Integrated retail decisions with multiple selling periods and customer segments: Optimization and insights

Integrating retail decisions on such aspects as assortment, pricing, and inventory greatly improves profitability. We examine a multi-period selling horizon where a retailer jointly optimizes assortment planning, pricing, and inventory decisions for a product line of substitutable products, in a market with multiple customer segments. Focusing on fast-moving retail products, the problem is modeled as a mixed-integer nonlinear program where demand is driven by exogenous consumer reservation prices and endogenous assortment and pricing decisions. A mixed-integer linear reformulation is developed, which enables an exact solution to large problem instances (with up to a hundred products) in manageable times. Empirical evidence is provided in support of a classical deterministic maximum-surplus consumer choice model. Computational results and managerial insights are discussed. We find that the optimal assortment and pricing decisions do not exhibit a simple, intuitive structure that could be analytically characterized, which reflects the usefulness of optimization approaches to numerically identify attractive trade-offs for the decision-maker. We also observe that suboptimal inventory policies significantly decrease profitability, which highlights the importance of integrated decision-making. Finally, we find that the seasonality of consumer preferences and supply costs present an opportunity for boosting the profit via higher inventory levels and wider assortments.     

A Model for Determining Retail Product Category Assortment and Shelf Space Allocation

We develop a category management model to aid retailers in the space constrained decisions of which products to stock (assortment) and how much shelf space to allocate to those products. The model is formulated as a constrained optimization problem with two basic decision variables: assortment and allocation of space to the items in the assortment. The non-linearities in the objective function and the zero-one decision variables disallow a closed form solution. We develop a heuristic solution procedure based on simulated annealing and test it on a problem with a known optimum. We also apply the technique to a larger problem without a known optimum. Finally, the solution found by simulated annealing is compared against a solution produced using a shelf allocation rule based on share of sales.     

消费者导向类型与电商全渠道决策研究

从现实出发，基于不同消费者导向类型研究了电商的全渠道决策问题。首先建立电商单渠道销售的基础模型，并得出最优产品组合、价格和交付时间。在此基础上，给出了消费者为产品导向型和渠道导向型情况下电商采取全渠道决策的条件，得出双渠道产品组合、价格及交付时间的最优决策；并进行了数值验证。研究发现，同一渠道提供的产品其最优价格相同，最优交付时间只和消费者耐心程度及交付成本函数有关。若消费者为产品导向型，仅当双渠道运营成本之差较小且消费者耐心程度较低时，电商进入线下渠道才有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供剩余产品。若消费者为渠道导向型，电商进入线下渠道必然有利可图，且在线下渠道提供最受欢迎的产品，线上渠道提供所有产品。     

Joint product assortment,inventory and price optimization to attract loyal and non-loyal customers

In this paper, we analyze the emerging retail practice of carrying a combined product assortment consisting of both regular “standard” products and more fashionable and short-lived “special” products. The purpose of this practice is to increase store traffic by attracting heterogeneous classes of customers, which drives up sales of standard products due to the potential cross-selling effect. Customers who are primarily attracted by special products will also buy some standard products. In this context, we analyze three decisions that are crucial for a retailer׳s commercial success: the product assortment, the inventory levels and the pricing. We propose an optimization model and an iterative heuristic to analyze the trade-offs between the combined product assortment, the inventory level and the price per product when there is limited shelf space. Using numerical experiments, we show that our heuristic can be trusted and that its accuracy improves when the number of products increases. Our findings indicate that to attract more customers for standard products, a retailer may benefit from carrying low priced special products which, if considered in isolation, would be non-profitable. As the cross-selling effect decreases, a retailer should focus more on the standard assortment by increasing its size and decreasing the prices. However, introducing special products and ignoring the cross-selling effect may decrease a retailer׳s profitability. We show that the introduction of special products involves more than just choosing the right specials for non-loyal customers but impacts the global assortment planning, the standard products and the products pricing.     

Category Captainship vs. Retailer Category Management under Limited Retail Shelf Space

Shelf‐space scarcity is a predominant aspect of the consumer goods industry. This paper analyzes its implications for category management. We consider a model where two competing manufacturers sell their differentiated products through a single retailer who determines the shelf space allocated to the category. The scope of category management is pricing. We consider two category management mechanisms: retailer category management (RCM), where the retailer determines product prices and category captainship (CC), where a manufacturer in the category determines them. Our analysis reveals that the retailer can use the form of category management and the category shelf space to control the intensity of competition between manufacturers to his benefit. We also show that the emergence of CC depends on the degree of product differentiation, the opportunity cost of shelf space, and the profit sharing arrangement in the alliance. The equilibrium category shelf space under CC may be higher than under RCM if the value to the retailer of eliminating double marginalization and putting price pressure on the non‐captain manufacturer dominates the loss from sharing the profit with the category captain. CC has been criticized for disadvantaging non‐captain manufacturers. While we provide some support for this claim, we also find that CC may benefit non‐captain manufacturers when implemented by a powerful retailer in categories with sufficiently differentiated products, because the shelf space allocated to the category increases in this case.     

