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Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
We examine a special class of dynamic pricing and advertising models for the sale of perishable goods, including marginal unit costs and inventory holding costs. The time horizon is assumed to be finite and we allow several model parameters to be dependent on time. For the stochastic version of the model, we derive closed-form expressions of the value function as well as of the optimal pricing and advertising policy in feedback form. Moreover, we show that for small unit shares, the model converges to a deterministic version of the problem, whose explicit solution is characterized by an overage and an underage case. We quantify the close relationship between the open-loop solution of the deterministic model and the expected evolution of optimally controlled stochastic sales processes. For both models, we derive sensitivity results. We find that in the case of positive holding costs, on average, optimal prices increase in time and advertising rates decrease. Furthermore, we analytically verify the excellent quality of optimal feedback policies of deterministic models applied in stochastic models.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 33
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Book Description
We examine a special class of dynamic pricing and advertising models for the sale of perishable goods, including marginal unit costs and inventory holding costs. The time horizon is assumed to be finite and we allow several model parameters to be dependent on time. For the stochastic version of the model, we derive closed-form expressions of the value function as well as of the optimal pricing and advertising policy in feedback form. Moreover, we show that for small unit shares, the model converges to a deterministic version of the problem, whose explicit solution is characterized by an overage and an underage case. We quantify the close relationship between the open-loop solution of the deterministic model and the expected evolution of optimally controlled stochastic sales processes. For both models, we derive sensitivity results. We find that in the case of positive holding costs, on average, optimal prices increase in time and advertising rates decrease. Furthermore, we analytically verify the excellent quality of optimal feedback policies of deterministic models applied in stochastic models.
Author: Rainer Schlosser
Publisher:
ISBN:
Category :
Languages : en
Pages : 21
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Book Description
This paper examines the sale of perishable and durable goods in a general class of time-dependent dynamic pricing and advertising models. We derive general qualitative insights in the complex interplay of optimal pricing and advertising decisions. Using a path-wise argumentation we prove structural properties of the optimal expected profits with respect to time, inventory level, price impact, advertising impact and different model parameters, such as discount rate, marginal unit costs, and the holding cost rate. Moreover, we identify sufficient conditions which imply structural properties of optimal joint pricing and advertising strategies. Our analysis also implies general results for other related models, such as pure pricing and pure advertising models.
Author: Rakhee Kulshrestha
Publisher: CRC Press
ISBN: 1000288676
Category : Mathematics
Languages : en
Pages : 172
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Book Description
This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems. The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research. The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.
Author: Victor F. Araman
Publisher:
ISBN:
Category :
Languages : en
Pages : 46
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Book Description
A retailer is endowed with a finite inventory of a non-perishable product. Demand for this product is driven by a price-sensitive Poisson process that depends on an unknown parameter, theta; a proxy for the market size. If theta is high then the retailer can take advantage of a large market charging premium prices, but if theta is small then price markdowns can be applied to encourage sales. The retailer has a prior belief on the value of theta which he updates as time and available information (prices and sales) evolve. We also assume that the retailer faces an opportunity cost when selling this non-perishable product. This opportunity cost is given by the long-term average discounted profits that the retailer can make if he switches and starts selling a different assortment of products.The retailer's objective is to maximize the discounted long-term average profits of his operation using dynamic pricing policies. We consider two cases. In the first case, the retailer is constrained to sell the entire initial stock of the non-perishable product before a different assortment is considered. In the second case, the retailer is able to stop selling the non-perishable product at any time to switch to a different menu of products. In both cases, the retailer's pricing policy trades-off immediate revenues and future profits based on active demand learning. We formulate the retailer's problem as a (Poisson) intensity control problem and derive structural properties of an optimal solution which we use to propose a simple approximated solution. This solution combines a pricing policy and a stopping rule (if stopping is an option) depending on the inventory position and the retailer's belief about the value of theta. We use numerical computations, together with asymptotic analysis, to evaluate the performance of our proposed solution.
Author: Steven Nahmias
Publisher: Springer Science & Business Media
ISBN: 1441979999
Category : Business & Economics
Languages : en
Pages : 89
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Book Description
A perishable item is one that has constant utility up until an expiration date (which may be known or uncertain), at which point the utility drops to zero. This includes many types of packaged foods such as milk, cheese, processed meats, and canned goods. It also includes virtually all pharmaceuticals and photographic film, as well as whole blood supplies. This book is the first devoted solely to perishable inventory systems. The book’s ten chapters first cover the preliminaries of periodic review versus continuous review and look at a one-period newsvendor perishable inventory model. The author moves to the basic multiperiod dynamic model, and then considers the extensions of random lifetime, inclusion of a set-up cost, and multiproduct models of perishables. A chapter on continuous review models looks at one-for-one policies, models with zero lead time, optimal policies with positive lead time, and an alternative approach. Additional chapters present material on approximate order policies, inventory depletion management, and deterministic models, including the basic EOQ model with perishability and the dynamic deterministic model with perishability. Finally, chapters explore decaying inventories, queues with impatient customers, and blood bank inventory control. Anyone researching perishable inventory systems will find much to work with here. Practitioners and consultants will also now have a single well-referenced source of up-to-date information to work with.
