Single versus multiple supplier sourcing strategies

Successful supply chain management necessitates an effective sourcing strategy to combat uncertainties in both supply and demand. In particular, supply disruption results in excessive downtime of production resources, upstream and downstream supply chain repercussions, and eventually a loss in the market value of the firm. In this paper we analyze single period, single product sourcing decisions under demand uncertainty. Our approach integrates product prices, supplier costs, supplier capacities, historical supplier reliabilities and firm specific inventory costs. A unique feature of our approach is the integration of a firm specific supplier diversification function. We also extend our analysis to examine the impact of minimum supplier order quantities. Our results indicate that single sourcing is a dominant strategy only when supplier capacities are large relative to the product demand and when the firm does not obtain diversification benefits. In other cases, we find that multiple sourcing is an optimal sourcing strategy. We also characterize a non-intuitive trade-off between supplier minimum order quantities, costs, and supplier reliabilities. Finally, we examine the robustness of our results through an extensive numerical analysis of the key parameters of our model.     

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.     

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.     

An optimization approach for supply chain management models with quantity discount policy

Owing to the difficulty of treating nonlinear functions, many supply chain management (SCM) models assume that the average prices of materials, production, transportation, and inventory are constant. This assumption, however, is not practical. Vendors usually offer quantity discounts to encourage the buyers to order more, and the producer intends to discount the unit production cost if the amount of production is large. This study solves a nonlinear SCM model capable of treating various quantity discount functions simultaneously, including linear, single breakpoint, step, and multiple breakpoint functions. By utilizing the presented linearization techniques, such a nonlinear model is approximated to a linear mixed 0–1 program solvable to obtain a global optimum.     

Distributed supply chain management using ant colony optimization

Successful supply chain management requires a cooperative integration between all the partners in the network. At the operational level, the partners individual behavior should be optimal and therefore their activities have to be planned using sophisticated optimization tools. However, these tools should take into account the planning of the remaining partners, through the exchange of information, in order to allow some kind of cooperation between the elements of the chain. This paper introduces a new supply chain management technique, based on modeling a generic supply chain with suppliers, logistics and distributers, as a distributed optimization problem. The different operational activities are solved by the optimization meta-heuristic called ant colony optimization, which allows the exchange of information between different optimization problems by means of a pheromone matrix. The simulation results show that the new methodology is more efficient than a simple decentralized methodology for different instances of a supply chain.     

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.     

Equilibrium analysis and corporate social responsibility for supply chain integration

This paper evaluates the profit of coordination between manufacturers on corporate social responsibility (CSR) under network equilibrium. A three-tier supply chain network with multiple manufacturers, distributors, and retailers is considered, and several mathematical models are established to investigate behavior and profits in a decentralized supply chain network, a centralized supply chain network, and a supply chain network with CSR. The system-optimal solution of a supply chain network problem is usually not achievable or stable since each member always tries to maximize its own profit. In order to make such a system-optimal solution in a stable state and ensure the maximization of total profits, a strategy of coordination between manufacturers on CSR is proposed. The amount of payment in CSR of each manufacturer is clearly defined. A hybrid diagonalization method with a super-network representation is proposed and tested with numerical examples. The results show that by taking CSR, the total profits of the whole supply chain network can increase with or without coordination.     

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.     

On the value of customer information for an independent supplier in a continuous review inventory system

We consider the inventory control problem of an independent supplier in a continuous review system. The supplier faces demand from a single customer who in turn faces Poisson demand and follows a continuous review (R, Q) policy. If no information about the inventory levels at the customer is available, reviews and ordering are usually carried out by the supplier only at points in time when a customer demand occurs. It is common to apply an installation stock reorder point policy. However, as the demand faced by the supplier is not Markovian, this policy can be improved by allowing placement of orders at any point in time. We develop a time delay policy for the supplier, wherein the supplier waits until time t after occurrence of the customer demand to place his next order. If the next customer demand occurs before this time delay, then the supplier places an order immediately. We develop an algorithm to determine the optimal time delay policy. We then evaluate the value of information about the customer’s inventory level. Our numerical study shows that if the supplier were to use the optimal time delay policy instead of the installation stock policy then the value of the customer’s inventory information is not very significant.     

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.     

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.     

A supply chain under limited-time promotion: The effect of customer sensitivity

We consider a two-echelon supply chain with a supplier and a retailer facing stochastic customer demands. The supplier is a leader who determines a wholesale price. In response, the retailer orders products and sets a price which affects customer demands. The goal of both players is to maximize their profits. We find the Stackelberg equilibrium and show that it is unique, not only when the supply chain is in a steady-state but also when it is in a transient state induced by a supplier’s promotion. There is a maximum length to the promotion, however, beyond which the equilibrium ceases to exist. Moreover, if customer sensitivity increases, then the wholesale equilibrium price decreases, product orders increase and product prices drop. This effect, well-observed in real life, does not, however, necessarily imply that the promotion is always beneficial. Conditions for the profitability of a limited-time promotion are shown and analyzed numerically. We discuss both open-loop and feedback policies and derive the conditions necessary for them to remain optimal under stochastic demand fluctuations.     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

Trends in transportation and logistics

Problems in transportation and logistics had to be tackled long before computers and Operational Research (OR) became available to support decision making. After the first optimization models were developed, OR has substantially contributed in making transportation systems efficient and companies with complex transportation and logistics problems competitive. Over the years, technology has evolved and the same has done OR. In this paper, the history of problems and OR contributions in transportation and logistics will be shortly reviewed together with the evolution of technology. Then, the future trends in this area will be discussed together with potential OR contributions.     

