Optimal pricing and production decisions in the presence of symmetrical and asymmetrical substitution

Firms may produce a variety of generally similar products or may practice “scientific pricing” or revenue management where the firm will offer similar or somewhat differentiated products in multiple market segments at different prices. Whenever generally similar products are available, the demand for the products is linked through the ability of the customer to substitute one product for another. One widely known type of demand substitution is referred to as inventory-driven substitution where a customer will substitute for a product that is out of stock by buying a similar product. A second type of substitution occurs as a response to price-differences when a customer substitutes a less expensive product for a similar higher priced product.     

Optimal ordering and pricing decisions for a target oriented newsvendor

This paper is the first to study pricing and target oriented decision making together in the newsvendor model. Specifically, this paper studies a newsvendor who decides on order quantity and selling price to maximize the probability of achieving both profit and revenue targets simultaneously. First, it is shown that the probability of a newsvendor achieving both targets depends critically on the relative magnitudes of the profit margin and the ratio between the profit target and the revenue target. Second, the closed-form expressions of the optimal order quantity, the optimal selling price, and the maximal profit and revenue probability are obtained. It is shown that if the product has greater price elasticity, the best strategy is always to price lower and order more.     

Linking aggregate production planning with marketing pricing decisions

In this paper, we link production planning decisions to marketing decisions that involve the price of product groups. The focus of this paper is the development of a closed-loop procedure for aggregate production planning and pricing. We seek to satisfy uncertain demand while minimizing total costs that include material, labour, and inventory holding costs. The procedure is useful for variable demand to update short-term aggregate plans.     

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.     

Supply chain configuration for diffusion of new products: An integrated optimization approach

We develop an integrated/hybrid optimization model for configuring new products’ supply chains while explicitly considering the impact of demand dynamics during new products’ diffusion. The hybrid model simultaneously determines optimal production/sales plan and supply chain configuration. The production and sales plan provides decisions on the optimal timing to launch a new product, as well as the production and sales quantity in each planning period. The supply chain configuration provides optimal selection of options and safety stock level kept at each supply chain function. Extensive computational experiments on randomly generated testbed problems indicate that the hybrid modeling and solution approach significantly outperforms non-hybrid alternative modeling and solution approaches under various diffusion and supply chain topologies. We provide insights on optimal production/sales plan and supply chain configuration for new products during their diffusion process. Also, managerial implications relevant to effectiveness of the hybrid approach are discussed.     

Production and pricing problems in make-to-order supply chain with cap-and-trade regulation

This paper studies the production and pricing problems in MTO (make-to-order) supply chain containing an upstream manufacturer who produces two products based on MTO production and a downstream retailer. The manufacturer is regulated by cap-and-trade regulation and determines the wholesale prices of the two products. To comply with the regulation, the manufacturer can buy or sell emission permits through an outside market. The retailer determines its order quantities to meet the price-sensitive demands. We derive the optimal total emissions and production quantities of the two products, and based on them, we analyze the impact of emission trading price on the optimal production decisions and the two firms’ optimal profits. The emission trading decisions follow a two-threshold policy and the optimal total emissions are increasing in the cap. However, contrary to intuition, the optimal production quantities of the two products may be decreasing in the cap. The manufacturer׳s optimal profit is decreasing (increasing) in the buying (selling) price of emission permits, and that the retailer׳s optimal profit is decreasing in the buying (selling) price of emission permits. The optimal total emissions are decreasing in buying or selling price of emission permits, however, the optimal production quantities of the two products may be increasing (decreasing) in the buying (selling) price of emission permits. Numerical examples are conducted to illustrate our findings and some managerial insights are presented.     

