The fast growth of e-commerce and omni/multi-channel retailing brings new challenges for efficient inventory management. One such challenge concerns service differentiation across channels when up-stream central warehouses satisfy both direct customer demand and replenishment orders from down-stream retailers. Motivated by industry collaboration, we address this issue by developing a combined stock method for control of one-warehouse-multiple-retailer inventory systems with direct customer de-mand at the central warehouse. The combined stock method, used for service differentiation at the cen-tral warehouse, may be described as a critical level policy. The computationally efficient heuristics we present are designed to deal with real-life one warehouse multiple retailer inventory systems character-ized by highly variable customer order-sizes, ( R, Q) policies at all stock points, and fill rate constraints. A numerical study, including real data from two different companies, illustrates that the heuristics perform well; offering near optimal solutions close to target fill rates, with significant opportunities to reduce total inventory costs compared to existing methods. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

The problem investigated in this paper is the one of finding the optimal combination of inventory and options in a stationary multi-period problem with an infinite horizon. The research complements existing literature as it considers the combination of option and wholesale contracts. The paper show how the problem can be transformed to a combination of newsvendor type problems. This alternative interpretation allows us to derive the necessary conditions for the pricing of an option contract that maximizes the system wide profit as well as the conditions for when the different parties will be able to design such a price scheme. It turns out that the possibility to do so depends on where it is optimal to keep inventory and how much inventory is kept under the pure wholesale contract. Moreover is it shown that the supply chain optimal solution cannot be guaranteed even if a Central planner prices the option contract.

Inspired by the observation that capacity contracts are used by some retailers to increase their transport provider's investments in green transport solutions, we investigate and compare a service provider's optimal investment, and its environmental implications under a volume and a capacity contract respectively. We solve the service provider's investment problem under the assumption that the retailer uses the service to replenish a warehouse with storable goods. We then show that a capacity contract leads to more green transports, but not necessarily a larger investment in green transport solutions. At the same time, the optimal solution involves heavy investment in inventory at the retailer. The investment in inventory is non-decreasing in the cost benefit of the green transports, which may have a significant negative environmental impact. The implication is that a capacity contract will lead to better environmental performance than a volume contract only when the green transports' cost benefit is within a given interval. Whether the capacity contract is the more profitable option for the service provider within this interval depends on inventory related costs and the relative environmental costs from transportation and inventory. Interestingly, owing to this, regulation that target the price of the conventional vehicles, such as a carbon tax, may lead to both an increase or a decrease in environmental performance. (C) 2017 Elsevier B.V. All rights reserved.

Managing inventories, and thereby material flows, is of key importance for achieving efficient and sustainable supply chains. Green inventory management is characterized by complementing the traditional economic (cost) focus with environmental (emissions) considerations. In this chapter we identify and discuss key questions and challenges for green inventory management research. We do so by categorizing the costs and emissions of operating an inventory system into those associated with: ordering and transporting items, holding items in stock, and not satisfying customer demand on time. A literature overview illustrates what issues have been addressed so far in this emerging field. We conclude that there is a promising potential for green inventory management practices to reduce both costs and emissions, but much remains to be done. Not least in terms of developing more general green inventory models for practical use.

In this article, we present a multistage model to optimize inventory control decisions under stochastic demand and continuous review. We first formulate the general problem for continuous stages and use a decomposition solution approach: since it is never optimal to let orders cross, the general problem can be broken into a set of single-unit subproblems that can be solved in a sequential fashion. These subproblems are optimal control problems for which a differential equation must be solved. This can be done easily by recursively identifying coefficients and performing a line search. The methodology is then extended to a discrete number of stages and allows us to compute the optimal solution in an efficient manner, with a competitive complexity. (c) 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 32-46, 2016

In this paper, we analyze how to continuously adjust the speed in a supply chain with stochastic demand. For each unit (e.g., truckload, shipping container) in the chain, one must decide at which speed it should be moved downstream, given the state of the system, to minimize total supply chain costs. We decompose the problem into a set of one-dimensional subproblems that can be easily solved and characterize the optimal variable speed policy: under some assumptions, we show that it is optimal to set a speed that is first increasing in the distance to the market, and then decreasing. As a result, at optimality a given unit will experience an accelerating speed and then it will be slowed down, unless a demand occurs, in which case, the speed will be adjusted upward. We finally provide a transportation case study where we estimate the benefits of a variable-speed compared to a fixed-speed policy and show them to be significant both financially and from a CO₂-emissions perspective.

Humanitarian organizations (HOs) often base their warehouse locations on individuals' experience and knowledge rather than on decision-support tools. Many HOs run separate supply chains for emergency response and ongoing operations. Based on reviews of humanitarian network design literature combined with an in-depth case study of United Nations High Commissioner for Refugees (UNHCR), this paper presents a warehouse location model for joint prepositioning that incorporates political and security situation factors. Although accessibility, co-location, security, and human resources are crucial to the practice of humanitarian operations management, such contextual factors have not been included in existing network optimization models before. We found that when quantified, and modeled, such factors are important determinants of network configuration. In addition, our results suggest that joint prepositioning for emergency response and ongoing operations allows for expansion of the global warehouse network, and reducing cost and response time.

Shipment consolidation has been advocated by researchers and politicians as a means to reduce cost and improve environmental performance of logistics activities. This paper investigates consolidated transport solutions with a common shipment frequency. When a service provider designs such a solution for its customers, she faces a trade-off: to have the most time-sensitive customers join the consolidated solution, the frequency must be high, which makes it difficult to gather enough demand to reach the scale economies of the solution; but by not having the most time-sensitive customers join, there will be less demand per time unit, which also makes it difficult to reach the scale economies. In this paper we investigate the service provider’s pricing and timing problem and the environmental implications of the optimal policy. The service provider is responsible for multiple customers’ transports, and offers all customers two long-term contracts at two different prices: direct express delivery with immediate dispatch at full cost, or consolidated delivery at a given frequency at a reduced cost. It is shown that the optimal policy is largely driven by customer heterogeneity: limited heterogeneity in customers’ costs leads to very different optimal policies compared to large heterogeneity. We argue that the reason so many consolidation projects fail may be due to a strategic mismatch between heterogeneity and consolidation policy. We also show that even if the consolidated solution is implemented, it may lead to a larger environmental impact than direct deliveries due to inventory build-up or a higher-than-optimal frequency of the consolidated transport

We consider a purchase/inventory control problem in which the purchase price and demand are stochastic, a common situation encountered by firms that replenish in a foreign currency or from commodity markets. More specifically, we assume that the demand follows a Poisson arrival process and that the log-price evolves according to a general Wiener process. Under these circumstances, the optimal policy is a state dependent base-stock policy that can be described as a series of threshold prices. An iterative procedure for determining the optimal thresholds has been derived earlier but, even for the simplest price process, the solution quickly becomes numerically intractable. To deal with this, we propose an approximation that allows us to derive simple heuristics for finding thresholds that are close to optimal. For certain price processes the heuristics are just a series of closed-form expressions. The computational complexity is reduced significantly, and the numerical study shows that the new heuristics perform considerably better than earlier suggested heuristics.