Modeling a stochastic multi-objective supplier quota allocation problem with price-dependent ordering

One of the interesting subjects in supply chain management is supply management, which generally relates to the activities regarding suppliers such as empowerment, evaluation, partnerships and so on. A major objective of supplier evaluation involves buyers determining the optimal quota allocated to each supplier when placing an order. In this paper, we propose a multi-objective model in which purchasing cost, rejected units, and late delivered units are minimized, while the obtained total score from the supplier evaluation process is maximized. We assume that the buyer obtains multiple products from a number of predetermined suppliers. The buyer faces a stochastic demand with a probability distribution of Poisson regarding each product type. A major assumption is that the supplier prices are linearly dependent on the order size of each product. Since demand is stochastic, the buyer may incur holding and stockout costs in addition to the regular purchasing cost. We use the well-known L-1 metric method to solve the supplier evaluation problem by utilizing two meta-heuristic algorithms to solve the corresponding mathematical problems.     

Evaluating and selecting the supplier in detergent production industry using hierarchical fuzzy TOPSIS

Supply chain management has increasingly attracted attention as a systematic approach to integrate the supply chain in order to planning and controlling the materials and information from suppliers to customers. One of the most important issues in supply chain management is selection of the appropriate supplier which has significant effect on purchasing cost decrease and increase in the organization’s competition ability. Selection of the best supplier is naturally complex with no definite structure, and dependent on the type of suppliers’ activity. In the process of decision making about suppliers and many qualitative and quantitative performance indicators such as quality, price, flexibility, and due date should be considered. Then, the supplier selection problem is a multi-criteria decision making problem where numerous methods have been proposed to solve this problem so far. In the current paper, four suppliers of imported raw material “Tripolyphosphate (TPP)” (primary material to produce the detergent powder with a case study in Iran) are evaluated based on 25 effective criteria using the hierarchical fuzzy TOPSIS (HFTOPSIS) approach.     

“Optimization of aircraft maintenance/support infrastructure using genetic algorithms—level of repair analysis”

Level of repair analysis (LORA) is an approach used during the design stage of complex equipment for analysis of the cost effectiveness of competing maintenance strategies. LORA is carried as a part of the life cycle cost and cost of ownership analysis and plays a significant role in minimizing the life cycle cost and cost of ownership of the capital equipment. Since many purchasing decisions of complex equipment are based on cost of ownership, it has become essential to carry out LORA to compete in the market. In this paper, we develop a mathematical model for LORA and propose a solution methodology based on genetic algorithms. The concept is illustrated using a hypothetical aircraft engine.     

Optimal purchasing policy in a two-component assembly system with different purchasing contracts for each component

This paper considers an assembly system where a firm produces a single product which is assembled using two types of components (component 1 and component 2). The components are provided by individual suppliers (supplier 1 and supplier 2). We assume that the firm makes different procurement contracts with supplier 1 and supplier 2. To supplier 1, the firm specifies the maximum inventory level of component 1 and makes a commitment to purchase the component as long as its inventory level is below this target level. To supplier 2, the firm has the option of purchasing or rejecting component 2 at each instant supplier 2 provides it. Formulating our model as a Markov decision problem, we identify a component 2 purchasing policy which maximizes the firm’s profits subject to the costs of rejecting component 1, holding component 2, and purchasing component 2. We also investigate how the changes in the sales price and cost parameters affect the optimal purchasing policy. Finally, we present numerical study for the optimal performance evaluation.This material is based upon work supported by the Korea Science and Engineering Foundation (KOSEF) through the Northeast Asia e-Logistics Research Center at University of Incheon.     

Determining sourcing strategies: a decision model based on activity and cost driver information

Determining sourcing strategies for different material groups provides a major challenge to most companies. There has been little research on the choice of the optimal number of different suppliers for a given product group and the determination of their market shares. In this paper we propose a mathematical programming model using activity based costing information to determine optimal order splitting among suppliers on the basis of the different costs associated with the purchasing decision. We argue that sourcing strategies should be based on the minimisation of the total cost of ownership resulting from external purchases. We demonstrate the model by a real life case regarding the procurement of ball bearings at Cockerill Sambre S.A., a Belgian multinational steel producer. This decision support system is currently used by the company. This case resulted in the decision by management to develop comprehensive, company wide purchasing software using our mathematical program based on the total cost of ownership concept.     

Profit oriented supply chain network optimization

This paper proposes a novel mixed integer linear programming model to solve a supply chain network design problem. The proposed model deals with major issues for supply chains; product quality and cost. These issues are usually solved separately, but in this paper, we investigate effects of product quality on supply chain design and transportation flow. A trade-off between raw material quality, its purchasing and reprocessing costs was considered. Assuming decision maker (DM) wishes to work with a supplier which serves a low quality raw material; this raw material should be in need of reprocessing. To avoid the reprocessing costs, a supplier which serves a high quality raw material should be chosen but at this time the DM has to face a high purchasing cost. A supply chain network which consists of multiple suppliers, manufacturers, distribution centers and retailers is tried to be designed to accomplish aforementioned above trade-offs. The paper examines and discusses the relationship between product quality and supply chain design and offers several managerial insights.     

