Order Allocation Problem Research Articles

Single Item Supplier Selection and Order Allocation Problem with a Quantity Discount and Transportation Costs

In this paper, we address a single item supplier selection, economic lot-sizing, and order assignment problem under quantity discount environment and transportation costs. A mixed-integer nonlinear program (MINP) model is developed with minimization of cost as its objective, while lead-time, the capacity of the supplier and demand of the product are incorporated as constraints. The total cost considered includes annual inventory holding cost, ordering cost, transportation cost and purchase cost. An efficient and effective genetic algorithm (GA) with problem-specific operators is developed and used to solve the proposed MINP model. The model is illustrated through a numerical example and the results show that the GA can solve the model in less than a minute. Moreover, the results of the numerical illustration show that the item cost and transportation cost are the deciding factors in selecting suppliers and allocating orders.
 Keywords: Supplier selection, Economic Order Quantity, Order allocation, Mixed-integer nonlinear programming.

The multi-objective supplier selection problem with fuzzy parameters and solving the order allocation problem with coverage

PurposeThis study aims to deal with supplier selection problem. The supplier selection problem has significantly become attractive to researchers and practitioners in recent years. Many real-world supply chain problems are assumed as multiple objectives combinatorial optimization problems.Design/methodology/approachIn this paper, the authors propose a multi-objective model with fuzzy parameters to select suppliers and allocate orders considering multiple periods, multiple resources, multiple products and two-echelon supply chain. The objective functions consist of total purchase costs, transportation, order and on-time delivery, coverage and the weights of suppliers. Distance-based partial and general coverage of suppliers makes the number of orders of products more realistic. In this model, the weights of suppliers are determined by fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method, as a multi-criteria decision analysis method, in the objective function. Also, the authors consider the parameters related to delays as triangular fuzzy numbers.FindingsA small-sized numerical example is provided to clearly show the proposed model. The exact epsilon constraint method is used to solve this given multi-objective combinatorial optimization problem. Subsequently, the sensitivity analysis is conducted to testify the proposed model. The obtained results demonstrate the validity of the proposed multiple objectives mixed integer mathematical programming model and the efficiency of the solution approach.Originality/valueIn real-life situations, supplier selection parameters are uncertain and incomplete. Hence, the fuzzy set theory is used to tackle uncertainty. In this paper, a multi-objective supplier selection problem is formulated taking into consideration the coverage of suppliers and suppliers’ weights. Integrating coverage of suppliers to select and allocate the order to them can be mentioned as the main contribution of this study. The proposed model considers the delay from suppliers as fuzzy parameters.

Integrated model for Multi-criteria Supplier Selection and Order Allocation Problem

This paper discusses an integrated model of selecting suppliers and order allocation for a company that wishes to decide the quantity to be ordered from each supplier on the basis of some qualitative criteria. Since each supplier may have a different performance with respect to these criteria, an integration of analytical hierarchy process and linear program model is proposed to solve the problem in two stages. In the first stage, suppliers are evaluated based on qualitative criteria to consider both tangible and intangible factors in choosing the best suppliers. The output of this stage is the final score of each supplier. In the second stage, a linear programming model is proposed to placing the optimum order quantities among them such that the total final scores of suppliers become maximum. The mathematical programming model is validated through numerical analysis, and the computation result shows that the model is effective and applicable.

Design of Modern Supply Chain Networks Using Fuzzy Bargaining Game and Data Envelopment Analysis

This article proposes a novel methodology for multistage, multiproduct, multi-item, and closed-loop Supply Chain Network (SCN) design under uncertainty. The method considers that multiple products are manufactured by the SCN, each composed by multiple items, and that some of the sold products may require repair, refurbishing, or remanufacturing activities. We solve the two main decisions that take place in the medium-/short-term planning horizon, namely partners’ selection and allocation of the received orders among them. The partners’ selection problem is solved by a cross-efficiency fuzzy Data Envelopment Analysis technique, which allows evaluating the efficiency of each SCN member and ranking them against multiple conflicting objectives under uncertain data on their performance. Then, according to the estimated customers’ demand, the order allocation problem is solved by a fuzzy bargaining game problem, where each SCN actor behaves to simultaneously maximize both its own profit and the service level of the overall SCN in terms of efficiency, costs, and lead time. An illustrative example from the literature is finally presented. Note to Practitioners —We present a decision tool to address the optimal design, performance evaluation, and continuous improvement of modern cooperative SCNs. We propose an effective method to jointly solve the members’ selection and the orders’ allocation, considering the complex structure of modern SCNs, the multiobjective nature of the problems, and the uncertainty characterizing economic markets. Competition within SCNs stages and cooperation along the chain are considered, with the aim to improve both financial and environmental sustainability, while ensuring the highest service levels to customers.