Integrated inventory management and supplier base reduction in a supply chain with multiple uncertainties

This paper considers a manufacturing supply chain with multiple suppliers in the presence of multiple uncertainties such as uncertain material supplies, stochastic production times, and random customer demands. The system is subject to supply and production capacity constraints. We formulate the integrated inventory management policy for raw material procurement and production control using the stochastic dynamic programming approach. We then investigate the supplier base reduction strategies and the supplier differentiation issue under the integrated inventory management policy. The qualitative relationships between the supplier base size, the supplier capabilities and the total expected cost are established. Insights into differentiating the procurement decisions to different suppliers are provided. The model further enables us to quantitatively achieve the trade-off between the supplier base reduction and the supplier capability improvement, and quantify the supplier differentiation in terms of procurement decisions. Numerical examples are given to illustrate the results.     

Mean–variance analysis of a single supplier and retailer supply chain under a returns policy

In the literature, most of the supply chain coordinating policies target at improving the supply chain’s efficiency in terms of expected cost reduction or expected profit improvement. However, optimizing the expected performance alone cannot guarantee that the realized performance measure will fall within a small neighborhood of its expected value when the corresponding variance is high. Moreover, it ignores the risk aversion of supply chain members which may affect the achievability of channel coordination. As a result, we carry out in this paper a mean–variance (MV) analysis of supply chains under a returns policy. We first propose an MV formulation for a single supplier single retailer supply chain with a newsvendor type of product. The objective of each supply chain decision maker is to maximize the expected profit such that the standard deviation of profit is under the decision maker’s control. We study both the cases with centralized and decentralized supply chains. We illustrate how a returns policy can be applied for managing the supply chains to address the issues such as channel coordination and risk control. Extensive numerical studies are conducted and managerial findings are proposed.     

A serial inventory system with supplier selection and order quantity allocation

Given the prevalence of both supplier selection and inventory control problems in supply chain management, this article addresses these problems simultaneously by developing a mathematical model for a serial system. This model determines an optimal inventory policy that coordinates the transfer of items between consecutive stages of the system while properly allocating orders to selected suppliers in stage 1. In addition, a lower bound on the minimum total cost per time unit is obtained and a 98% effective power-of-two (POT) inventory policy is derived for the system under consideration. This POT algorithm is advantageous since it is simple to compute and yields near optimal solutions.     

The impact of cost uncertainty on the location of a distribution center

The location of a distribution center (DC) is a key consideration for the design of supply chain networks. When deciding on it, firms usually allow for transportation costs, but not supplier prices. We consider simultaneously the location of a DC and the choice of suppliers offering different, possibly random, prices for a single product. A buying firm attempts to minimize the sum of the price charged by a chosen supplier, and inbound and outbound transportation costs. No costs are incurred for switching suppliers. We first derive a closed-form optimal location for the case of a demand-populated unit line between two suppliers offering deterministic prices. We then let one of the two suppliers offer a random price. If the price follows a symmetric and unimodal distribution, the optimal location is closer to the supplier with a lower mean price. We also show the dominance of high variability: the buyer can decrease the total cost more for higher price variability for any location. The dominance result holds for normal, uniform, and gamma distributions. We propose an extended model with more than two suppliers on a plane and show that the dominance result still holds. From numerical examples for a line and a plane, we observe that an optimal location gets closer to the center of gravity of demands as the variability of any supplier’s price increases.     

Modeling and analysis of an auction-based logistics market

We consider a logistics spot market where the transportation orders from a number of firms are matched with two types of carriers through a reverse auction. In the spot market, local carriers compete with in-transit carriers that have lower costs. In order to analyze the effects of implementing a logistics spot market on these three parties: firms, local carriers, and in-transit carriers and also the effects of various system parameters, we develop a two-stage stochastic model. We first model the auction in a static setting and determine the expected auction price based on the number of carriers engaging in the auction and their cost distributions. We then develop a continuous-time Markov chain model to evaluate the performance of the system in a dynamic setting with random arrivals and possible abandonment of orders and carriers. By combining these two models, we evaluate the performance measures such as the expected auction price, price paid to the carriers, distribution of orders between local and in-transit carriers, and expected number of carriers and orders waiting at the logistics center in the long run. We present analytical and computational results related to the performance of the system and discuss operation of such a logistics spot market in Turkey.     

Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty

In this paper, a mixed integer linear programming (MILP) formulation is developed for the design and planning of supply chains with reverse flows while considering simultaneously production, distribution and reverse logistics activities. It is also considered products’ demand uncertainty using a scenario tree approach. As main goal the model defines the maximization of the expected net present value and the results provide details on sizing and location of plants, warehouses and retailers, definition of processes to install, establishment of forward and reverse flows and inventory levels to attain. The model is applied to a representative European supply chain case study and its applicability is demonstrated.