Aggregate constrained inventory systems with independent multi-product demand: control practices and theoretical limitations

In practice, inventory managers are often confronted with a need to consider one or more aggregate constraints. These aggregate constraints result from available workspace, workforce, maximum investment or target service level. We consider independent multi-item inventory problems with aggregate constraints and one of the following characteristics: deterministic leadtime demand, newsvendor, basestock policy, rQ policy and sS policy. We analyze some recent relevant references and investigate the considered versions of the problem, the proposed model formulations and the algorithmic approaches. Finally we highlight the limitations from a practical viewpoint for these models and point out some possible direction for future improvements

An interior-point and decomposition approach to multiple stage stochastic programming

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Improving promotional effectiveness through supplier-retailer collaboration

Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2007.Includes bibliographical references (leaves 60-61).In the consumer products industry, retail chains and manufacturers run promotions to maintain consumer and brand loyalty. The two major issues in planning and executing promotions are to accurately forecast demand and to control Out-of-Stock at the shelf. This thesis addresses both these issues. At the strategic level, "Collaborative, Planning, Forecasting and Replenishment" is used to define a process for two companies to collaboratively plan and execute promotions. At an operational level, the single period multi-item newsboy concept with a budget constraint is used to define an optimization model that helps determine the right budget and order quantities for products under a promotion at a targeted service level to improve profit or sales. The concept of Supply Contracts is researched to identify some ways that can be used to optimize the whole supply chain rather than just the retailer's. The value of optimal collaboration was confirmed in the results shown by the model. When optimizing the entire chain, the maximize profit optimization model achieved combined profit improvements of 37% as compared to an actual promotion.(cont.) When only the retailer profit was maximized, the optimization model resulted in 5.9% profit improvements for the retailer and 0.3% profit improvements for the supplier as compared to an actual promotion. Finally, the revenue maximization model showed that after a certain point, increasing the budget did not result in increased service levels. This research can also be applied to new product launches, seasonality of products as well as daily replenishments.by Gautam Kapur and Bin Liu.M.Eng.in Logistic

Multi-item quick response system with budget constraint

Cataloged from PDF version of article.Quick response mechanisms based on effective use of up-to-date demand information help retailers to reduce their inventory management costs. We formulate a single-period inventory model for multiple products with dependent (multivariate normal) demand distributions and a given overall procurement budget. After placing orders based on an initial demand forecast, new market information is gathered and demand forecast is updated. Using this more accurate second forecast, the retailer decides the total stocking level for the selling season. The second order is based on an improved demand forecast, but it also involves a higher unit supply cost. To determine the optimal ordering policy, we use a computational procedure that entails solving capacitated multi-item newsboy problems embedded within a dynamic programming model. Various numerical examples illustrate the effects of demand variability and financial constraint on the optimal policy. It is found that existence of a budget constraint may lead to an increase in the initial order size. It is also observed that as the budget available decreases, the products with more predictable demand make up a larger share of the procurement expenditure. & 2012 Elsevier B.V. All rights reserved

An interior-point and decomposition approach to multiple stage stochastic programming

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Constructive solution methodologies to the capacitated newsvendor problem and surrogate extension

The newsvendor problem is a single-period stochastic model used to determine the order quantity of perishable product that maximizes/minimizes the profit/cost of the vendor under uncertain demand. The goal is to fmd an initial order quantity that can offset the impact of backlog or shortage caused by mismatch between the procurement amount and uncertain demand. If there are multiple products and substitution between them is feasible, overstocking and understocking can be further reduced and hence, the vendor\u27s overall profit is improved compared to the standard problem. When there are one or more resource constraints, such as budget, volume or weight, it becomes a constrained newsvendor problem. In the past few decades, many researchers have proposed solution methods to solve the newsvendor problem. The literature is first reviewed where the performance of each of existing model is examined and its contribution is reported. To add to these works, it is complemented through developing constructive solution methods and extending the existing published works by introducing the product substitution models which so far has not received sufficient attention despite its importance to supply chain management decisions. To illustrate this dissertation provides an easy-to-use approach that utilizes the known network flow problem or knapsack problem. Then, a polynomial in fashion algorithm is developed to solve it. Extensive numerical experiments are conducted to compare the performance of the proposed method and some existing ones. Results show that the proposed approach though approximates, yet, it simplifies the solution steps without sacrificing accuracy. Further, this dissertation addresses the important arena of product substitute models. These models deal with two perishable products, a primary product and a surrogate one. The primary product yields higher profit than the surrogate. If the demand of the primary exceeds the available quantity and there is excess amount of the surrogate, this excess quantity can be utilized to fulfill the shortage. The objective is to find the optimal lot sizes of both products, that minimize the total cost (alternatively, maximize the profit). Simulation is utilized to validate the developed model. Since the analytical solutions are difficult to obtain, Mathematical software is employed to find the optimal results. Numerical experiments are also conducted to analyze the behavior of the optimal results versus the governing parameters. The results show the contribution of surrogate approach to the overall performance of the policy. From a practical perspective, this dissertation introduces the applications of the proposed models and methods in different industries such as inventory management, grocery retailing, fashion sector and hotel reservation