Closed-loop supply chain configuration for new and reconditioned products: An integrated optimization model

Closed-Loop Supply Chain Management (CLSCM) is considered as a strategic response to the call for corporate sustainability while further expanding the scope of value creation to include product reconstruction. The Closed-Loop Supply Chain (CLSC) performance is directly related to the CLSC network design. The CLSC network design, with long-term and strategic connotations, involves selection of an integrated network of partner organizations to be engaged on one hand in the forward supply chain processes relevant to families of existing and new products and also involved in reverse supply chain activities relevant to reconstruction of the returned products. At the tactical level, Closed-Loop Supply Chain Configuration (CLSCC) attempts to address issues pertinent to launch of a new product and its reconstruction. The CLSC network design is well studied in the current literature, but addressing the CLSCC is neglected. To study the CLSCC problem we: (a) develop an integrated optimization model for problem; (b) present a real-world case study of a battery manufacturer; (c) based on the case study, we conduct a comprehensive set of computational experiments followed by a series of what-if analyses to compare profitability of the Forward Supply Chain Configuration (FSCC) versus the CLSCC; and (c) discuss the key observations and managerial implications drawn from the computational experiments, applicable to other real-world instances. The significant outcomes of the study suggest that: (i) performance of the firm׳s base case integrated CLSCC model is significantly better than the current supply chain model (ii) the sales-price ratio of new battery is found to be negatively related with the maximum acquiring price of used batteries; (iii) combination of sales price ratios of new and reconditioned batteries determines the total net profit for a given return rate. Finally, important managerial insights and scope for future research are discussed.     

Reducing Packaging Waste and Cost via Consumer Price Discounts

Low‐waste packaging may imply an inconvenience to consumers and cause firms to offer a compensating price discount. For example, Starbucks’ “Take the Mug Pledge” campaign provides a 10‐cent discount for customers who purchase coffee without a standard cup (i.e., customers provide their own cup). Understanding how such a discount drives demand and profit is the focus of this article. We consider a monopolist that can offer a reduced‐packaging option for its product at a variable cost savings. That option implies a transactional “inconvenience” cost for consumers. While that transactional cost is generally positive, our model also permits some consumers to associate convenience with reduced packaging. We derive the optimal price and discount that maximize profits. We show the optimal discount is bounded by the magnitude of the variable cost savings associated with the packaging reduction. We explore when the optimal discount is negative (a price premium), which requires a specific proportion of consumers to associate convenience with reduced packaging. We also derive conditions under which the firm should price to eliminate demand for the standard product, rather than segment the market, to leverage the variable cost savings of reduced packaging. When the variable cost savings are low (e.g., as is true for Starbucks), we show the profit curve for the segmenting policy is relatively flat for a discount up to several multiples of the cost differential. Finally, we demonstrate the potential for the reduced packaging option, with optimal discounting, to simultaneously increase profit and consumer surplus while reducing waste.     

Coordinating Sales and Raw Material Discounts in a Global Supply Chain

In this paper, the supplier of a key component to a global manufacturer offers a one‐time price discount; we study the firm's optimal response to the discount under two different strategies. In the first strategy, the firm does not pass along the discount to its customers (sales subsidiaries); the firm simply coordinates purchasing and production among the different factories to take advantage of this one‐time price discount. In the second strategy, the firm offers price discounts for its most profitable products in different sales subsidiaries to increase their demand. We carried out experiments for the two strategies based on a mathematical programming model, built around Toshiba's global notebook supply chain. Model constraints include, among others, material constraints, bill‐of‐materials, capacity and transportation constraints, minimum lot size constraints, and a constraint on minimum fill rate (service level constraint). Unlike most models of this type in the literature, which define variables in terms of single arc flows, we employ path variables, which allow for direct identification and manipulation of profitable and non‐profitable products.     

The Individually Responsible and Rational Decision Approach to Economic Lot Sizes for One Vendor and Many Purchasers

Banerjee's [2] joint economic lot size (JELS) model, along with related works by Monahan [12] and Lal and Staelin [10], represents one approach to minimizing the total inventory carrying and ordering costs of a vendor and his purchaser(s). Noting that JELS philosophy requires a coordinated system and that its practical implementation is problematic, we present an alternative approach to the same problem: the individually responsible and rational decision (IRRD) approach. The IRRD approach is consistent with a free enterprise system and easy to implement. In order to show that the IRRD approach is also more economical than the JELS approach, we first build a more refined JELS model for the case of one vendor and many identical purchasers. Drawing on earlier criticisms of specific JELS models, our refinement relaxes the lot-for-lot assumption commonly used by JELS scholars. To be comparable with earlier works, we retain the assumption of deterministic conditions and demonstrate the economic advantages of IRRD over JELS through a numerical example. An algebraic proof of IRRD's superiority over JELS is offered in the more general and realistic case of a vendor dealing with K nonidentical purchasers with reasonably predictable annual demand but uncertain order quantities and timings.     

