Heuristics for sourcing from multiple suppliers with alternative quantity discounts

In this paper, we analyze the impact of supplier pricing schemes and supplier capacity limitations on the optimal sourcing policy for a single firm. We consider the situation where the total quantity to be procured for a single period is known by the firm and communicated to the supplier set. In response to this communication, each supplier quotes a price and a capacity limit in terms of a maximum quantity that can be supplied to the buyer. Based on this information, the buyer makes a quantity allocation decision among the suppliers and corresponding to this decision is the choice of a subset of suppliers who will receive an order. Based on industry observations, a variety of supplier pricing schemes from the constituent group of suppliers are analyzed, including linear discounts, incremental units discounts, and all units discounts. Given the complexity of the optimization problem for certain types of pricing schemes, heuristic solution methodologies are developed to identify a quantity allocation decision for the firm. Through an extensive computational comparison, we find that these heuristics generate near-optimal solutions very quickly. Data from a major office products retailer is used to illustrate the resulting sourcing strategies given different pricing schemes and capacity limitations of suppliers in this industry. We find for the case of capacity constrained suppliers, the optimal quantity allocations for two complex pricing schemes (linear discount, and incremental units discount) are such that at most one selected supplier will receive an order quantity that is less than its capacity.     

A dynamic model of supplier switching

While a broad branch of literature deals with the development of buyer–supplier relationships, limited research exists under which circumstances a buyer should terminate such a relationship and switch to a new supplier. Recently, Wagner and Friedl (2007) have developed a framework to analyze a static one-shot supplier switching decision when the buyer has asymmetric information about the supplier’s production costs. We extend their basic framework to a dynamic one, assuming that the supplier learns the production costs over time when he sets up the production process. Since the supplier’s cost information at the individual stages crucially determines the setup and the switching decision, it becomes essential for supply chain management to provide proper incentives so that the supplier reveals his cost information truthfully over time. We characterize the optimal setup and switching strategy as well as the optimal supply chain contract. We also compare our findings with those of the static setting to provide further insights.     

Integrated optimization of customer and supplier logistics at Robert Bosch LLC

Large automotive supply chains typically involve manufacturers pulling materials from their suppliers along the chain, usually by using round-trip truckload routes. The return trips on these routes are used to return empty containers back to the suppliers. The mismatch between the amount of materials and empty containers results in underutilization of the return trips. A supplier can utilize this unused capacity by identifying a subset of promising customer routes that can be combined with its existing supplier routes to save overall costs of the system. Such an integration also leads to other supply chain coordination benefits such as the potential of using crossdocks, more frequent milkruns and ensuing reductions in inventories.     

An a posteriori decision support methodology for solving the multi-criteria supplier selection problem

This research presents a novel, state-of-the-art methodology for solving a multi-criteria supplier selection problem considering risk and sustainability. It combines multi-objective optimization with the analytic network process to take into account sustainability requirements of a supplier portfolio configuration. To integrate ‘risk’ into the supplier selection problem, we develop a multi-objective optimization model based on the investment portfolio theory introduced by Markowitz. The proposed model is a non-standard portfolio selection problem with four objectives: (1) minimizing the purchasing costs, (2) selecting the supplier portfolio with the highest logistics service, (3) minimizing the supply risk, and (4) ordering as much as possible from those suppliers with outstanding sustainability performance. The optimization model, which has three linear and one quadratic objective function, is solved by an algorithm that analytically computes a set of efficient solutions and provides graphical decision support through a visualization of the complete and exactly-computed Pareto front (a posteriori approach). The possibility of computing all Pareto-optimal supplier portfolios is beneficial for decision makers as they can compare all optimal solutions at once, identify the trade-offs between the criteria, and study how the different objectives of supplier portfolio configuration may be balanced to finally choose the composition that satisfies the purchasing company's strategy best. The approach has been applied to a real-world supplier portfolio configuration case to demonstrate its applicability and to analyze how the consideration of sustainability requirements may affect the traditional supplier selection and purchasing goals in a real-life setting.     

Optimizing Supply Shortage Decisions in Base Stock Distribution Operations

This paper addresses policies and agreements between suppliers and customers for handling supply shortages in base-stock systems under uncertain demand. We investigate the impacts that backlogging and expediting decisions have on inventory and transportation costs in these systems and develop a model for deciding whether a supplier should completely backlog, completely expedite, or employ some combination of backlogging and expediting shortages. Our results indicate that practical cases exist where some combination of both expediting and backlogging supply shortages outperforms either completely expediting or backlogging all shortages. Including transportation costs in our model provides incentive to employ `hybrid' policies that partially expedite and partially backlog excess demands within a given period. Our model demonstrates how inventory policy decisions directly impact transportation costs and provides a heuristic approach for jointly minimizing expected inventory and transportation costs.     