REVENUE AND ORDER MANAGEMENT UNDER DEMAND UNCERTAINTY

We consider a firm that delivers its products across several customers or markets, each with unique revenue and uncertain demand size for a single selling season. Given that the firm experiences a long procurement lead time, the firm must decide, far in advance of the selling season not only the markets to be pursued but also the procurement quantity. In this dissertation, we present several operational scenarios in which the firm must decide which customer demands to satisfy, at what level to satisfy each customer demand, and how much to produce (or order) in total. Traditionally, a newsvendor approach to the single period problem assumes the use of an expected profit objective. However, maximizing expected profit would not be appropriate for firms that cannot afford successive losses or negligible profits over several consecutive selling seasons. Such a setting would most likely require minimizing the downside risk of accepting uncertain demands into the production plan. We consider the implications of such competing objectives. We also investigate the impact that various forms of demand can have on the flexibility of a firm in their customer/market selection process. a firm may face a small set of unconfirmed orders, and each order will often either come in at a predefined level, or it will not come in at all. We explore optimization solution methods for this all-or-nothing demand case with risk-averse objective utilizing conditional value at risk (CVaR) concept from portfolio management. Finally, in this research, we explore extensions of the market selection problem. First, we consider the impact of incorporating market-specific expediting costs into the demand selection and procurement decisions. Using a lost sales assumption instead of an expediting assumption, we perform a similar analysis using market-specific lost sales costs. For each extension we investigate two different approaches: i) Greedy approach: here we allocate order quantity to market with lowest expediting cost (lowest expected revenue) first. ii) Rationing approach: here we find the shortage (lost sale) then ration it across all the markets. We present ideas and approaches for each of these extensions to the selective newsvendor problem

A Multiproduct Single-Period Inventory Management Problem under Variable Possibility Distributions

In multiproduct single-period inventory management problem (MSIMP), the optimal order quantity often depends on the distributions of uncertain parameters. However, the distribution information about uncertain parameters is usually partially available. To model this situation, a MSIMP is studied by credibilistic optimization method, where the uncertain demand and carbon emission are characterized by variable possibility distributions. First, the uncertain demand and carbon emission are characterized by generalized parametric interval-valued (PIV) fuzzy variables, and the analytical expressions about the mean values and second-order moments of selection variables are established. Taking second-order moment as a risk measure, a new credibilistic multiproduct single-period inventory management model is developed under mean-moment optimization criterion. Furthermore, the proposed model is converted to its equivalent deterministic model. Taking advantage of the structural characteristics of the deterministic model, a domain decomposition method is designed to find the optimal order quantities. Finally, a numerical example is provided to illustrate the efficiency of the proposed mean-moment credibilistic optimization method. The computational results demonstrate that a small perturbation of the possibility distribution can make the nominal optimal solution infeasible. In this case, the decision makers should employ the proposed credibilistic optimization method to find the optimal order quantities

Robust Solutions of Optimization Problems Affected by Uncertain Probabilities

In this paper we focus on robust linear optimization problems with uncertainty regions defined by ø-divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on ø-divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with ø-divergence uncertainty is tractable for most of the choices of ø typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach.robust optimization;ø-divergence;goodness-of-fit statistics