Pricing decisions in a multi-criteria setting for product recovery facilities

Unpredictability in the arrival time and quantity of discarded products at product recovery facilities (PRFs) and varying demand for recovered components contribute to the volatility in their inventory levels. Achieving profit under such capricious inventory levels and stringent environmental legislations remains a challenge to many PRFs. This paper presents a multi-criteria decision model to determine a pricing policy that can simultaneously address two issues: stabilize inventory fluctuations and boost profits. The model considers that PRFs passively accepts discarded products as well as acquires them proactively if necessary. Under a multi-criteria setting, the current work determines prices of reusable and recyclable components to maximize revenue and minimize product recovery costs. A genetic algorithm is employed to solve the multi-criteria decision making problem. Sensitivity analysis is performed to investigate the effect of sorting yield, disassembly yield, and reusable component yield on the profits, prices, inventory levels, and disposal quantities.     

Advance selling with freebies and limited production capacity

We consider a two-period pricing model in which a seller offers freebies along with the product when making advance sales, and production is constrained by capacity. The seller can offer freebies to increase both market base and customer׳s valuation toward the product in advance. The customers strategically determine whether to purchase the product in advance and gain freebies when their valuation on the product is uncertain, or delay their purchase decision until the regular selling period. We characterize the optimal pricing, quality level of the freebie and production quantity decisions that maximize the expected profits of the seller over the two periods.     

Production planning for remanufactured products

This paper presents a methodology for production planning within facilities involved in the remanufacture of products. Remanufacturing refers to the process of accepting inoperable units, salvaging good and repairable components from those units, and then re-assembling good units to be re-issued into service. These types of facilities are common, yet many suffer from the unpredictability of good and repairable component yields, as well as processing time variation. These problems combine to make it extremely difficult to predict whether overall production output will be sufficient to meet demand. Low yields of key components can lead to shortages which require the facility to purchase new components for legacy systems, often with long lead times, thus causing overall delays. The approach developed here is a probabilistic form of standard material requirements planning (MRP), which considers variable yield rates of good, bad, and repairable components that are harvested from incoming units, and probabilistic processing times and yields at each stage of the remanufacturing process. The approach provides estimates of the expected number of remanufactured units to be completed in each future period. In addition, we propose a procedure for generating a component purchase schedule to avoid shortages in periods with a low probability of meeting demand. The proposed methodology is applied to an antenna remanufacturing process at the Naval Surface Warfare Center (NSWC). In this case study the proposed methodology identifies a potential shortage of a key component and suggests a corrective action to avoid significant delay in the delivery of remanufactured units.     

A branch-and-price algorithm for production routing problems with carbon cap-and-trade

This study presents a model for a pollution production-routing problem under carbon cap-and-trade. The aim is to incorporate carbon emissions into production inventory and routing decisions. The model is characterized by an additional flow-related cost structure, which generalizes models for pollution-routing problems and production inventory and routing problems. Correspondingly, we develop a branch-and-price heuristic by incorporating a column-generation formulation based on the Dantzig–Wolfe decomposition. In addition, we design an ad hoc label-setting algorithm to deal with time-slice networks in pricing subproblems. Computational results allow us to provide managerial insights concerning reduction of carbon emissions in supply chains. We prove that the model has the potential to reduce emission levels of carbon dioxide and operational costs.     