A Single‐Period Assortment Optimization Model

This paper studies a single‐period assortment optimization problem with unequal cost parameters. The consumer choice process is characterized by a Multinomial Logit (MNL) model. When the store traffic is a continuous random variable, we explicitly derive the structure of the optimal assortment. Our approach is to use a comprehensive measure–profit rate to evaluate the profitability of each variant and then determine which product should be offered. We demonstrate that the optimal assortment contains the few items that have the highest profit rate. When the store traffic is discrete, the optimal solution is difficult to obtain. We propose a “profit rate” heuristic, which is inspired by the result for the case of continuous store traffic. In a special case with equal cost parameters and normal demand distribution, the profit rate heuristic is indeed optimal. Using randomly generated data, we test the effectiveness of the heuristic and find that the average percentage error is less than 0.1% and that the hit rate is above 90%. Our research provides managerial insights on assortment planning and accentuates the importance of measuring the profitability of each product when the demand is random and cannibalization among different products exists.     

A shelf-space optimization model when demand is stochastic and space-elastic

The more customer demand is impulse-driven, the more it is space-dependent and the more it is subject to variation. We investigate the corresponding problem of retail shelf-space planning when demand is stochastic and sensitive to the number and position of facings. We develop a model to maximize a retailer׳s profit by selecting the number of facings and their shelf position under the assumption of limited space. The model is particularly applicable to promotional or temporary products.We develop the first optimization model and solution approach that takes stochastic demand into account, since the current literature applies deterministic models for shelf-space planning. By the means of an innovative modeling approach for the case with space- and positioning effects and the conversion of our problem into a mixed-integer problem, we obtain optimal results within very short run times for large-scale instances relevant in practice. Furthermore, we develop a solution approach to account for cross-space elasticity, and solve it using an own heuristic, which efficiently yields near-optimal results. We demonstrate that correctly considering space elasticity and demand variation is essential. The corresponding impacts on profits and solution structures become even more significant when space elasticity and stochastic demand interact, resulting in up to 5% higher profits and up to 80% differences in solution structures, if both effects are correctly accounted for. We develop an efficient modeling approach, compare the model results with approaches applied in practice and derive rules-of-thumb for planners.     

Late season low inventory assortment effects in the newsvendor problem

The assumption of the newsvendor being able to satisfy demand as long as on-hand inventory is positive does not hold for a non-homogenous product. Consumers who do not find a unit of the product which satisfies their secondary features preferences may not purchase the product even though the newsvendor has positive on-hand inventory. This is likely to occur late in the season as inventory level declines. We solve a newsvendor problem in which the probability of purchase by consumers is increasing in on-hand inventory for any inventory level below that which is needed to have a complete assortment. We identify the sufficient optimality condition for the order quantity. We show that, unlike the case of inventory-dependent demand models in the literature, the optimal order quantity may decrease due to the assortment effect. We investigate two types of pre-end of season discounts, immediate all-units and delayed, as ways to mitigate the late season assortment effect and show that in some cases, they can increase the newsvendor׳s profit and free up the shelf space for other products.     

Data and Model Management in a Generalized MCDM-DSS*

Drawing upon the choice models developed in the multiple criteria decision making (MCDM) area, this paper proposes an architecture for designing an intelligent decision support system (DSS) that is intended to aid in making choices among multiple alternatives along multiple dimensions. It argues that effective support can be provided to the decision maker when the knowledge-based DSS is capable of dynamically selecting choice models appropriate to the domain and context of a particular problem being specified by the decision maker, and of properly applying them to the problem solution. Development of a prototype intended to partially represent application of the architecture is described. The paper concludes with suggestions for research extensions.     

