Stochastic Optimization Models for Perishable Products

For many years, researchers have focused on developing optimization models to design and manage supply chains. These models have helped companies in different industries to minimize costs, maximize performance while balancing their social and environmental impacts. There is an increasing interest in developing models which optimize supply chain decisions of perishable products. This is mainly because many of the products we use today are perishable, managing their inventory is challenging due to their short shelf life, and out-dated products become waste. Therefore, these supply chain decisions impact profitability and sustainability of companies and the quality of the environment. Perishable products wastage is inevitable when demand is not known beforehand. A number of models in the literature use simulation and probabilistic models to capture supply chain uncertainties. However, when demand distribution cannot be described using standard distributions, probabilistic models are not effective. In this case, using stochastic optimization methods is preferred over obtaining approximate inventory management policies through simulation. This dissertation proposes models to help businesses and non-prot organizations make inventory replenishment, pricing and transportation decisions that improve the performance of their system. These models focus on perishable products which either deteriorate over time or have a fixed shelf life. The demand and/or supply for these products and/or, the remaining shelf life are stochastic. Stochastic optimization models, including a two-stage stochastic mixed integer linear program, a two-stage stochastic mixed integer non linear program, and a chance constraint program are proposed to capture uncertainties. The objective is to minimize the total replenishment costs which impact prots and service rate. These models are motivated by applications in the vaccine distribution supply chain, and other supply chains used to distribute perishable products. This dissertation also focuses on developing solution algorithms to solve the proposed optimization models. The computational complexity of these models motivated the development of extensions to standard models used to solve stochastic optimization problems. These algorithms use sample average approximation (SAA) to represent uncertainty. The algorithms proposed are extensions of the stochastic Benders decomposition algorithm, the L-shaped method (LS). These extensions use Gomory mixed integer cuts, mixed-integer rounding cuts, and piecewise linear relaxation of bilinear terms. These extensions lead to the development of linear approximations of the models developed. Computational results reveal that the solution approach presented here outperforms the standard LS method. Finally, this dissertation develops case studies using real-life data from the Demographic Health Surveys in Niger and Bangladesh to build predictive models to meet requirements for various childhood immunization vaccines. The results of this study provide support tools for policymakers to design vaccine distribution networks

Solving Practical Dynamic Pricing Problems with Limited Demand Information

Dynamic pricing problems have received considerable attention in the operations management literature in the last two decades. Most of the work has focused on structural results and managerial insights using stylized models without considering business rules and issues commonly encountered in practice. While these models do provide general, high-level guidelines for managers in practice, they may not be able to generate satisfactory solutions to practical problems in which business norms and constraints have to be incorporated. In addition, most of the existing models assume full knowledge about the underlying demand distribution. However, demand information can be very limited for many products in practice, particularly, for products with short life-cycles (e.g., fashion products). In this dissertation, we focus on dynamic pricing models that involve selling a fixed amount of initial inventory over a fixed time horizon without inventory replenishment. This class of dynamic pricing models have a wide application in a variety of industries. Within this class, we study two specific dynamic pricing problems with commonly-encountered business rules and issues where there is limited demand information. Our objective is to develop satisfactory solution approaches for solving practically sized problems and derive managerial insights. This dissertation consists of three parts. We first present a survey of existing pricing models that involve one or multiple sellers selling one or multiple products, each with a given initial inventory, over a fixed time horizon without inventory replenishment. This particular class of dynamic pricing problems have received substantial attention in the operations management literature in recent years. We classify existing models into several different classes, present a detailed review on the problems in each class, and identify possible directions for future research. We then study a markdown pricing problem that involves a single product and multiple stores. Joint inventory allocation and pricing decisions have to be made over time subject to a set of business rules. We discretize the demand distribution and employ a scenario tree to model demand correlation across time periods and among the stores. The problem is formulated as a MIP and a Lagrangian relaxation approach is proposed to solve it. Extensive numerical experiments demonstrate that the solution approach is capable of generating close-to-optimal solutions in a short computational time. Finally, we study a general dynamic pricing problem for a single store that involves two substitutable products. We consider both the price-driven substitution and inventory-driven substitution of the two products, and investigate their impacts on the optimal pricing decisions. We assume that little demand information is known and propose a robust optimization model to formulate the problem. We develop a dynamic programming solution approach. Due to the complexity of the DP formulation, a fully polynomial time approximation scheme is developed that guarantees a proven near optimal solution in a manageable computational time for practically sized problems. A variety of managerial insights are discussed