The newsvendor problem: Review and directions for future research

In this paper, we review the contributions to date for analyzing the newsvendor problem. Our focus is on examining the specific extensions for analyzing this problem in the context of modeling customer demand, supplier costs, and the buyer risk profile. More specifically, we analyze the impact of market price, marketing effort, and stocking quantity on customer demand; how supplier prices can serve as a coordination mechanism in a supply chain setting; integrating alternative supplier pricing policies within the newsvendor framework; and how the buyer’s risk profile moderates the newsvendor order quantity decision. For each of these areas, we summarize the current literature and develop extensions. Finally, we also propose directions for future research.     

A continuous-review inventory model with random disruptions at the primary supplier

We consider a continuous-review inventory problem for a retailer facing constant customer demand for a single product. This retailer is assumed to follow the well known and widely used order-up-to policy in making replenishment decisions, and can order from two suppliers who differ in reliability and costs. Supplier 1, the primary supplier, is cheaper, but is subject to random disruptions. Supplier 2, the backup supplier or the contingent source, is more expensive, but is perfectly reliable. If Supplier 1 is available when the inventory level at the retailer reaches the reorder point, the retailer orders from Supplier 1. Otherwise, it will wait for a while to see if Supplier 1 can recover from the disruption quickly. If so, it will still get replenishment from Supplier 1 to take advantage of its lower charge. However, the retailer will reroute to the backup supplier if Supplier 1 still does not recover from the disruption when the cap of waiting (the maximal waiting time of the retailer if Supplier 1 is disrupted) is reached. We analytically study the optimal sourcing and replenishment decisions at the retailer, and the impacts of various problem parameters on the optimal decisions. We also conduct extensive numerical experiments to compare different sourcing and replenishment decisions the retailer can make and get further managerial insights into the problem.     

Central versus local multiple stage inventory planning: An analysis of solutions

Supply chain management refers to the integration of all activities associated with moving goods from raw material stages through to end users. Yet this system-wide vision of inventory planning often requires the coordination of several commercially independent entities, such as suppliers, manufacturers and distributors. This study explores the issue of friction between replenishment policies, defined as the disparity between centrally and locally planned solutions to 98,820 deterministic, multiple stage inventory planning problems modeling systems of varying levels of complexity. Friction is found to be strongly related to certain cost factors, suggesting that certain supply chains could be more vulnerable to tension and inefficiencies when replenishment policies are derived without cooperation between commercially independent yet logistically interdependent stages. These results can also be applied to identify relationships between the findings of otherwise seemingly disparate previous studies of coordination schemes for supply chain partners.     

On stability of collaborative supplier selection

This note discusses the possibility of fair gain sharing in cooperative situations where players optimally partition themselves across a number of alternative channels. An example is group purchasing among a set of buyers facing with a range of suppliers. We introduce channel selection games as a new class of cooperative games and give a representation of their cores. With two channels (suppliers), the game has a non-empty core if the gain functions across every individual channel is supermodular.     

The value of early order commitment in a two-level supply chain

One approach to supply chain coordination is early order commitment, whereby a retailer commits to purchase a fixed-order quantity at a fixed delivery time before demand uncertainty is resolved. In this paper, we develop an analytical model to quantify the cost savings of an early order commitment in a two-level supply chain where demand is serially correlated. A decision rule is derived to determine whether early order commitment will benefit the supply chain, and accordingly to determine the optimal timing for early commitment. Our results indicate that the supply chain would experience greater savings from early order commitment when – (a) the inventory item receives less value-added activities at the retailer site; (b) the manufacturing lead time is short; (c) demand correlation over time is positive but weak; or (d) the delivery lead time is long (if a condition exists). We also propose a rebate scheme for the supply chain partners to share the gains of practicing early order commitment.     

Don’t forget your supplier when remanufacturing

A popular assumption in the current literature on remanufacturing is that the whole new product is produced by an integrated manufacturer, which is inconsistent with most industries. In this paper, we model a decentralised closed-loop supply chain consisting of a key component supplier and a non-integrated manufacturer, and demonstrate that the interaction between these players significantly impacts the economic and environmental implications of remanufacturing. In our model, the non-integrated manufacturer can purchase new components from the supplier to produce new products, and remanufacture used components to produce remanufactured products. Thus, the non-integrated manufacturer is not only a buyer but also a rival to the supplier. In a steady state period, we analyse the performances of an integrated manufacturer and the decentralised supply chain. We find that, although the integrated manufacturer always benefits from remanufacturing, the remanufacturing opportunity may constitute a lose–lose situation to the supplier and the non-integrated manufacturer, making their profits be lower than in an identical supply chain without remanufacturing. In addition, the non-integrated manufacturer may be worse off with a lower remanufacturing cost or a larger return rate of used products due to the interaction with the supplier. We further demonstrate that the government-subsidised remanufacturing in the non-integrated (integrated) manufacturer is detrimental (beneficial) to the environment.     

