Supplier Selection for Framework Agreements in Humanitarian Relief

In this study, we consider the supplier selection problem of a relief organization that wants to establish framework agreements (FAs) with a number of suppliers to ensure quick and cost‐effective procurement of relief supplies in responding to sudden‐onset disasters. Motivated by the FAs in relief practice, we focus on a quantity flexibility contract in which the relief organization commits to purchase a minimum total quantity from each framework supplier over a fixed agreement horizon, and, in return, the suppliers reserve capacity for the organization and promise to deliver items according to pre‐specified agreement terms. Due to the uncertainties in demand locations and amounts, it may be challenging for relief organizations to assess candidate suppliers and the offered agreement terms. We use a scenario‐based approach to represent demand uncertainty and develop a stochastic programming model that selects framework suppliers to minimize expected procurement and agreement costs while meeting service requirements. We perform numerical experiments to understand the implications of agreement terms in different settings. The results show that supplier selection decisions and costs are generally more sensitive to the changes in agreement terms in settings with high‐impact disasters. Finally, we illustrate the applicability of our model on a case study.     

Integrated Procurement Planning in Multi‐division Firms

For large multi‐division firms, coordinating procurement policies across multiple divisions to leverage volume discounts from suppliers based on firm‐wide purchasing power can yield millions of dollars of savings in procurement costs. Coordinated procurement entails deciding which suppliers to use to meet each division's purchasing needs and sourcing preferences so as to minimize overall purchasing, logistics, and operational costs. Motivated by this tactical procurement planning problem facing a large industrial products manufacturer, we propose an integrated optimization model that simultaneously considers both firm‐wide volume discounts and divisional ordering and inventory costs. To effectively solve this large‐scale integer program, we develop and apply a tailored solution approach that exploits the problem structure to generate tight bounds. We identify several classes of valid inequalities to strengthen the linear programming relaxation, establish polyhedral properties of these inequalities, and develop both a cutting‐plane method and a sequential rounding heuristic procedure. Extensive computational tests for realistic problems demonstrate that our integrated sourcing model and solution method are effective and can provide significant economic benefits. The integrated approach yields average savings of 7.5% in total procurement costs compared to autonomous divisional policies, and our algorithm generates near‐optimal solutions (within 0.75% of optimality) within reasonable computational time.     

The Retail Planning Problem Under Demand Uncertainty

We consider the retail planning problem in which the retailer chooses suppliers and determines the production, distribution, and inventory planning for products with uncertain demand to minimize total expected costs. This problem is often faced by large retail chains that carry private‐label products. We formulate this problem as a convex‐mixed integer program and show that it is strongly NP‐hard. We determine a lower bound by applying a Lagrangian relaxation and show that this bound outperforms the standard convex programming relaxation while being computationally efficient. We also establish a worst‐case error bound for the Lagrangian relaxation. We then develop heuristics to generate feasible solutions. Our computational results indicate that our convex programming heuristic yields feasible solutions that are close to optimal with an average suboptimality gap at 3.4%. We also develop managerial insights for practitioners who choose suppliers and make production, distribution, and inventory decisions in the supply chain.     

Push or Pull? Auctioning Supply Contracts

Consider a buyer, facing uncertain demand, who sources from multiple suppliers via online procurement auctions (open descending price‐only auctions). The suppliers have heterogeneous production costs, which are private information, and the winning supplier has to invest in production capacity before the demand uncertainty is resolved. The buyer chooses to offer a push or pull contract, for which the single price and winning supplier are determined via the auction. We show that, with a pull contract, the buyer does not necessarily benefit from a larger number of suppliers participating in the auction, due to the negative effect of supplier competition on the incentive of supplier capacity investment. We thus propose an enhanced pull mechanism that mitigates this effect with a floor price. We then analyze and compare the outcomes of auctions for push and (enhanced) pull contracts, establishing when one form is preferred over the other based on the buyer's profits. We also compare our simple, price‐only push and pull contract auctions to the optimal mechanisms, benchmarking the performance of the simple mechanisms as well as establishing the relative importance of auction design and contract design in procurement auctions.     