零售货架的线性补贴策略与供应链协调

考虑由一个供应商和一个零售商构成的供应链,供应商提供零售商单一产品,零售阶段的市场需求量随机地依赖于零售商的货架展示量。由于货架空间的稀缺,零售商的成本为非线性的成本函数以符合实际的情况。如果零售商在观察到需求之前决定货架空间,货架补贴可以提高渠道效率;如果零售商在观察需求之后,进行货架决策,补贴降低了供应链效率。由于零售商的努力水平可以验证,供应商可以使用回购加零售货架的线性补贴策略协调供应链,但是需要考虑零售阶段的库存决策与货架分配的决策顺序,而采取完全不同的协调方式。最后通过数值算例说明了所得结论。     

基于谈判机制的优质货架与通道费

大型零售企业能够收取通道费的重要基础在于它所提供的货架资源尤其是优质货架能够在较大程度上提升制造商的市场销量,改善制造商的经营状况,增加制造商的利润。本文以货架对消费者效用的影响机制为研究基础,构建了相应的需求函数,并通过三阶段动态博弈模型分析了货架对零售价格、市场销量、厂商利润的影响,然后从制造商、零售商的参与约束以及渠道成员的利益协调等角度出发,讨论了通道费的可能性、存在性与合理性,最后从消费者福利的角度对零售商收取通道费的行为提出了相应的政策建议。     

基于品类管理和需求外生模型的医药电商网页空间优化策略

网页空间优化对电子商务企业的绩效有着显著影响。本文结合医药品的特性,利用需求外生模型从品类管理的角度研究医药电商的网页空间优化问题,即有限网页空间内的内容优化与内容布局优化。考虑存在商品缺货以及蚕食效应的情况下,本文首先基于需求外生模型使用极大似然估计法估计了商品市场份额与商品替代率,然后提出最大市场份额指标并构建了一个加权最大市场份额最大化的整数规划模型来优化医药电商网页的内容与内容布局。通过对中国知名医药电商1药网2015年8月1日到10月31日的乙肝类抗病毒药物专栏的销售数据进行实证分析,结果表明,本模型优化的推送内容和布局顺序可以有效提高1药网各药品专栏最高至27.21%的销量,乙肝其他抗病药物专栏可以提高8.06%。研究表明,本文提出的基于最大市场份额最大化的优化模型能有效决策网页空间优化来提高医药电商的销量与市场占有率。     

不同货架空间分配顺序下农产品供应链优化问题研究

货架是超市和生鲜便利店的重要资源，不仅具有储存和展示农产品的功能，同时货架空间大小对农产品的销量具有重要影响。针对产品需求受货架空间与零售价格共同影响的两级农产品供应链，在考虑供应商主导和零售商主导的情况下，分别对零售商在销售季节来临前和来临后分配货架空间四种分散式农产品供应链的最优决策与利润进行了分析，并与一体化供应链的最优决策进行了比较。研究发现，不论是在供应商主导还是在零售商主导的农产品供应链中，零售商在销售季节来临前分配货架空间，相比在销售季节来临后分配货架空间，农产品的批发价格与零售价格更高，分配的货架空间更小，供应商和零售商均获得更少的利润，相应的农产品供应链整体利润更少。因此，零售商在销售季节来临后分配货架空间对农产品供应链更有利。相比一体化供应链，分散式供应链的零售价格更高，分配的货架空间更小，供应链整体利润小于一体化供应链的最优利润，本文给出了基于利润共享与成本共担的合同对分散式供应链进行协调。最后，通过数值算例研究了参数变化对最优决策和供应链利润的影响。     

An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming

In this paper, we present an aggregate production planning (APP) model applied to a Portuguese firm that produces construction materials. A multiple criteria mixed integer linear programming (MCMILP) model is developed with the following performance criteria: (1) maximize profit, (2) minimize late orders, and (3) minimize work force level changes. It includes certain operational features such as partial inflexibility of the work force, legal restrictions on workload, work force size (workers to be hired and downsized), workers in training, and production and inventory capacity. The purpose is to determine the number of workers for each worker type, the number of overtime hours, the inventory level for each product category, and the level of subcontracting in order to meet the forecasted demand for a planning period of 12 months. Additionally, a decision support system (DSS) based on the MCMILP model is proposed. It will help practitioners find the “best” solution for an APP problem without having to familiarize themselves with the mathematical complexities associated with the model. An example to illustrate the use of the DSS is also included.     

A decision support methodology for strategic planning in maritime transportation

This paper presents a decision support methodology for strategic planning in tramp and industrial shipping. The proposed methodology combines simulation and optimization, where a Monte Carlo simulation framework is built around an optimization-based decision support system for short-term routing and scheduling. The simulation proceeds by considering a series of short-term routing and scheduling problems using a rolling horizon principle where information is revealed as time goes by. The approach is flexible in the sense that it can easily be configured to provide decision support for a wide range of strategic planning problems, such as fleet size and mix problems, analysis of long-term contracts and contract terms. The methodology is tested on a real case for a major Norwegian shipping company. The methodology provided valuable decision support on important strategic planning problems for the shipping company.     