Operations Research for green logistics – An overview of aspects,issues, contributions and challenges

The worldwide economic growth of the last century has given rise to a vast consumption of goods while globalization has led to large streams of goods all over the world. The production, transportation, storage and consumption of all these goods, however, have created large environmental problems. Today, global warming, created by large scale emissions of greenhouse gasses, is a top environmental concern. Governments, action groups and companies are asking for measures to counter this threat. Operations Research has a long tradition in improving operations and especially in reducing costs. In this paper, we present a review that highlights the contribution of Operations Research to green logistics, which involves the integration of environmental aspects in logistics. We give a sketch of the present and possible developments, focussing on design, planning and control in a supply chain for transportation, inventory of products and facility decisions. While doing this, we also indicate several areas where environmental aspects could be included in OR models for logistics.     

A fuzzy newsvendor approach to supply chain coordination

In the absence of a clear command and control structure, a key challenge in supply chain management is the coordination and alignment of supply chain members who pursue divergent and often conflicting goals. The newsvendor model is typically used as a framework to quantify the cost of misalignment and to assess the impact of various coordination initiatives. The application of the newsvendor framework, however, requires the specification of some probability distribution for the sources of uncertainty, and in particular, for the market demand. The specification of an adequate demand distribution becomes difficult in the absence of statistical data. We therefore consider a fuzzy approach to the newsvendor problem. We use several fuzzy parameters in the model for the demand, the wholesale price, and the market sales price. We solve the fuzzy newsvendor problem to study three coordination policies: quantity discounts, profit sharing, and buyback. For each coordination policy, the optimal order quantity of the retailer is computed. The possible profits of the members in the supply chain are calculated with minimum sharing of private information. We further extend the fuzzy newsvendor model to a setting with a single manufacturer and multiple retailers under the assumption of ample capacity for the manufacturer. Detailed numerical examples are also provided.     

Manufacturer cooperation in supplier development under risk

Supplier development involves efforts undertaken by manufacturing firms to improve their suppliers’ capabilities and performance. These improvement efforts can be targeted at a variety of areas such as quality management, product development, and cost reduction. Since supplier development requires investments on the part of the manufacturer, it is important to optimally allocate investment dollars among multiple suppliers to minimize risk while maintaining an acceptable level of return. This paper presents a set of optimization models that address this issue. We consider two scenarios: single-manufacturer and multiple suppliers (SMMS) and two-manufacturer and multiple suppliers (TMMS). In the SMMS case, we suggest optimal investments in various suppliers by effectively considering risk and return. The TMMS case investigates whether manufacturers with differing capabilities could gain risk reduction benefits from cooperating with each other in supplier development. Through illustrative applications, we identify conditions in which both cooperation and non-cooperation are beneficial for manufacturers. Under conditions of cooperation, we propose optimal investments for manufacturers to achieve high levels of risk reduction benefits.     

Incorporating quantity discounts and their inventory impacts into the centralized purchasing decision

Multi-site organizations must balance conflicting forces to determine the appropriate degree of purchasing centralization for their respective supplies. The ability to garner quantity discounts represents one of the primary reasons that organizations centralize procurement. This paper provides methodologies to calculate optimal order quantities and compute total purchasing and inventory costs when products have quantity discount pricing. Procedures for both all-units and incremental quantity discount schedules are provided for four different strategic purchasing configurations (scenarios): complete decentralization, centralized pricing with decentralized purchasing, centralized purchasing with local distribution, and centralized purchasing and warehousing. For ordering decisions under local distribution, procedures to determine optimal order quantities and costs are presented in a precise form that could be easily implemented into spreadsheets by practicing managers. For the more complicated multi-echelon scenarios, we introduce a single-cycle policy with a tailored aggregation refinement step that performs very well under experimentation when compared to a conservative bound.     

The risk of second-tier supplier failures in serial supply chains: Implications for order policies and distributor autonomy

As organizations decrease inventory, the potential impact of a supply disruption increases. However, due to supply chain structural changes, the likelihood of a disruption may be less. Additionally independent supply chain actors may react to policy changes, changing supply chain configurations and perhaps reducing loss magnitudes. If risk is a product of likelihood and magnitude, does higher inventory reduce an organization’s supply related risk? This paper examines the supply risk issue within the context of a second-tier supply failure, and is grounded in inventory and resource dependency theories. By evaluating risk assessment in a simulation environment, exploratory findings suggest that increased inventory in a tiered supply chain can sometimes increase supply risk rather than decrease it. Managerial insights into the effects of supply chain stability and coordination are provided. By taking a systems perspective of supply risk management, organizations will be better able to manage supply risk concerns.     