Sustainable supplier selection and order allocation: Distributionally robust goal programming model and tractable approximation

A challenge of planning real-life sustainable supplier selection and order allocation (SS/OA) problems for purchasing companies is to gather the extensive data and exact distributions of input data. Motivated by this challenge, this paper addresses imprecise probability distributions of uncertain per unit cost, CO2 emissions, demand, supply capacity and the minimum order quality and characterizes these distribution uncertainty by ambiguity sets including the true distributions. Moreover, the purchasing company decisions to be optimized simultaneously include four conflicting objectives regarding cost, CO2 emissions, society and suppliers’ comprehensive value while considering risk measures incurred by cost and CO2 emissions to achieve company sustainability. To help decision makers formulate practicable policy, a novel distributionally robust sustainable SS/OA goal programming model is developed with expected constraints and joint chance constraints. The proposed optimization model can balance multiple conflicting objectives, and effectively solve our sustainable SS/OA problem. More importantly, we structure ambiguous distributions sets, and thus derive the computationally tractable approximation form of the proposed practical model. Finally, we illustrate our optimization method through a case study about a steel company, conduct a thorough inquiry into the effect of uncertainty and summarize the management implications of the results.

Supplier selection and order allocation problem through option contracts under supply disruption risks

Selecting well-performed suppliers and ordering at the right time are the keys to success. Many types of unpredictable disasters such as breakdowns, labour strikes, and natural calamities have occurred, which are essential elements, resulting in supply disruption risk. This paper presents a supplier selection model and order allocation to minimise costs incurred in multi-product supply chains under disruption risks at supplier sites or groups of suppliers in the same situation under cap-and-trade regulation. In order to reduce disruption risk, options contracts are applied to hedge against adverse effects of supplier disruptions. Numerical instances exemplify the proposed method. The results indicate that option contracts reduce costs significantly and, even at a very high initial cost, are still cost-effective. The results of sensitivity analyses also show carbon emissions levels can have a significant impact on the income and behaviour of decision makers.

Supplier selection and order allocation problem through option contracts under supply disruption risks

Selecting well-performed suppliers and ordering at the right time are the keys to success. Many types of unpredictable disasters such as breakdowns, labour strikes, and natural calamities have occurred, which are essential elements, resulting in supply disruption risk. This paper presents a supplier selection model and order allocation to minimise costs incurred in multi-product supply chains under disruption risks at supplier sites or groups of suppliers in the same situation under cap-and-trade regulation. In order to reduce disruption risk, options contracts are applied to hedge against adverse effects of supplier disruptions. Numerical instances exemplify the proposed method. The results indicate that option contracts reduce costs significantly and, even at a very high initial cost, are still cost-effective. The results of sensitivity analyses also show carbon emissions levels can have a significant impact on the income and behaviour of decision makers.

Development and implementation of an autonomous control system for target-optimised use of intralogistics transport systems in the Learning Factory Werk 150 at Reutlingen University

Rapidly changing market conditions and global competition are leading to an increasing complexity of logistics systems and require innovative approaches with respect to the organisation and control of these systems. In scientific research, concepts of autonomously controlled logistics systems show a promising approach to meet the increasing requirements for flexible and efficient order processing. In this context, this work aims to introduce a system that is able to adjust order processing dynamically, and optimise intralogistics transportation regarding various generic intralogistics target criteria. The logistics system under consideration consists of various means of transport for autonomous decision-making and fulfilment of transport orders with defined source-sink relationships. The context of this work is set by introducing the Learning Factory Werk 150 with its existing hardware and software infrastructure and its defined target figures to measure the performance of the system. Specifically, the important target figures cost and performance are considered for the transportation system. The core idea of the system’s logic is to solve the problem of order allocation to specific means of transport by linking a Genetic Algorithm with a Multi-Agent System. The implementation of the developed system is described in an application scenario at the learning factory.

Multiobjective Sustainable Order Allocation Problem Optimization with Improved Genetic Algorithm Using Priority Encoding

Recently, incorporating carbon emissions into order allocation decisions has attracted considerable attention among scholars and industrialists. Moreover, affected by the random fluctuations of the man, machine, material, method, and environment (4M1E), the production process is usually imperfect with defective products. Reducing product defective rates can effectively improve the quality of the order allocation process. Therefore, considering product defective rate and carbon emission, a multiobjective integer nonlinear programming (INLP) formulation is presented to address this multiproduct, multiperiod, and multi-OEM order allocation problem. Furthermore, exploring the existing literatures, an improved genetic algorithm using priority encoding (IGAUPE) is put forward as a novel optimization technique. Finally, numerical experiments are conducted to validate the correctness of the proposed INLP model as well as the effectiveness of the proposed algorithm. Compared with the genetic algorithm using binary encoding (GAUBE), genetic algorithm using two-layer encoding (GAUTE), and LINGO software, the experiment results show that IGAUPE can improve the efficiency and effectiveness within the predetermined time limit when solving large-scale instances.