生产能力储备模式下应急物资储备与采购定价模型

为更好地促进政企双方开展应急物资生产能力储备合作,政府和协议企业需对物资的采购定价及生产能力的储备数量进行合理决策。基于此,文章从供应链的角度出发,利用供应链契约中的数量柔性契约建立了生产能力储备模式下的应急物资储备与采购定价模型,并进一步考虑了协议企业存在储备约束的情况。在利用逆序归纳法求解出合作下企业的生产能力储备量及相应的政府采购定价决策后,文章进一步分析了储备周期内灾害事件的发生概率与企业最大储备量约束对双方决策及各自成本收益的影响,为政府的采购定价及企业的储备策略提供了科学依据。此外,文章还给出了约束双方决策时的参数条件,因而也为政府在目标企业的选择方面提供了参考。     

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.     

Joint pricing and ordering policy for a deteriorating inventory with partial backlogging

In this paper, a deterministic inventory model for deteriorating items with time-dependent backlogging rate is developed. The demand and deterioration rate are known, continuous, and differentiable function of price and time, respectively. Under these general assumptions, we first prove that the optimal replenishment schedule not only exists but is unique, for any given selling price. Next, we show that the total profit is a concave function of price when the replenishment schedule is given. We then provide a simple algorithm to find the optimal selling price and replenishment schedule for the proposed model. Finally, we use a numerical example to illustrate the algorithm.     

Correct accounting for duty drawbacks with outward and inward processing in global production networks

We develop a new model for the correct accounting of customs duties levied on a product. We examine inward and outward processing – that is, processed components can be either imported or produced in a foreign country – in the strategic planning of a global production network. This complex modeling problem is structured with path variables, and the duty drawbacks can be simultaneously and correctly entered for n production stages in m market regions (with corresponding duty regions) for all products with a maximum n-level bill of materials. We present a case study from the automotive industry to examine whether or not the possibility of future duty rate changes or free trade agreements, such as one between the United States and the European Union, could affect the design of a production network and hence should be considered in strategic planning. We show that correctly accounting for duty drawbacks can lead to changes in the global footprint of production. We also demonstrate that intercontinental trade barriers (in the form of duties) diminish working capital and entail longer delivery routes. Eliminating these political trade barriers could increase the returns to capital while reducing both delivery lead times and environmental costs.     

A stochastic programming model for production planning of perishable products with postponement

This study addresses the production planning problem for perishable products, in which the cost and shortage of products are minimised subject to a set of constraints such as warehouse space, labour working time and machine time. Using the concept of postponement, the production process for perishable products is differentiated into two phases to better utilise the resources. A two-stage stochastic programming with recourse model is developed to determine the production loading plan with uncertain demand and parameters. A set of data from a toy company shows the benefits of the postponement strategy: these include lower total cost and higher utilisation of resources. The impact of unit shortage cost under different probability distribution of economic scenarios on the total cost is analyzed. Comparative analysis of solutions with and without postponement strategies is also performed.     

The Agency Model for Digital Goods

While digital goods industries such as entertainment, software, and publishing are growing at a rapid pace, traditional supply chain contract models have failed to evolve with the new digital economy. To illustrate, the agency model utilized by the e‐book publishing industry has recently received much negative attention brought by the U.S. Department of Justice's lawsuit against Apple, Inc. The emerging agency model in the e‐book industry works as follows: the publisher sets the price of the digital goods and the retailers who serve as agents retain a percentage of the revenue associated with a consumer purchase. The regulators claim that the agency model is hurting this industry as well as the consumer's welfare because e‐book prices have increased after the introduction of the agency model. We investigate the strategic impact of the agency model by examining a digital goods supply chain with one supplier and two competing retailers. In comparison to the benchmark wholesale model, we find that the agency model can coordinate the competing retailers by dividing the coordinated profits into a prenegotiated revenue sharing proportion. Further, we also identify the Pareto improving region whereby both the supplier and the retailers prefer the agency model to the wholesale model. Our main qualitative insight regarding the agency model still holds even when we consider the presence of the printed books in the marketplace. Thus, contrary to current press presaging the negative impact of the agency model on the e‐books industry, we find the agency model to be superior to the traditional wholesale contracts for publishers, retailers and consumers in this digital goods industry.