Optimal allocation of profit across companies operating with a joint salesforce Optimale Allokation von Deckungsbeiträgen bei Unternehmen mit einem gemeinsamen Vertrieb

We investigate the problem of companies that want to cooperate either by combining their salesforces or by operating a joint salesforce. Companies may have salesforces of different sizes that also differ in their effectiveness. They need an instrument to evaluate how much they gain from a cooperation, and a mechanism to allocate the profit in a fair way. In the typical case of a lack of response data we suggest to infer additional sales based on response functions for which the Dorfman-Steiner theorem is holding in the optimum. Searching for an appropriate allocation mechanism becomes difficult because typical cooperative solutions where each company pays its own salesforce but benefits from increased sales, or where commission rates on sales are paid to a joint subsidiary, may lead to asymmetric distributions of profit contribution across companies. We suggest that companies follow the Nash-solution for cooperative games which recommends that each company receive in advance the profit it would achieve in the case of non-cooperation, and that the remaining profit be shared equally.     

Optimal pricing and two-dimensional warranty policies for a new product

For commercial products, pricing and warranty are two crucial marketing strategies, which are used to promote the potential market share. The warranty policy adopted by most of the capital-intensive products, such as machines and automobiles, usually has two dimensions, i.e. warranty age and warranty usage. In this paper, we propose to investigate the profit-maximisation problem, in which the revenue and costs will be affected by the product price and the area of warranty region, for a new product sold under two-dimensional warranty. We assume that the product sales can be captured by a stochastic Bass model based on the nonhomogeneous Poisson process. The product follows a two-dimensional failure process and is covered by a non-renewable free minimal-repair warranty, with age and usage limits. We focus on three revenue/cost components, i.e. sales revenue, warranty cost and production cost, that will significantly affect a firm’s total profit. The profit is maximised by jointly optimising three decision variables, i.e. product price, warranty age limit and warranty usage limit. Numerical experiments are conducted to illustrate the effects of some key parameters, including product reliability, price elasticity, warranty elasticity and learning effect factor, on the optimal settings of the price and warranty region.     

Ordering and sales effort investment for temperature-sensitive products considering retailer’s disappointment aversion and elation seeking

We investigate a retailer’s optimal policy of ordering and sales effort investment for temperature-sensitive products in a stylised newsvendor setting considering the effects of the retailer’s disappointment aversion and elation seeking. We provide a function to describe the demand for temperature-sensitive products and a psychological utility function to capture the retailer’s perceived utility of disappointment aversion and elation seeking. Next, we construct four joint ordering and sales effort decision models by integrating the profit and psychological utility for high temperature-sensitive products, medium temperature-sensitive products, low temperature-sensitive products and high–low temperature-sensitive products, respectively. By solving the constructed models, we determine the optimal policy of order quantity and sales effort level. We find that the average temperature in the selling season, the temperature sensitivity parameter, disappointment aversion degree and elation seeking degree can affect the retailer’s optimal policy, and the trends and extents of the effects for each temperature-sensitive product may be different from those for the other temperature-sensitive products. Our models also suggest that the optimal policy for temperature-sensitive products is more conservative than the one for general non-temperature-sensitive products. The policy of a retailer who is primarily concerned with disappointment aversion is more conservative than the one of a disappointment-neutral retailer. The policy of a retailer who mainly focuses on elation seeking is more radical than the one of an elation-neutral retailer. Our results show that a retailer must consider the effects of temperature and psychological behaviour on policy and should make decisions regarding order quantity and sales effort level according to the temperature sensitivity type of selling products and degrees of disappointment aversion and elation seeking.     

电子商务环境下耐用品制造商和零售商策略的博弈

构造了由一个制造商和一个零售商组成的两周期双渠道耐用品销售模型,制造商同时通过零售商和自有电子直销渠道销售产品。通过求解每个周期优化问题的Kuhn-Tucker条件,得到供应链成员每个周期的最优策略和利润。通过与单一渠道比较分析,发现产品的耐用性和电子直销渠道的成本影响着双方的最优策略,当制造商电子渠道的销售成本高于一定门槛时,制造商开通电子渠道,但不接收订单获利会更多。通过分析还发现当制造商电子渠道的销售成本较高时,制造商开通电子直销渠道,零售商将获利。     

Achieving product variety through optimal choice of module variations

The trade-off in designing products typically involves consideration of manufacturing and development costs, and the potential market share. Modular design of products has been identified as one way of providing firms with a competitive advantage. In the context of modular product design, some of the pertinent questions are: (i) how many product varieties in a product group should be introduced in the market; and (ii) what is the minimum number of module-options required to support this variety? In this paper we study the optimality of such decisions related to modularization in two separate scenarios: (i) the module supplier is an independent operator whose decisions are not coordinated with that of the firm; and (ii) the module supplier is a wholly owned subsidiary of the firm. For these scenarios, we show how the choice of module-options affects product variety, total sales, product development cost, and hence, the firm's profit. We establish that the module-options can be rank ordered, based on profit margin and customer rating, and that the optimal set of module-options to be acquired or developed would include only the top ranked options. We also show how to determine the number and type of module-options a firm should acquire to maximize its profit. Finally, we discuss how our algorithm can be extended to the case of firms that deal with products having multiple module-types.     