A Dynamic Pricing Model for Coordinated Sales and Operations

Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in operations and supply chain management. The interactions between pricing and operations/supply chain performance, however, are not as well understood. In this paper, we examine this linkage by developing a deterministic, finite-horizon dynamic programming model that captures a price/demand effect as well as a stockpiling/consumption effect – price and market stockpile influence demand, demand influences consumption, and consumption influences the market stockpile. The decision variable is the unit sales price in each period. Through the market stockpile, pricing decisions in a given period explicitly depend on decisions in prior periods. Traditional operations models typically assume exogenous demand, thereby ignoring some of the market dynamics. Herein, we model endogenous demand, and we develop analytical insights into the nature of optimal prices and promotions. We develop conditions under which the optimal prices converge to a constant. In other words, price promotion is suboptimal. We also analytically and numerically illustrate cases where the optimal prices vary over time. In particular, we show that price dynamics may be driven by both (a) revenue effects, due to nonlinear market responses to prices and/or inventory, and (b) cost effects, due to economies of scale in operations. The paper concludes with a discussion of directions for future research

Evaluating Lexical Approximation of Program Dependence

Complex dependence analysis typically provides an underpinning approximation of true program dependence. We investigate the effectiveness of using lexical information to approximate such dependence, introducing two new deletion operators to Observation-Based Slicing (ORBS). ORBS provides direct observation of program dependence, computing a slice using iterative, speculative deletion of program parts. Deletions become permanent if they do not affect the slicing criterion. The original ORBS uses a bounded deletion window operator that attempts to delete consecutive lines together. Our new deletion operators attempt to delete multiple, non-contiguous lines that are lexically similar to each other. We evaluate the lexical dependence approximation by exploring the trade-off between the precision and the speed of dependence analysis performed with new deletion operators. The deletion operators are evaluated independently, as well as collectively via a novel generalization of ORBS that exploits multiple deletion operators: Multi-operator Observation-Based Slicing (MOBS). An empirical evaluation using three Java projects, six C projects, and one multi-lingual project written in Python and C finds that the lexical information provides a useful approximation to the underlying dependence. On average, MOBS can delete 69% of lines deleted by the original ORBS, while taking only 36% of the wall clock time required by ORBS

Supply chain contracting coordination for fresh products with fresh-keeping effort

Purpose – Fresh product loss rates in supply chain operations are particularly high due to the nature of perishable products. This paper aims to maximize profit through the contract between retailer and supplier. The optimized prices for the retailer and the supplier, taking the fresh-keeping effort into consideration, are derived. Design/methodology/approach – To address this issue, we consider a two-echelon supply chain consisting of a retailer and a supplier (i.e., wholesaler) for two scenarios: centralized and decentralized decision-making. We start from investigating the optimal decision in the centralized supply chain and then comparing the results with those of the decentralized decision. Meanwhile, a fresh-keeping cost-sharing contract and a fresh-keeping cost- and revenue-sharing contract are designed. Numerical examples are provided, and managerial insights are discussed at end. Findings – The results show that (a) the centralized decision is more profitable than the decentralized decision; (b) a fresh product supply chain can only be coordinated through a fresh-keeping cost- and revenue-sharing contract; (c) the optimal retail price, wholesale price and fresh-keeping effort can all be achieved; (d) the profit of a fresh product supply chain is positively related to consumers’ sensitivity to freshness and negatively correlated with their sensitivity to price. Originality/value – Few studies have considered fresh-keeping effort as a decision variable in the modelling of supply chain. In this paper, a mathematical model for the fresh-keeping effort and for price decisions in a supply chain is developed. In particular, fresh-keeping cost sharing contract and revenue-sharing contract are examined simultaneously in the study of the supply chain coordination problem

Management of Stochastic Demand in Make-to-Stock Manufacturing

Up to now, demand fulfillment in make-to-stock manufacturing is usually handled by advanced planning systems. Orders are fulfilled on the basis of simple rules or deterministic planning approaches not taking into account demand fluctuations. The consideration of different customer classes as it is often done today requires more sophisticated approaches explicitly considering stochastic influences. This book reviews current literature, presents a framework that addresses revenue management and demand fulfillment at once and introduces new stochastic approaches for demand fulfillment in make-to-stock manufacturing based on the ideas of the revenue management literature

Contextual Bandits for Evaluating and Improving Inventory Control Policies

Solutions to address the periodic review inventory control problem with nonstationary random demand, lost sales, and stochastic vendor lead times typically involve making strong assumptions on the dynamics for either approximation or simulation, and applying methods such as optimization, dynamic programming, or reinforcement learning. Therefore, it is important to analyze and evaluate any inventory control policy, in particular to see if there is room for improvement. We introduce the concept of an equilibrium policy, a desirable property of a policy that intuitively means that, in hindsight, changing only a small fraction of actions does not result in materially more reward. We provide a light-weight contextual bandit-based algorithm to evaluate and occasionally tweak policies, and show that this method achieves favorable guarantees, both theoretically and in empirical studies