Coordination in a two-stage capacitated supply chain with multiple suppliers

The aim of this paper is to coordinate the inventory policies in a decentralized supply chain with stochastic demand by means of contracts. The system considered is a decentralized two-stage supply chain consisting of multiple independent suppliers and a manufacturer with limited production capacities. The suppliers operate on a make-to-stock basis and apply base stock policy to manage their inventories. On the other hand, the manufacturer employs a make-to-order strategy. Under the necessary assumptions, each supplier is modeled as an M/M/1 make-to-stock queue; and the manufacturer is modeled as a GI/M/1 queue after deriving an approximate distribution for the interarrival times of the manufacturer. Once the supply chain is modeled as a queuing system, centralized and decentralized models are developed. Comparison of the optimal solutions to these models reveals that the supply chain needs coordination. Three different transfer payment contracts are examined in this paper. These are the backorder and holding cost subsidy contracts, the transfer payment contract based on Pareto improvement, and the cost sharing contract. Each contract is evaluated according to its coordination ability and whether it is Pareto improving or not. The results indicate that all three contracts can coordinate the supply chain. However, when the Pareto improvement is taken into account, the cost sharing contract seems to be the one that will be preferred by all parties.     

Improving reliability of a shared supplier with competition and spillovers

Supplier reliability is a key determinant of a manufacturer’s competitiveness. It reflects a supplier’s capability of order fulfillment, which can be measured by the percentage of order quantity delivered in a given time window. A perfectly reliable supplier delivers an amount equal to the order placed by its customer, while an unreliable supplier may deliver an amount less than the amount ordered. Therefore, when suppliers are unreliable, manufacturers often have incentives to help suppliers improve delivery reliability. Suppliers, however, often work with multiple manufacturers and the benefit of enhanced reliability may spill over to competing manufacturers. In this study, we explore how potential spillover influences manufacturers’ incentives to improve supplier’s reliability. We consider two manufacturers that compete with imperfectly substitutable products on Type I service level (i.e., in-stock probability). The manufacturers share a common supplier who, due to variations in production quality or yield, is unreliable. Manufacturers may exert efforts to improve the supplier’s reliability in the sense that the delivered quantity is stochastically larger after improvement. We develop a two-stage model that encompasses supplier improvement, uncertain supply and random demand in a competitive setting. In this complex model, we characterize the manufacturers’ equilibrium in-stock probability. Moreover, we characterize sufficient conditions for the existence of the equilibrium of the manufacturers’ improvement efforts. Finally, we numerically test the impact of market characteristics on the manufacturers’ equilibrium improvement efforts. We find that a manufacturer’s equilibrium improvement effort usually declines in market competition, market uncertainty or spillover effect, although its expected equilibrium profit typically increases in spillover effect.     

Multi-criteria supplier segmentation using a fuzzy preference relations based AHP

One of the strategic activities of a firm is supplier segmentation, whereby a firm creates groups of suppliers to handle them differently. Existing literature provides several typologies of suppliers, each of which uses different dimensions/variables. In this paper, different typologies are combined by distinguishing two overarching dimensions, the capabilities and the willingness of suppliers to cooperate with a particular firm. These dimensions cover almost all the existing supplier segmentation criteria mentioned in existing literature. For each particular situation, these dimensions can be specified using a multi-criteria decision-making method. A methodology is proposed that includes a fuzzy Analytic Hierarchy Process (AHP) which uses fuzzy preference relations to incorporate the ambiguities and uncertainties that usually exist in human judgment. The proposed methodology is used to segment the suppliers of a broiler company. The result is a segmentation of suppliers based on two aggregated dimensions. Finally some strategies to handle different segments are discussed and concluding remarks and suggestions for future research are provided.     

A heuristic for single-warehouse multiretailer supply chains with all-unit transportation cost discounts

In supply chain management research, transportation costs, if explicitly considered at all, are frequently assumed to be linear. These costs often have a more complex form, such as an all-unit discount structure – this piecewise cost function adds significant complexity when included in supply chain management problems and is therefore often ignored due to solution time or tractability concerns. We present and evaluate a new heuristic procedure which provides good solutions to problems involving all-unit discount cost functions while significantly reducing solution times. The general nature of this procedure does not require assumptions about the supply chain structure or policies, and is therefore applicable in a wide range of settings.