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.     

Retailer��s optimal sourcing strategy by using one major supplier and one emergent supplier

Fast-changing market demand, short product life cycle, and unpredictable events have been enforcing companies in a supply chain to respond to customers’ needs as quickly as possible. While many firms are still seeking a better inventory management within the general business environment, this paper develops an ordering decision support model within a business environment with more unpredictable events. To reduce the uncertainty, a retailer adopts a double sourcing policy with one major supplier and one emergent supplier. Through a two-period dynamic programming model formulation and the simulations based on design of experiments, we analyzed the effects of factors such as penalty cost, backup ratio, purchasing cost ratio, and demand correlation coefficient on retailer’s ordering policy and expected profit. Detailed sensitivity analysis is further conducted based on combinations of penalty cost and backup ratio. Results show that the use of an emergent supplier help increase the retailer’s expected profits. It not only increases the retailer’s upstream sourcing flexibility, but also increases the retailer’s service level with a lower inventory level. As penalty cost or backup ratio increases, the contribution of emergent supplier increases.     

Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain

This paper investigates the economic order quantity (EOQ) — based inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation in the fuzzy sense. It is assumed that the retailer maintains a powerful position and can obtain the full trade credit offered by the supplier yet the retailer just offers a partial trade credit to customers. The demand rate, holding cost, ordering cost, purchasing cost and selling price are taken as fuzzy numbers. Under these conditions, the retailer can obtain the most benefits. Study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem in the fuzzy sense. The annual total variable cost for the retailer in fuzzy sense is defuzzified using Graded Mean Integration Representation method. Then the present study shows that the defuzzified annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. Numerical examples are given to illustrate the theorems and the algorithms. Finally, the results in this paper generalize some already published results in the crisp sense.     

Impact of product pricing and timing of investment decisions on supply chain co-opetition

In supply chain co-opetition, firms simultaneously compete and co-operate in order to maximize their profits. We consider the nature of co-opetition between two firms: The product supplier invests in the technology to improve quality, and the purchasing firm (buyer) invests in selling effort to develop the market for the product before uncertainty in demand is resolved. We consider three different decision making structures and discuss the optimal configuration from each firm’s perspective. In case 1, the supplier invests in product quality and sets the wholesale price for the product. The buyer then exerts selling effort to develop the market and following demand potential realization, sets the resale price. In case 2, the supplier invests in product quality followed by the buyer’s investment in selling effort. Then, after demand potential is observed, the supplier sets the wholesale price and the buyer sets the resale price. Finally, in case 3, both firms simultaneously invest in product quality and selling effort, respectively. Subsequently, observing the demand potential, the supplier sets the wholesale price and the buyer sets the resale price. We compare all configuration options from both the perspective of the supplier and the buyer, and show that the level of investment by the firms depends on the nature of competition between them and the level of uncertainty in demand. Our analysis reveals that although configuration 1 results in the highest profits for the integrated channel, there is no clear dominating preference on system configuration from the perspective of both parties. The incentives of the co-opetition partners and the investment levels are mainly governed by the cost structure and the level of uncertainty in demand. We examine and discuss the relation between system parameters and the incentives in desiging the supply contract structure.     

Web based casting supplier evaluation using analytical hierarchy process

Manufacturing companies are increasingly dependent on outsourcing to improve their competitive position. At the same time, the approach to supplier selection has dramatically changed from being price-driven to one based on overall capability of the supplier, very much in evidence in the automobile castings sector facing the challenge of mass customization. In this study, 18 criteria have been identified for casting supplier assessment and segregated in four groups—product development capability, manufacturing capability, quality capability, and cost and delivery. A systematic approach to evaluating casting quality suppliers has been developed using the analytical hierarchy process, which enables the combination of tangible and intangible criteria and checking the consistency of decision-making. The approach has been implemented in a prototype web-based system.     

Supply chain coordination in quality improvement with reference effects

With increasing public attention on product quality, supply chain quality management has been the focus of considerable research attention in recent years. However, only a few published articles have considered reference effects in supply chain quality management. In practice, reference effects influence consumer purchasing behaviours. Therefore, we have developed a dynamic model that incorporates the effects of the reference quality and reference price on the demand function of a ‘single-supplier single-manufacturer’ supply chain system. In our model, the demand function is assumed to be influenced by the reference price and reference quality. The reference price formation is assumed to be affected by the gap between quality and the reference quality. By utilizing differential game theory, we calculate and compare the open-loop equilibrium quality levels in two different scenarios: (i) Each channel member makes decisions within a subsidy programme and (ii) the supplier vertically integrates with the manufacturer. In addition, a total cost-sharing contract based on quality improvement efforts is proposed and proven to be effective in the supply chain system that is under consideration.     