多部件采购外包的两阶段均衡投标策略

本文考虑一个由单个制造商和多个供应商群体组成的供应链——该制造商需要采购多个部件,对于每个部件在市场上均存在多个供应商。不同于传统的从各供应商群体分别采购各个部件,制造商考虑将所有部件的采购整体外包给某个供应商。在第一阶段,制造商使用一级价格密封投标的逆向拍卖来确定赢得整体采购合约的供应商。接下来,第一阶段投标的获胜者生产其所能供应的部件,并使用逆向拍卖向第一阶段中未获胜的其他竞标者采购其余部件。我们分析了供应商在两个阶段的均衡竞价策略,并比较了制造商在亲自逐件采购和外包整体采购两种情况下的期望采购成本。我们证明了在两种机制下制造商的总的期望采购成本相等。     

Inventory management with variable lead-time dependent procurement cost

A reduction in the inventory replenishment lead-time allows reducing safety stock requirements and improving customer service. However, it might be accompanied by increased procurement costs because of premium charges imposed by suppliers, or higher transportation costs. This paper studies a single-stage variable lead-time inventory system with lead-time dependent procurement cost. Selection of the lead-time value represents finding the trade-off between benefits of lead-time reduction and increase in the procurement cost. A model for joint optimization of inventory and procurement costs is developed. Numerical studies are conducted to identify conditions under which lead-time reduction is favorable compared to procuring at the lowest cost.     

SHORT‐TERM E‐PROCUREMENT STRATEGIES VERSUS LONG‐TERM CONTRACTS

In this paper we compare the following procurement strategies based on their expected costs: strategic partnership, which is based on a long‐term relationship with a single supplier; online search, which is a short‐term strategy; and a combined strategy, which is some combination of the first two strategies. In addition, we determine for the online search and combined strategy the optimal number of suppliers to contact for a price quote, and analyze how it depends on the various cost and demand parameters. The main contribution of this paper is that it does not assume a single procurement strategy, but rather compares three alternatives.     

A Multi‐Supplier Sourcing Problem with a Preference Ordering of Suppliers

We study a sourcing problem faced by a firm that seeks to procure a product or a component from a pool of alternative suppliers. The firm has a preference ordering of the suppliers based on factors such as their past performance, quality, service, geographical location, and financial strength, which are commonly included in a supplier scorecard system. Thus, the firm first uses available inventory from supplier 1, if any, then supplier 2, if any, and so on. The suppliers differ in costs and prices. The buyer firm seeks to determine which suppliers to purchase from and in what quantities to maximize its total expected profit subject to the preference ordering constraint. We present the optimal solution to this problem, and show that it has a portfolio structure. It consists of a sub‐set of suppliers that are ordered by their underage and overage costs. This portfolio achieves a substantial profit gain compared to sourcing from a unique supplier. We present an efficient algorithm to compute the optimal solution. Our model applies to component sourcing problems in manufacturing, merchandizing problems in retailing, and capacity reservation problems in services.     

Electronic markets in support of procurement processes along the automotive supply chain

Since the introduction of the internet, firms have continued to seek ways to use these public networks to gain competitive advantage. The procurement function is beginning to take on greater strategic importance as these networks started providing firms wider opportunities such as choices of suppliers. This aims not only to reduce procurement costs, but also to build stronger relationships with suppliers to improve quality and flexibility in meeting customer demand. This type of linkage of firms with their suppliers when the product manufactured is complex and supply-chain is heavily tiered, such as the case of the automobile industry, creates challenges to any electronic market or exchange that is aiming to support such a system. Based on discussions with some key individuals in an automotive supply chain and an in-depth analysis of a supply-chain segment, this paper explores the role electronic markets may have to play, if they are to support the procurement processes of various agents along the supply chain.     

Managing stochastic demand in an Inventory Routing Problem with transportation procurement

We study an Inventory Routing Problem in which the supplier has a limited production capacity and the stochastic demand of the retailers is satisfied with procurement of transportation services. The aim is to minimize the total expected cost over a planning horizon, given by the sum of the inventory cost at the supplier, the inventory cost at the retailers, the penalty cost for stock-out at the retailers and the transportation cost. First, we show that a policy based just on the average demand can have a total expected cost infinitely worse than the one obtained by taking into account the overall probability distribution of the demand in the decision process. Therefore, we introduce a stochastic dynamic programming formulation of the problem that allows us to find an optimal policy in small size instances. Finally, we design and implement a matheuristic approach, integrating a rollout algorithm and an optimal solution of mixed-integer linear programming models, which is able to solve realistic size problem instances. Computational results allow us to provide managerial insights concerning the management of stochastic demand.     

Optimal Descending Mechanisms for Constrained Procurement

Descending mechanisms for procurement (or, ascending mechanisms for selling) have been well‐recognized for their simplicity from the viewpoint of bidders—they require less bidder sophistication as compared to sealed‐bid mechanisms. In this study, we consider procurement under each of two types of constraints: (1) Individual/Group Capacities: limitations on the amounts that can be sourced from individual and/or subsets of suppliers, and (2) Business Rules: lower and upper bounds on the number of suppliers to source from, and on the amount that can be sourced from any single supplier. We analyze two procurement problems, one that incorporates individual/group capacities and another that incorporates business rules. In each problem, we consider a buyer who wants to procure a fixed quantity of a product from a set of suppliers, where each supplier is endowed with a privately known constant marginal cost. The buyer's objective is to minimize her total expected procurement cost. For both problems, we present descending auction mechanisms that are optimal mechanisms. We then show that these two problems belong to a larger class of mechanism design problems with constraints specified by polymatroids, for which we prove that optimal mechanisms can be implemented as descending mechanisms.     

