Local Water Storage Control for the Developing World

Most cities in India do not have water distribution networks that provide water throughout the entire day. As a result, it is common for homes and apartment buildings to utilize water storage systems that are filled during a small window of time in the day when the water distribution network is active. However, these water storage systems do not have disinfection capabilities, and so long durations of storage (i.e., as few as four days) of the same water leads to substantial increases in the amount of bacteria and viruses in that water. This paper considers the stochastic control problem of deciding how much water to store each day in the system, as well as deciding when to completely empty the water system, in order to tradeoff: the financial costs of the water, the health costs implicit in long durations of storing the same water, the potential for a shortfall in the quantity of stored versus demanded water, and water wastage from emptying the system. To solve this problem, we develop a new Binary Dynamic Search (BiDS) algorithm that is able to use binary search in one dimension to compute the value function of stochastic optimal control problems with controlled resets to a single state and with constraints on the maximum time span in between resets of the system

Optimal Planning Quantities for Product Transition

The replacement of an existing product with a new one presents many challenges. In particular, uncertainties in a new product introduction often lead to extreme cases of demand and supply mismatches. This paper addresses inventory planning decisions for product upgrades when there is no replenishment opportunity during the transition period. We allow product substitution: when a company runs out of the old product, a customer may be offered the new product as a substitute. We show that the optimal substitution decision is a time-varying threshold policy and establish the optimal planning policy. Further, we determine the optimal delay in a new product introduction, given the initial inventory of the old product

Optimal Policy for Inventory Management with Periodic and Controlled Resets

Inventory management problems with periodic and controllable resets occur in the context of managing water storage in the developing world and retailing limited-time availability products. In this paper, we consider a set of sequential decision problems in which the decision-maker must not only balance holding and shortage costs but discard all inventory before a fixed number of decision epochs, with the option for an early inventory reset. Finding optimal policies using dynamic programming for these problems is particularly challenging since the resulting value functions are non-convex. Moreover, this structure cannot be easily analyzed using existing extended definitions, such as $K$-convexity. Our key contribution is to present sufficient conditions that ensure the optimal policy has an easily interpretable structure that generalizes the well-known $(s, S)$ policy from the operations literature. Furthermore, we demonstrate that the optimal policy has a four-threshold structure under these rather mild conditions. We then conclude with computational experiments, thereby illustrating the policy structures that can be extracted in several inventory management scenarios

A Multiechelon Inventory Problem with Secondary Market Sales

Published version made available in SMU repository with permission of INFORMS, 2014, February 28</p

Essays on supply chain contracting and tactical decisions for inter-generational product transitions

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 2007.Includes bibliographical references ().In this dissertation, we explore problems in two areas of Supply Chain Management. The first relates to strategic supplier management. The second focuses on tactical decisions on inventory and pricing during inter-generational product transition. In many industries, manufacturing firms use multiple competing suppliers in their component or product sourcing strategy. Chapter 2 studies optimal history-dependent contracts with multiple suppliers in a dynamic, uncertain, imperfect-information environment. The results provide an optimal contract structure for the manufacture and optimal performance and effort paths for the suppliers. We compare incentives in the form of product margin and that of business volume. Our results suggest that a volume contract may increase the total profit for the supply chain, partly due to its ability to allocate higher volume to the supplier that is more likely to input high effort, and partly through relative performance evaluation. However, for two suppliers with large asymmetry, it is better to contract independently with each supplier using margin incentive, rather than forcing them into a volume race. Chapter 3 studies the inventory planning decisions in the context of a technology product transition, i.e., when a new generation product replaces an old one. High uncertainties in a new product introduction coupled with long lead-time often lead to extreme cases of demand and supply mismatches. When a company runs out of the old product, a customer may be offered the new product as a substitute. We show that the optimal substitution decision is a time-varying threshold policy and establish the optimal planning policy. Further, we determine the optimal delay in new product introduction, given the initial inventory of the old product.(cont.) In Chapter 4, we study the optimal pricing decisions during a product transition. We restrict the new product price to be constant and formulate the dynamic pricing problem for the old product. We derive a closed-form solution for the optimal price under non-homogeneous Poisson demands. In addition, we compare three heuristic pricing policies: fixed-price, two-price, and myopic rolling-horizon policies. The results suggest that changing price once during the transition (the two-price policy) improves the profit dramatically and is near optimal.by Hongmin Li.Ph.D