Author: Sajjad Najafi
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
We study a firm offering a line of vertically differentiated perishable products with fixed initial inventory over a finite sales season. Consumers arrive at the firm randomly and inspect products sequentially until they find a product to purchase (if any). Consumers evaluate each product in terms of its overall utility revealed to them. Each consumer incurs a positive cost to inspect a product and hence may stop the sequential search without inspecting all the available items. Upon a product's inspection, the utility of the product is known to the consumer, who then decides whether to continue the search. We formulate the firm's and consumer's problems using stochastic dynamic programming and determine the consumers' optimal search decision, the firm's optimal price to charge for each product at each time and the optimal sequence in which to show the products to consumers. We show that consumers' optimal stopping rule, under certain conditions, is myopic and takes a threshold structure. We show that it is optimal for the firm to sequence products in decreasing order of product quality. We show that, in some cases, it is optimal for the firm to increase a perishable product's price over time. This result is in stark contrast to the common result from the literature that prices for perishable products should be reduced over time. However, the fact that a consumer may not be able to see all products during the search can cause the opposite price behavior.
Author: Jing-Sheng J. Song
Publisher: Edward Elgar Publishing
ISBN: 180037710X
Category : Technology & Engineering
Languages : en
Pages : 565
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Book Description
This comprehensive Handbook provides an overview of state-of-the-art research on quantitative models for inventory management. Despite over half a century’s progress, inventory management remains a challenge, as evidenced by the recent Covid-19 pandemic. With an expanse of world-renowned inventory scholars from major international research universities, this Handbook explores key areas including mathematical modelling, the interplay of inventory decisions and other business decisions and the unique challenges posed to multiple industries.
Author: Nita H. Shah
Publisher: Springer Nature
ISBN: 9811396981
Category : Business & Economics
Languages : en
Pages : 470
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Book Description
This book discusses inventory models for determining optimal ordering policies using various optimization techniques, genetic algorithms, and data mining concepts. It also provides sensitivity analyses for the models’ robustness. It presents a collection of mathematical models that deal with real industry scenarios. All mathematical model solutions are provided with the help of various optimization techniques to determine optimal ordering policy. The book offers a range of perspectives on the implementation of optimization techniques, inflation, trade credit financing, fuzzy systems, human error, learning in production, inspection, green supply chains, closed supply chains, reworks, game theory approaches, genetic algorithms, and data mining, as well as research on big data applications for inventory management and control. Starting from deterministic inventory models, the book moves towards advanced inventory models. The content is divided into eight major sections: inventory control and management – inventory models with trade credit financing for imperfect quality items; environmental impact on ordering policies; impact of learning on the supply chain models; EOQ models considering warehousing; optimal ordering policies with data mining and PSO techniques; supply chain models in fuzzy environments; optimal production models for multi-items and multi-retailers; and a marketing model to understand buying behaviour. Given its scope, the book offers a valuable resource for practitioners, instructors, students and researchers alike. It also offers essential insights to help retailers/managers improve business functions and make more accurate and realistic decisions.
Author: Li-Ming Chen
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
ABSTRACT: A perishable item is characterized by its usefulness over a limited period of time, known as \life." Once the \life" is over, these items spoil, which obviously is a loss. The bottom line of a firm can improve significantly if some of this spoilage is prevented, i.e., if the perishable nature of products is managed properly. One mechanism by which this may be achieved is demand management using price. Through an appropriate selection of price, demand can be modulated to improve profit. The modulation of demand can not only increase revenue but also reduce shortage, holding, and spoilage costs. Potential spoilage due to limited life-time of the perishable products is the main reason demand management of perishable products is even more important than for non-perishable products. Whereas for non-perishable products the only cost of unsold inventory is the cost for holding inventory, for perishable products the unsold inventory not only incurs inventory holding cost but, in addition, with increasing age of the inventory the risk of it remaining unsold by the end of its lifetime increases. Therefore, this dissertation explores joint demand and replenishment decisions on the inventory control of perishable items with random demand. The first part of the dissertation is primarily motivated by a dilemma routinely faced by food retailers: when to replace old inventory of perishable products with fresh units when economies of scale exist in order placement. On one hand, economies of scale make it more attractive to place orders for large quantities. On the other hand, the demand for perishable products declines as their age approaches their lifetime; the reduction occurs since customers prefer fresh units and/or avoid units that are close to expiry.
Author: Hawking Wang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this article, we investigate a joint pricing and inventory problem for a retailer selling fresh-agri products (FAPs) with two-period shelf lifetime in a dynamic stochastic setting, where new and old FAPs are on sale simultaneously. At the beginning of each period, the retailer makes ordering decision for new FAP and sets regular and discount prices for new and old inventories, respectively. After demand realisation, the expired leftover is disposed and unexpired inventory is carried to the next period, for continuing selling. Unmet demand of all FAPs is backordered. The objective is to maximise the total expected discount profit over the whole planning horizon. We present a price dependent, stochastic dynamic programming model taking into account zero lead-time, linear ordering costs, inventory holding and backlogging costs, as well as disposal cost. As the influence of the perishability, each customer selects his preferred choice based on the utility of product price and quality. By the way of constructing demand rate vector, the original formulation can be transferred to be jointly concave and tractable. Finally, we characterise the optimal policy and develop effective methods to solve the problem. We also conduct numerical studies to further characterise the optimal policy, and to evaluate the loss of efficiency under static policies when compared to the optimal dynamic policy.