Dynamic Supply Risk Management with Signal‐Based Forecast,Multi‐Sourcing,and Discretionary Selling

We examine the critical role of advance supply signals—such as suppliers’ financial health and production viability—in dynamic supply risk management. The firm operates an inventory system with multiple demand classes and multiple suppliers. The sales are discretionary and the suppliers are susceptible to both systematic and operational risks. We develop a hierarchical Markov model that captures the essential features of advance supply signals, and integrate it with procurement and selling decisions. We characterize the optimal procurement and selling policy, and the strategic relationship between signal‐based forecast, multi‐sourcing, and discretionary selling. We show that higher demand heterogeneity may reduce the value of discretionary selling, and that the mean value‐based forecast may outperform the stationary distribution‐based forecast. This work advances our understanding on when and how to use advance supply signals in dynamic risk management. Future supply risk erodes profitability but enhances the marginal value of current inventory. A signal of future supply shortage raises both base stock and demand rationing levels, thereby boosting the current production and tightening the current sales. Signal‐based dynamic forecast effectively guides the firm's procurement and selling decisions. Its value critically depends on supply volatility and scarcity. Ignoring advance supply signals can result in misleading recommendations and severe losses. Signal‐based dynamic supply forecast should be used when: (a) supply uncertainty is substantial, (b) supply‐demand ratio is moderate, (c) forecast precision is high, and (d) supplier heterogeneity is high.     

An integrated supplier selection and inventory problem with multi-sourcing and lateral transshipments

In this research, we consider the supplier selection problem of a firm offering a single product via multiple warehouses. The warehouses face stationary, stochastic demand and replenish their inventory via multiple suppliers, to be determined from a set of candidates, with varying price, capacity, quality, and disruption characteristics. Additionally, the warehouses may simultaneously replenish their inventory from other warehouses proactively. With these characteristics, the problem is a multi-sourcing, supplier selection, and inventory problem with lateral transshipments. Even though the benefits of multi-sourcing and lateral transshipments have been presented in the literature individually to mitigate risks associated with uncertain demand and disrupted supply, the intertwined sourcing and inventory decisions under these settings have not been investigated from a quantitative perspective. We develop a decomposition based heuristic algorithm, powered with simulation. While the decomposition based heuristic determines a solution with supplier selection and inventory decisions, the simulation model evaluates the objective function value corresponding to each generated solution. Experimental results show, contrary to the existing literature, inferior decisions may result when considering the selection of suppliers solely on unit and/or contractual costs. We also evaluate the impact of multi-sourcing with rare but long disruptions compared to frequent but short ones.     

考虑供应商违约风险的CVaR最优订货模型

供应商违约引发供应中断或延迟会使下游制造商造成巨大损失。同时考虑了供应商具有随机的违约概率及需求不确定的情况,基于CVaR的风险度量准则,建立了基于条件风险价值最小的制造商最优订货模型,数值分析表明订货量与供应商可靠性具有正相关性;当制造商风险参数很高时,可靠性只有达到一定程度,订货量才会有较大幅度提高;当供应商可靠性较低时,降低预定价格会吸引更多的订货。     

A continuous-time supply-driven inventory-constrained routing problem

We address an inventory routing problem (IRP) in which routing and inventory decisions are dictated by supply rather than demand. Moreover, inventory is held in containers that act as both a storage container and a movable transport unit. This problem emanates from logistics related to biogas transportation in which biogas is transported in containers from many suppliers to a single facility. We present a novel and compact formulation for the supply-driven IRP which addresses the routing decisions in continuous-time in which inventory levels within the containers are continuous. Valid inequalities are included and realistic instances are solved to optimality. For all experiments, we found that the total transportation time is minimized when the storage capacity at each supplier is larger than or equal to the vehicle capacity. These routes are characterized by tours in which mostly single suppliers are visited. In 95% of the instances, the average content level of the exchanged containers exceeded 99.6%.     

