Evaluating Retail Distribution Strategies During Covid-19 Pandemic in South Africa Using Best Worst Method Multicriteria Decision Technique

This paper evaluates the distribution strategies adopted by South African retailers during the Covid-19 pandemic and how such strategies have been adjusted for a more resilient post-Covid-19 world. Using the Best Worst method multicriteria decision technique and exploiting data collected from decision makers from the retail industry to rank the distribution strategies according to their level of importance, we show that omnichannel distribution strategy ranked highest, followed by direct shipment distribution capability in contributing to the success of retail distribution during the Covid-19 pandemic. On the other hand, inventory pooling, transhipment, centralised or decentralised strategy, and cross-docking ranked lower while retail distribution strategy was lowest ranked. Finally, particular emphasis must be placed on the critical factors identified in the evaluation in terms of their challenging dimension and impact as they pave way for a more capable retail resilience distribution capability

On the learning benefits of resource flexibility

Resource flexibility, arguably among the most celebrated operational concepts, is known to provide firms facing demand uncertainty with such benefits as risk pooling, revenue-maximization optionality, and operational hedging. In this paper, we uncover a heretofore unknown benefit: we establish that resource flexibility facilitates learning the demand when the latter is censored, which could, in turn, enable firms to make better-informed future operational decisions, thereby increasing profitability. Further, we quantify these learning benefits of flexibility and find that they could be of the same order of magnitude as the extensively studied risk-pooling benefits of flexibility. This suggests that flexibility’s learning benefits could be a first-order consideration and that extant theories, which view flexibility only as the ability to act ex post, could be underestimating its true value when learning the demand is desirable, for example, when it enables managers to make better ex ante capacity, assortment, or pricing decisions in future periods

On-demand last-mile distribution network design with omnichannel inventory

E-commerce delivery deadlines are getting increasingly tight, driven by a growing ‘I-want-it-now’ instant gratification mindset of consumers and the desire of online and omnichannel retailers to capitalize on the growth of on-demand e-commerce. On-demand deliveries with delivery deadlines as tight as one or two hours force companies to rethink their last-mile distribution network, since tight delivery deadlines require decentralization of order picking and inventory holding to ensure close proximity to consumers. This fundamentally changes the strategic design process of last-mile distribution networks. We study the impact of incorporating inventory order-up-to level decisions into the strategic design process of last-mile distribution networks with tight delivery deadlines. We develop an approximate inventory model by including an estimate of the cost of late delivery and additional transportation due to local stock-outs in a newsvendor formulation. Such local stock-outs require an order to be delivered from a more distant facility, which may lead to late delivery and additional transportation cost. We integrate our approximate inventory model and a location-allocation mixed-integer program that determines optimal facility locations, associated order-up-to inventory levels, and fleet composition, into a metamodel simulation-based optimization approach. Our numerical analyses demonstrate that pooling the additional online inventory with brick-and-mortar (B&M) inventories leads to cannibalization by the B&M network and higher B&M service levels. However, the pooling benefits to the online network outweigh the cost of inventory cannibalization. Furthermore, we show under which circumstances omnichannel retailers may have an incentive to consolidate online inventory in specific B&M facilities

Seller-Orchestrated Inventory Financing under Bank Capital Regulation

To help small firms secure bank financing, large sellers often orchestrate joint finance programs, linking their small dealers with major banks that lend to all participating dealers based on the information the seller provides. We examine supply chain decisions (pricing and inventory) and lending terms under such seller-orchestrated financing programs. In loan pricing, we highlight a form of financial friction that is of particular importance under such schemes – bank capital regulation. Banks are globally mandated to maintain regulatory capital to mitigate unforeseen loan losses, using either the standardized approach (where regulatory capital is a fixed percentage of the loan amount) or the internal rating-based (IRB) approach (where it depends on the loan's Value-at-Risk). We consider a game-theoretic model consisting of a large seller and multiple capital-constrained newsvendor-type dealers, who obtain financing from banks who are subject to capital regulation. The seller decides the wholesale price and whether to orchestrate a joint finance program for its dealers by collaborating with a bank, and the dealers choose their inventory level and the financing channel. We find that a seller should only orchestrate the joint financing program when the bank adopts the IRB approach and the dealers are of low risk. Such a program is more profitable to the seller when the demand correlation among dealers is low, and there is a large number of dealers. Although always benefiting the seller, these programs may hurt dealers with intermediate risk. Facing dealers with varying financial situations, the terms under the joint finance program should be designed as if the financially strong dealers subsidize the weak ones. Finally, allowing the seller to share part of the loan loss could further enhance the performance of joint financing, but only when the seller's opportunity cost of capital is low. Our findings provide guidance to large sellers on how to orchestrate joint finance schemes, and to small dealers on making their corresponding operational decisions

Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

With rapidly increasing e-commerce sales, firms are leveraging the virtual pooling of online demands across customer locations in deciding the amount of inventory to be placed in each node in a fulfillment network. Such solutions require knowledge of the joint distribution of demands; however, in reality, only partial information about the joint distribution may be reliably estimated. We propose a distributionally robust multi-location newsvendor model for network inventory optimization where the worst-case expected cost is minimized over the set of demand distributions satisfying the known mean and covariance information. For the special case of two homogeneous customer locations with correlated demands, we show that a six-point distribution achieves the worst-case expected cost, and derive a closed-form expression for the optimal inventory decision. The general multi-location problem can be shown to be NP-hard. We develop a computationally tractable upper bound through the solution of a semidefinite program (SDP), which also yields heuristic inventory levels, for a special class of fulfillment cost structures, namely nested fulfillment structures. We also develop an algorithm to convert any general distance-based fulfillment cost structure into a nested fulfillment structure which tightly approximates the expected total fulfillment cost.https://deepblue.lib.umich.edu/bitstream/2027.42/146785/1/1389_Govindarajan.pd

Closed-Form Solutions for Distributionally Robust Inventory Management: A Controlled Relaxation Method

When only the moments (mean, variance or t-th moment) of the underline distribution are known, a variety of many max-min optimization models choose actions to maximize the firm’s expected profit against the most unfavorable distribution. We introduce relaxation scalars to reformulate the max-min model as a relaxed model and demonstrate that the closed form solutions (if they exist in the first place) can be quickly identified when we reduce the relaxation scalars to zero. To demonstrate the effectiveness of this new method, we provide closed-form solutions, hitherto unknown, for several distributionally robust inventory models, including the newsvendor problem with mean and t-th moment (for t > 1), the pricing model, the capacity planning model with multiple supply sources, and the two-product inventory system with common component

Closed-Form Solutions for Distributionally Robust Inventory Management: Extended Reformulation using Zero-Sum Game

When only the moments (mean, variance or t-th moment) of the underline distribution are known, numerous max-min optimization models can be interpreted as a zero-sum game, in which the decision maker (DM) chooses actions to maximize her expected profit while Adverse Nature chooses a distribution subject to the moments conditions to minimize DM’s expected profit. We propose a new method to efficiently solve this class of zero-sum games under moment conditions. By applying the min-max inequality, our method reformulates the zero-sum game as a robust moral hazard model, in which Adverse Nature chooses both the distribution and actions to minimize DM’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the first-order conditions, which give rise to extra moment constraints. Interestingly, these extra moment constraints drastically reduce the number of corner points to be considered in the corresponding semi-infinite programming models. We show that in the equilibrium, these moment constraints are binding but have zero Lagrangian multipliers and thus facilitate closed-form solutions in several application examples with different levels of complexity. The high efficiency of the method enables us to solve a large class of zero-sum games and the corresponding max-min robust optimization models

A New Method to Solve Zero-Sum Games under Moment Conditions

When only the moments (mean, variance or t-th moment) of the underline distribution are known, numerous max-min optimization models can be interpreted as a zero-sum game, in which the decision maker (DM) chooses actions to maximize her expected profit while Adverse Nature chooses a distribution subject to the moments conditions to minimize DM’s expected profit. We propose a new method to efficiently solve this class of zero-sum games under moment conditions. By applying the min-max inequality, our method reformulates the zero-sum game as a robust moral hazard model, in which Adverse Nature chooses both the distribution and actions to minimize DM’s expected profit subject to incentive compatibility (IC) constraints. Under quasi-concavity, these IC constraints are replaced by the first-order conditions, which give rise to extra moment constraints. Interestingly, these extra moment constraints drastically reduce the number of corner points to be considered in the corresponding semi-infinite programming models. We show that in the equilibrium, these moment constraints are binding but have zero Lagrangian multipliers and thus facilitate closed-form solutions in several application examples with different levels of complexity. The high efficiency of the method enables us to solve a large class of zero-sum games and the corresponding max-min robust optimization models