考虑最优定价与质量决策的平台销售模式选择研究

为了研究电商平台与制造商的销售模式选择问题,在产品质量外生和内生情况下,分别建立制造商领导的转售与平台零售商领导的代理销售动态博弈模型,通过逆序归纳法求解出各决策方的最优定价与质量水平,并运用数值分析法验证结论的有效性。研究发现,平台边际运营成本与市场异质性共同决定产品市场覆盖率,平台与制造商可根据市场环境参数的不同选择最优的销售策略。质量外生时,平台与制造商的产品零售价格相同,但两者的最优销售模式选择总是不一致。质量内生时,当平台边际运营成本较低,且市场异质性较大时,平台与制造商均选择代理销售模式,此时双方均实现帕累托改进。     

Optimal price and maximum deal size on group-buying websites for sellers with finite capacity

This paper presents an analytical model for sellers with finite capacity to optimise their price and maximum deal size limit on group-buying websites. For the general demand functions that satisfy some mild regularity conditions, the optimal strategies and the corresponding deal parameters are characterised. The optimal strategies demonstrate that deep online discounts (selling products below the cost or even selling products for free) can be optimal if the maximum deal size is used strategically. Moreover, deep discounts can be beneficial even if the capacity is tight, which explains the use of deep discounts commonly observed in practice. Our results also provide the operators of group-buying websites with useful suggestions on how to induce sellers to offer deep discounts. Sensitivity analysis with regard to the minimum deal size and capacity is provided. Our analysis shows that counter-intuitively selling out capacity may not always be optimal, even if the amount of capacity cannot satisfy the unconstrained optimal sales quantity online. Finally, we extend the model to consider offline prices being sellers’ decisions and discuss the robustness of the optimal strategies when the demand is stochastic.     

Optimal pricing and core acquisition strategy for a hybrid manufacturing/remanufacturing system

Remanufacturing is one of the product recovery options where the quality of used products (cores) is upgraded to ‘as-good-as-new’ conditions. In this article, we consider a monopolist firm selling new and remanufactured products to quality-conscious primary customers and price-sensitive secondary customers, respectively, with one-way substitution, i.e. some primary customers may substitute new products by remanufactured products while secondary customers can never afford to buy new products. We develop economic models under two scenarios – when the supply of cores is unconstrained and when manufacturers have to procure cores at an acquisition price. The major observations of the article are as follows. A firm is better off when there is no constraint on the supply of cores. Even when cores have to be acquired at an acquisition price, the profitability is higher than that when the firm does not engage in remanufacturing activities. When a larger number of primary customers replace new products with remanufactured products, there is partial cannibalization of new product sales; however, the combined market share and profitability of the firm increase. When core supply is constrained and customers are less sensitive to core prices, the limited supply of cores may render remanufacturing an infeasible option for the firm. Therefore, firms should not only generate awareness among primary customers to buy remanufactured products, but also step up efforts to ensure a steady supply of cores. We conclude the article with managerial implications and directions for future research.     

Advance booking discount in the presence of spot market

We consider a risk-neutral firm that can procure raw material via long-term contract as well as in spot market, using the material as a one-to-one input to produce a seasonal product and selling it in the customer market. The firm can use the advance booking discount (ABD) program to entice customers to place their orders prior to the selling season. The ABD program provides an opportunity for the firm to update its understanding of the regular demand and spot price. We separately analyse two cases: (NI) no information updating and (IU) information updating cases. In each case, we derive the optimal discount pricing strategy and corresponding expected profit of the firm. By comparing them, we investigate the value of information updating obtained from the pre-committed order. Among others, our study finds that if the product has a relatively high profit margin, or a low profit margin where the raw material spot price is more sensitive to the trading volume, it is optimal for the firm to implement the discount strategy. The optimal discount coefficient in the IU case is never lower than in the NI case. We further find that the optimal discount coefficient in the NI case decreases in spot market volatility; however, it increases in spot market volatility if and only if the firm’s market share is larger than half of the total market demand in the IU case.     