Supplier selection and order allocation problem using a two-phase fuzzy multi-objective linear programming

The aim of this paper is to solve a supplier selection problem under multi-price level and multi-product using interactive two-phase fuzzy multi-objective linear programming (FMOLP) model. The proposed model attempts to simultaneously minimize total purchasing and ordering costs, a number of defective units, and late delivered units ordered from suppliers. The piecewise linear membership functions are applied to represent the decision maker’s fuzzy goals for the supplier selection and order allocation problem, and can be resulted in more flexibility via an interactive decision-making process. To demonstrate effectiveness of the proposed model, results of applying the proposed model are shown by a numerical example. The analytical results show that the proposed approach is effective in uncertain environments and provide a reliable decision tool for integrated multi-objective supplier selection problems.     

Contracting with an urgent supplier under cost information asymmetry

We investigate a contract setting problem faced by a manufacturer who can procure major modules from an overseas supplier, as well as a local supplier. The overseas supplier is prime and offers quality products, whereas the local supplier is viewed only as a backup, and its products are inferior in quality. As the local supplier needs to put in additional effort to fulfill the urgent orders, it is difficult for the manufacturer to estimate this urgent supplier’s production cost. This asymmetric cost information becomes an obstacle for the manufacturer in managing the urgent supplier. In this paper, we study two types of contingent contracts. One is the common price-only contract, and the other is a contract menu consisting of a transfer payment and a lead time quotation. We construct a Stackelberg game model and evaluate how the involvement of an urgent supplier with private cost information affects performances of the prime supplier and the manufacturer in different scenarios (with or without the urgent supplier, under different contingent contracts). We also conduct numerical experiments to show how the parameters of the contracts affect profits of the manufacturer.     

A dynamic inventory model with supplier selection in a serial supply chain structure

Considering the inherent connection between supplier selection and inventory management in supply chain networks, this article presents a multi-period inventory lot-sizing model for a single product in a serial supply chain, where raw materials are purchased from multiple suppliers at the first stage and external demand occurs at the last stage. The demand is known and may change from period to period. The stages of this production–distribution serial structure correspond to inventory locations. The first two stages stand for storage areas for raw materials and finished products in a manufacturing facility, and the remaining stages symbolize distribution centers or warehouses that take the product closer to customers. The problem is modeled as a time-expanded transshipment network, which is defined by the nodes and arcs that can be reached by feasible material flows. A mixed integer nonlinear programming model is developed to determine an optimal inventory policy that coordinates the transfer of materials between consecutive stages of the supply chain from period to period while properly placing purchasing orders to selected suppliers and satisfying customer demand on time. The proposed model minimizes the total variable cost, including purchasing, production, inventory, and transportation costs. The model can be linearized for certain types of cost structures. In addition, two continuous and concave approximations of the transportation cost function are provided to simplify the model and reduce its computational time.     

Effect of coordinated replenishment policies on quality

Coordinated replenishment is a supply chain policy that affects many operational performance measures, including cost, lead time, and quality. In this paper, we develop a mathematical model of a simplified supply chain in which conformance quality is one of the supplier's decision variables and both the supplier and its customer are trying to minimize expected annual cost. Our expected cost model includes the important quality costs (appraisal, prevention, internal failure, and external failure) as well as holding, set-up, and ordering costs. Our results indicate that coordination leads to a decline in total cost but that coordination does not necessarily lead to an improvement in quality. In other words, buyers who are using coordinated replenishment may be trading higher quality for lower cost.     

On an EPQ model for deteriorating items under permissible delay in payments

This paper derives a production model for the lot-size inventory system with finite production rate, taking into consideration the effect of decay and the condition of permissible delay in payments, in which the restrictive assumption of a permissible delay is relaxed to that at the end of the credit period, the retailer will make a partial payment on total purchasing cost to the supplier and pay off the remaining balance by loan from the bank. At first, this paper shows that there exists a unique optimal cycle time to minimize the total variable cost per unit time. Then, a theorem is developed to determine the optimal ordering policies and bounds for the optimal cycle time are provided to develop an algorithm. Numerical examples reveal that our optimization procedure is very accurate and rapid. Finally, it is shown that the model developed by Huang [1] can be treated as a special case of this paper.     

Supplier Performance and Order Allocation

A supplier's overall performance can be gauged by his unit price and adherence to quality standards and delivery schedules. The cost of substandard quality and non-adherence to delivery schedule is computed and added to the cost of purchase. A set of order quantity and supplier combination is chosen dynamically and the total cost computed to determine the best choice (least total cost).     

The use of total cost of ownership for strategic procurement: a company-wide management information system

We present a general company-wide management information system for defining procurement strategies. We believe that existing practices for determining purchasing strategies can be improved and a new approach developed. The system uses total cost of ownership information. We argue that mathematical programming models should be used for exploiting this information, when evaluating the firm's strategic procurement options. As an example, we show how we have successfully applied our approach to develop a decision support system at Usinor, a European multinational steel company.     

Analytic network process in supplier selection: A case study in an electronic firm

Supplier selection, which is the first step of the activities in the product realization process starting from the purchasing of material till to the end of delivering the products, is evaluated as a critical factor for the companies desiring to be successful in nowadays competition conditions. With the scope of this paper, supplier selection was considered as a multi criteria decision problem. A model aiming the usage of analytic network process (ANP) in supplier selection is developed owning to the evaluation of the relations between supplier selection criterias in a feedback systematic. The proposed model is implemented in a company of electronic.