不确定需求下考虑供应商参与机制的应急资源配置鲁棒优化研究

突发事件应急资源优化配置是突发事件发生后救援工作有效开展的前提和基本保障。本文在调研国内外相关研究的基础上，以应对地震灾难为背景研究考虑供应商参与机制的应急资源保障策略，在灾前选择供应商建立政府与供应商的合作机制完成政府储备仓库的选址与资源配置，突发事件发生后依托政府储备仓库和供应商生产能力共同满足应急救援对应急资源的分时段需求，以期协调供应商与政府储备、灾前实物采购与灾后生产能力采购的比例，在保障救援效率的同时降低应急资源保障体系的成本。同时由于地震灾难发生具有需求不确定性的特点，本文引入L1范数描述需求的不确定性，建立了备灾与灾害救援两阶段决策的鲁棒优化模型，并给出了鲁棒模型对应问题的转化方法。最后通过算例仿真验证了模型和对应问题转换方法的有效性，为地震的应对提供理论指导和决策支持。     

Supplier competition and its impact on firm׳s sourcing strategy

Most research on firms׳ sourcing strategies assumes that wholesale prices and reliability of suppliers are exogenous. It is of our interest to study suppliers׳ competition on both wholesale price and reliability and firms׳ corresponding optimal sourcing strategy under complete information. In particular, we study a problem in which a firm procures a single product from two suppliers, taking into account suppliers׳ price and reliability differences. This motivates the suppliers to compete on these two factors. We investigate the equilibria of this supplier game and the firm׳s corresponding sourcing decisions. Our study shows that suppliers׳ reliability often plays a more important role than wholesale price in supplier competition and that maintaining high reliability and a high wholesale price is the ideal strategy for suppliers if multiple options exist. The conventional wisdom implies that low supply reliability and high demand uncertainty motivate dual-sourcing. We notice that when the suppliers׳ shared market/transportation network is often disrupted and demand uncertainty is high, suppliers׳ competition on both price and reliability may render the sole-sourcing strategy to be optimal in some cases that depend on the format of suppliers׳ cost functions. Moreover, numerical study shows that when the cost or vulnerability (to market disruptions) of one supplier increases, its profit and that of the firm may not necessarily decrease under supplier competition.     

STOCK LEVELS AND DELIVERY RATES IN VENDORMANAGED INVENTORY PROGRAMS

Using the latest information technology, powerful retailers like Wal‐Mart have taken the lead in forging shorter replenishment‐cycles, automated supply systems with suppliers. With the objective to reduce cost, these retailers are directing suppliers to take full responsibility for managing stocks and deliveries. Suppliers' performance is measured according to how often inventory is shipped to the retailer, and how often customers are unable to purchase the product because it is out of stock. This emerging trend also implies that suppliers are absorbing a large part of the inventory and delivery costs and, therefore, must plan delivery programs including delivery frequency to ensure that the inherent costs are minimized. With the idea to incorporate this shift in focus, this paper looks at the problem facing the supplier who wants quicker replenishment at lower cost. In particular, we present a model that seeks the best trade‐off among inventory investment, delivery rates, and permitting shortages to occur, given some random demand pattern for the product. The process generating demand consists of two components: one is deterministic and the other is random. The random part is assumed to follow a compound Poisson process. Furthermore, we assume that the supplier may fail to meet uniform shipping schedules, and, therefore, uncertainty is present in delivery times. The solution to this transportationinventory problem requires determining jointly delivery rates and stock levels that will minimize transportation, inventory, and shortage costs. Several numerical results are presented to give a feel of the optimal policy's general behavior.     

A comparison of fixed and dynamic pricing policies in revenue management

We consider the problem of selling a fixed capacity or inventory of items over a finite selling period. Earlier research has shown that using a properly set fixed price during the selling period is asymptotically optimal as the demand potential and capacity grow large and that dynamic pricing has only a secondary effect on revenues. However, additional revenue improvements through dynamic pricing can be important in practice and need to be further explored. We suggest two simple dynamic heuristics that continuously update prices based on remaining inventory and time in the selling period. The first heuristic is based on approximating the optimal expected revenue function and the second heuristic is based on the solution of the deterministic version of the problem. We show through a numerical study that the revenue impact of using these dynamic pricing heuristics rather than fixed pricing may be substantial. In particular, the first heuristic has a consistent and remarkable performance leading to at most 0.2% gap compared to optimal dynamic pricing. We also show that the benefits of these dynamic pricing heuristics persist under a periodic setting. This is especially true for the first heuristic for which the performance is monotone in the frequency of price changes. We conclude that dynamic pricing should be considered as a more favorable option in practice.     

The optimal value range problem for the Interval (immune) Transportation Problem

We address the problem of finding the range of the optimal cost of a transportation problem when supply and demand vary over an interval. We consider the specific version of a transportation problem with supply inequality constraints and demand equality constraints under the assumption that the transportation costs are immune against the transportation paradox. We investigate some theoretical properties of the problem which constitute the basis of a novel solution algorithm. Our results show that the proposed algorithm hugely outperforms the best existing solution approaches.