Optimal purchase and selling strategy for wholesaler of produce: sorted or unsorted selling?

Produce (e.g. fruit and vegetable) varies in quality when it is picked from plants. Then a produce wholesaler has two sales strategies: (1) unsorted selling (US), i.e. selling the produce to the market at one price and (2) sorted selling (SS), i.e. pre-sorting the produce into different grades by quality and selling them at different prices. When the SS strategy is adopted, the demands of the different grades are uncertain and substitutable. In this paper, we study the joint optimal purchase and sales strategy for selling mixed quality produce to customers with heterogeneous quality preferences. We first derive the optimal purchase policies under the two strategies and then identify the conditions under which the SS or US strategy is optimal. We show that the optimal sales strategy is determined by the marginal purchase and sorting cost and the fixed investment cost, the overall quality level of the produce, and the substitution rate for the high-quality and low-quality produce. This finding differs from the conventional wisdom that the SS strategy is optimal in the produce retail business. Finally, we conduct numerical studies based on real-world data to generate managerial insights from the analytical findings.     

The effectiveness of investment in lead time reduction for a make-to-stock product

This paper focuses on a firm selling a make-to-stock product with a constant customer demand rate. The firm follows an exact (Q, r) policy for raw material inventory control and faces a random replenishment lead time. Through this research, we wish to gain a better understanding of the impact of investing in reducing supply lead time when the investment costs have to be borne, partly or fully, by the firm. This work is motivated by the recognition that lead time reduction is now of strategic importance in the successful operation of a firm. We examine different types of investment schemes in replenishment lead time reduction and the different cost models they generate. We present analytical and numerical results and insights for each type of model, compute the optimal (Q, r) policy and the associated investment levels. The work presents new results, and sheds light on some apparently counter-intuitive observations.     

Multi-product selective newsvendor problem with service level constraints and market selection flexibility

We consider a multi-product multi-market newsvendor problem where the decision-maker could select some markets to serve. The considered problem involves the integration of procurement and market selection decisions. The products are procured from an external supplier. We assume that the realised demand for each product should be satisfied. In the case of shortages, the firm procures items at a higher cost. The paper considers the case where the selling prices, market entry costs, and product demand distributions are market dependent. Specifically, we discuss three cases of the Multi-Product Selective Newsvendor Problem: flexible market entry case, full market entry case and partial market entry case. The mathematical models of the above cases result in binary nonlinear programmes. We develop solution algorithms for solving the resulting combinatorial problems. Some managerial insights are provided.     

Optimal ordering policy for a price-setting newsvendor with option contracts under demand uncertainty

In this article, we investigate the newsvendor problem in a joint ordering and pricing setting in the presence of option contracts under demand uncertainty. At the beginning of a single selling season, the newsvendor who faces additive stochastic demand can obtain goods through two ways: ordering from a firm or purchasing and exercising call options. Single ordering (ordering from a firm only or purchasing and exercising call options only) and mixed ordering (ordering from a firm and purchasing and exercising call options simultaneously) cases are investigated. We find that the newsvendor’s optimal pricing and ordering strategies exist and are unique for both cases, respectively. In addition, when both cases are available, mixed ordering is the newsvendor’s optimal ordering policy. If only single ordering is available, the newsvendor prefers ordering from a firm when demand risk is low, while enjoys purchasing and exercising call options when demand risk is high. We also find that with option contracts, the newsvendor’s optimal order quantity and maximum expected profit are all decreasing in the option price and exercise price of product, while the optimal retail price in terms of option price and exercise price of product are intricate. Moreover, we show that, mixed ordering is more capable to deal with supply price volatility risk.     

新鲜度差异下两种可替代生鲜品的多阶段定价策略研究

研究单个零售商销售2种可替代生鲜产品时的价格决策,建立3种定价策略下的决策模型,得到2种产品的最优固定价格、最优折扣价格和最优捆绑价格售价;通过数值仿真分析影响零售商价格决策的因素及其影响大小。研究结果表明,3种策略下产品价格都与产品新鲜度临界值同方向变化;最优固定价格随销售期临近度的增大而变高;对比3种策略下零售商的利润发现,有时捆绑价格是占优策略,有时折扣价格是占优策略,参数的大小是关键因素。     

Case study: Determining the range of standard sizes of capital goods to be manufactured

This paper describes a project that was performed to maximize profit from the manufacture of a particular type of fork lift truck, with consideration given to manufacturing quantity, range of sizes and sales price. Sales revenue and manufacturing costs were evaluated for each size of truck at different sales levels. The optimal range of sizes was thon determined using a dynamic programming approach. The results of the study together with an outline of how the work may be extended in the future are discussed.     