Sequence Matters: Shelf‐Space Allocation under Dynamic Customer‐Driven Substitution

Customers who face a stockout situation often decide to purchase a different product in the same category. We analyze the resulting dynamic substitution problem in a retail environment, where customers serve themselves from the store shelves, such that the sequence of customer arrivals affects how scarce products are allocated to customers. We consider a setting with constrained shelf space, and we study how a retailer should optimally allocate such space between substitute products. We characterize environments where the sequence of customer arrivals can have a substantial impact on profitability.     

Decision support system for the batching problems of steelmaking and continuous-casting production

This paper investigates two batching problems for steelmaking and continuous-casting (SCC) production in an integrated iron and steel enterprise. The tasks of the problems are to make the decisions as how to consolidate ordered slabs into charges, and then how to group charges into casts. The effective decisions on these batching problems can help to balance the requirements of materials in downstream production lines, improve the customer satisfaction levels, and reduce production costs (including reduction of open ordered slabs, less slabs quality upgrading, reduction of steel-grade changeovers, and reduction of inefficient utilization of tundishes lives). We first formulate the problems as integer-programming models by consider practical constraints and requirements, and then develop the two heuristic algorithms for the corresponding batching problems. By embedding above models and algorithms, we develop decision support system (DSS) software with interactive planning editor. The DSS has been tested by using practical data set collected from the steelmaking plant in Baosteel which is one of the most advanced iron and steel enterprises in China. Computational experiments demonstrate that the models and algorithms developed can generate the satisfactory solutions when they work together with the planning editor in the DSS.     

Inventory management maximization based on sales forecast: case study

The major purpose of this paper is to present a concept for reliable planning of the sales of small firms, where the large number of product variants complicates the implementation of this kind of system considerably. First, a methodology is presented to set up sales forecasting so that it can be integrated into the inventory management process. This inventory management software interprets forecasting information and provides users with a decision support system to minimize stocks in stores while at the same time avoiding missed sales. It is best applied in company types requiring high precision inventories, notably those in the textile industry; a large range of patterns are produced with many small variations (colors, size, customizations, etc.) and these products have a limited lifetime. Inventory management is difficult due to the multitude of products to account for and the necessity to sell them quickly. The methodology is intended for inventory management at the end of the supply chain. In store, the number of references, their similarities and the necessity to minimize unsold stock greatly complicates the reordering and restocking process. These types of companies do not easily lend themselves to classic techniques of sales forecasting and require specialized methods to estimate their needs precisely.     

Fusion Product Planning: A Market Offering Perspective*

Devices that integrate multiple functions together are popular in consumer electronic markets. We describe these multifunction devices as fusion products as they fuse together products that traditionally stand alone in the marketplace. In this article, we investigate the manufacturer's fusion product planning decision, adopting a market offering perspective that allows us to address the design and product portfolio decisions simultaneously. The general approach adopted is to develop and analyze a profit‐maximizing model for a single firm that integrates product substitution effects in identifying an optimal market offering. In the general model, we demonstrate that the product design and portfolio decisions are analytically difficult to characterize because the number of possible portfolios can be extremely large. The managerial insight from a stylized all‐in‐one model and numerical analysis is that the manufacturer should, in most cases, select only a subset of fusion and single‐function products to satisfy the market's multidimension needs. This may explain why the function compositions available in certain product markets are limited. In particular, one of the key factors driving the product portfolio decision is the margin associated with the fusion products. If a single all‐in‐one fusion product has relatively high margins, then this product likely dominates the product portfolio. Also, the congruency of the constituent single‐function products is an important factor. When substitution effects are relatively high (i.e., the product set is more congruent), a portfolio containing a smaller number of products is more likely to be optimal.     

The resource recovery level decision for end-of-life products

Resource recovery from end-of-life (EOL) products is becoming increasingly engaged in by companies as a response to customer, consumer, government and social pressures, the electronics industry cites competitor pressures as being the main driver of EOL product take-back and recovery. Recovery can occur at three levels; i.e. product, part and material. Each of these options has economic and environmental advantages and disadvantages depending on the product type and a host of other influencing factors. The work described in this paper supports the decision as to the most favourable route from a cost and value perspective, a software model that provides such support is also described.