply chain with multiple demand classes

This paper proposes a production and differential pricing decision model in a two-echelon supply chain that involves a demand from two or more market segments. In this framework, the retailer is allowed to set different prices during the planning horizon. While integrated production-marketing management has been a key research issue in supply chain management for a long time, little attention has been given to set prices and marketing expenditures in integrated multi-site (parallel) manufacturing systems and multiple demand classes. Generally, the presence of multiple demand classes induced by different market segments may impose demand leakage and then change production plan and ordering policies throughout the supply chain system. To tackle this problem, this paper develops a novel approach in order to provide an optimal aggregate production and marketing plan by interconnecting the sales channels of the retailer and demand. A non-linear model is established to determine optimal price differentiation, marketing expenditures and production plans of manufacturing sites in a multi-period, multi-product and multi-sale channels production planning problem by maximizing total profit of the supply chain. To handle the model and obtain solutions, we propose an efficient analytical model based upon convex hulls. Finally, we apply the proposed procedure to a clothing company in order to show usefulness and significance of the model and solution method.     

灾后运输网络中的最短路修复合作博弈

在最短路修复合作博弈中,当灾后运输网络规模较大时,最优成本分摊问题难以直接求解。基于拉格朗日松弛理论,提出了一种最短路修复合作博弈成本分摊算法。该算法将最短路修复合作博弈分解为两个具有特殊结构的子博弈,进而利用两个子博弈的结构特性,可以{高效地}求解出二者的最优成本分摊,将这两个成本分摊相加,可以获得原博弈的一个近乎最优的稳定成本分摊。结果部分既包含运输网络的随机仿真,也包含玉树地震灾区的现实模拟,无论数据来源于仿真还是现实,该算法都能在短时间内为最短路修复合作博弈提供稳定的成本分摊方案。     

The implications of postponement on contract design and channel performance

We analyze a supply chain consisting of one manufacturer and one retailer under consignment sales with a revenue sharing contract. The manufacturer produces before, but charges price to sell the products through the retailer after the demand curve is revealed. The retailer deducts a fraction from the selling price for each unit sold and remits the balance to manufacturer. We refer to the capability whereby firms delay price decision and make sales in response to actual market condition as postponement. We find that, when market demand admits a multiplicative structure, the revenue share and allocation of channel profit between the firms when they have postponement capability are similar to when they do not have such capability. Postponement improves the profits of individual firms. Such an effect is more phenomenal in the centralized system than in decentralized system, and when the market demand is more sensitive to price changes. However, it causes the profit loss, defined as the percentage deviation of channel profit in the decentralized system relative to the centralized system, to worsen, and the gap widens with retailer’s sales cost. When the demand has an additive structure, while the roles of postponement on firms’ decisions differ slightly from those under the multiplicative structure, the structure of the strategic interactions between firms and relative channel performance are not significantly altered.     

The multiple resource constrained project scheduling problem: A breadth-first approach

We describe a simple breadth-first tree search scheme for minimizing the makespan of a project consisting of a partially ordered network of activities under multiple resource constraints. The method compares quite favourably with existing techniques that employ depth-first or best-first search; in particular, it is able to solve optimally on a Pentium PC running SCO UNIX the entire set of 680 benchmark problems (First Lot: 480, Second Lot: 200) generated by Kolisch et al., 1995. The new algorithm has also been checked out experimentally on additional random test problems at graded levels of difficulty that were generated using two parameters: the threshold, which determined the predecessors of an activity, and the total resource availability of each resource type. The breadth-first scheme can be modified quite readily to do best-first search or to minimize measures other than makespan such as mean flow time and maximum tardiness.     

Using mixture‐amount modeling to optimize the advertising media mix and quantify cross‐media synergy for specific target groups

One of the critical decisions in media planning is how to allocate advertising efforts across different media. While studies indicate that marketers can create positive synergy effects by spreading their effort across several media, there is little understanding of how much should be invested in each specific medium to optimize advertising results. In this study, we apply a novel methodology, mixture‐amount modeling, which allows advertisers to determine the optimal allocation of advertising effort across media as a function of the total advertising effort. Moreover, we test how the optimal allocation and the resulting response change for consumers with distinctive media usage patterns and varying degrees of product category experience. Based on these results, we quantify the potential synergy between media and calculate the synergistic capacity for specific target groups. We apply the model to data from 52 beauty care advertising campaigns that ran on TV and in magazines in the Netherlands and Belgium. We determine the optimal allocation of advertising investments (measured through Gross Rating Points) to maximize campaign recognition. Our findings support the existence of positive synergistic effects between magazine and TV advertising and illustrate that these effects depend on consumers' media usage and product category experience.