Strategic Allocation of Inspection Effort In A Serial, Multi-Product Production System

For a multi-stage production system, optimal location of inspection activities is an important consideration in minimizing the inspection-related and salvage costs. Set-up and inventory carrying costs also become important factors when several products are produced on the same line due to the product changeovers involved.

In this paper we discuss the effect of these additional costs (set-up and inventory carrying) on the inspection strategy, i.e., “all or none” versus partial inspection. We suggest a shortest path heuristic to determine the strategic location of inspection activities and the production lot sizes.     

Scope versus focus: issues of flexibility, capacity, and number of production facilities

How should a multi-product manufacturing firm design production facilities? How many facilities should it have? How many and which products should be assigned to each facility? What batch sizes/scheduling rules are appropriate for facilities making more than one product? These are questions that have become more relevant now as advances in manufacturing technologies offer an increasing array of equipment choices. In this article, we introduce models that can help operations managers answer the above questions. For a specific product mix, these models lead to explicit expressions for the number of facilities, the number of products assigned to each facility and their corresponding capacities. We evaluate the effect of different operating parameters and scheduling policies on the optimality of different configurations. In particular, we show that the choice of the scheduling and batch sizing policies can have a significant effect on the nature of the optimal mix of flexible and d edicated facilities as well the size of these facilities.     

Multi-generation pricing and timing decisions in new product development

When planning for the introduction of a stream of new products into the marketplace, managers must consider both the timing and dynamic pricing decisions to determine an appropriate entry strategy into the marketplace. Literature in new product development (NPD) typically addresses optimal timing and pricing decisions independently. We develop an analytical model of coordinated product timing and pricing decisions when there are two generations of a new product under consideration. Factors driving the timing and pricing decisions include the unit sales and cost relationships for each generation as well as NPD costs for introducing the next generation of products. We derive analytic results that characterise the optimal timing and pricing strategies for a single product rollover scenario. We analyse several numerical examples to illustrate the interplay between optimal pricing and time-to-market strategies under more general settings.     

Inventory competition and incentives to back-order

In this paper we consider the issue of inventory control in a multi-period environment with competition on product availability. Specifically, when a product is out of stock, the customer often must choose between placing a back-order or turning to a competitor selling a similar product. We consider a competition in which customers may switch between two retailers (substitute) in the case of a stock-out at the retailer of their first choice. In a multi-period setting, the following four situations may arise if the product is out of stock: (i) sales may be lost; (ii) customers may back-order the product with their first-choice retailer; (iii) customers may back-order the product with their second-choice retailer; or (iv) customers may attempt to acquire the product according to some other more complex rule. The question we address is: how do the equilibrium stocking quantities and profits of the retailers depend on the customers' back-ordering behaviors? In this work we consider the four alternative back-ordering scenarios and formulate each problem as a stochastic multi-period game. Under appropriate conditions, we show that a stationary base-stock inventory policy is a Nash equilibrium of the game that can be found by considering an appropriate static game. We derive conditions for the existence and uniqueness of such a policy and conduct a comparative statics analysis. Analytical expressions for the optimality conditions facilitate managerial insights into the effects of various back-ordering mechanisms. Furthermore, we recognize that often a retailer is willing to offer a monetary incentive to induce a customer to back-order instead of going to the competitor. Therefore, it is necessary to coordinate incentive decisions with operational decisions about inventory control. We analyze the impact of incentives to back-order the product on the optimal stocking policies under competition and determine the conditions that guarantee monotonicity of the equilibrium inventory in the amount of the incentive offered. Our analysis also suggests that, counterintuitively, companies might benefit from making their inventories “visible” to competitors' customers, since doing so reduces the level of competition, decreases optimal inventories and simultaneously increases profits for both players.     

The news-vendor problem with drop-shipping and resalable returns

As e-commerce expands, more and more products are offered online to attract internet consumers’ interest. These products are then shipped to consumers’ home by a drop-shipper. Drop-shipping seems to be a good option to sell products in addition to physical stores. Furthermore, both types of products, either sold in store or on Internet can be returned by consumers, with often a higher return ratio for those purchased on Internet. To model these two sales channel and the interactions between them, we consider a News-Vendor (NV) managing both a physical store and an online sale channel that can be fulfilled by a drop-shipping option. We also consider the possibility of reselling products that are returned by consumers during the selling season. The concavity of the expected profit is proven and the optimality condition is obtained. Promising results are obtained from a numerical analysis. In particular, we show that the expected profit can be 14.4% less than the optimal expected profit if the return effect is ignored. Using drop-shipping option can reduce the optimal store inventory by 31.2% and if the NV has no drop-shipping option, the expected profit can be 9% less.