A systematic review on supplier selection and order allocation problems

The supplier selection and order allocation are two key strategic decisions in purchasing problem. The review presented in this paper focuses on the supplier selection problems (SSP) and order allocation from year 2000 to 2017 in which a new structure and classification of the existing research streams and the different MCDM methods and mathematical models used for SSP will be presented. The review was examined in three aspects: the summaries of the existing evidence concerning the problems, the identification of gaps in the current research to help determine where further investigation might be needed and positioning new research activities.

Research on order allocation of single-cycle multi-type logistics service

Based on the logistics service supply chain, there are many fuzzy factors in the real market competition environment, and the relationship between them is complicated, in order to make the research more in line with the actual situation. In this paper, the supply capacity of logistics service providers and the demand for logistics service capacity are set as fuzzy variables, and the problem of order allocation of logistics service supply chain under fuzzy environment is studied. Firstly, the problem is described, and the multi-objective logistics service order allocation model with fuzzy parameters is established. Secondly, the credibility theory is used to fuzzed. Finally, the feasibility of the calculation model is verified by a specific example, and the logistics service integrator is used. The order allocation decision provides a theoretical basis.

A weight-consistent model for fuzzy supplier selection and order allocation problem

Decision support for Supplier Selection and Order Allocation (SSOA) is an important application area of multiple criteria decision making (MCDM) problems. In Amid et al. (Int J Prod Econ 131(1):139–145, 2011) proposed and developed a weighted maximin model to ensure the weight-consistent solution for SSOA in an MCDM problem under an uncertain environment. Essentially, this model is based on a weight-consistent constraint and a maximin aggregation operator. This paper reanalyzes the weighted maximin model in terms of the weight-consistent constraint, and then proposes a general weight-consistent model for SSOA in MCDM problems under uncertainty. In this paper, two existing models are reviewed and compared with the proposed model. Three datasets with different ranges of fuzzy demand and full factorial patterns of criteria weights are used to test the performances of the related models. The results showed that the proposed model always generates a weight-consistent Pareto-optimal solution in all cases, while the other existing models do not.

Integrated order allocation and order routing problem for e-order fulfillment

In this article, we study the order fulfillment problem, which integrates order allocation and order routing decisions of an online retailer. Our problem is to find the best way to fulfill each customer’s order to minimize the transportation cost. We first present a mixed-integer programming formulation to help online retailers optimally fulfill customers’ order. We then introduce an adaptive large neighborhood search-based approach for this problem. With extensive computational experiments, we demonstrate the effectiveness of the proposed approach, by benchmarking its performance against a leading commercial solver and a greedy heuristic. Our approach can produce high-quality solutions in short computing times. We also experimentally show that products overlap among different fulfillment centers does affect the operation expense of e-tailers.

Supplier Selection and Order Allocation Problem Modeling with the Aim of Comparing Incremental Discounts Versus Wholesale Discounts by Using GA and NSGA Algorithms

Supplier Selection and Order Allocation Problem Modeling with the Aim of Comparing Incremental Discounts Versus Wholesale Discounts by Using GA and NSGA Algorithms

G-NETWORKS AND THE OPTIMIZATION OF SUPPLY CHAINS

Supply chains are fundamental to the economy of the world and many supply chains focus on perishable items, such as food, or even clothing that is subject to a limited shelf life due to fashion and seasonable effects. G-networks have not been previously applied to this important area. Thus in this paper, we apply G-networks to supply chain systems and investigate an optimal order allocation problem for a N-node supply chain with perishable products that share the same order source of fresh products. The objective is to find an optimal order allocation strategy to minimize the purchase price per object from the perspective of the customers. An analytical solution based on G-networks with batch removal, together with optimization methods are shown to produce the desired results. The results are illustrated by a numerical example with realistic parameters.

Resilient supplier selection and optimal order allocation under disruption risks

Resilient supplier selection is a key strategic decision in the context of the supply chain (SC) disruption management. We offer an efficient solution to the resilient supplier selection and optimal order allocation problem. We first show how to compute the likelihood of disruption scenarios for the supplier selection problem using a probabilistic graphical model. That model can capture (i) a large number of disruptive events with no computational burden, and (ii) the dependencies among disruptive events and their impacts on supplier performance, i.e., the ripple effect. We then propose a stochastic bi-objective mixed integer programming model to support the decision-making in how and when to use both proactive and reactive strategies in supplier selection and order allocation. The outcomes of this research, if utilized properly, can benefit suppliers to find the optimal set of operational decisions (e.g., the optimal level of surplus capacity and restorative capacity) that enhance their resilience capabilities. Finally, the proposed model can be utilized as a decision support tool to assist manufacturers in performance assessment of supplier alternatives when costs and resilience are considered simultaneously, which helps to build up both efficient and resilient SC (i.e., to achieve the SC resilience) to ensure the operations continuity. These outcomes can help SC managers organize their disruption risk mitigation efforts with balancing the efficiency and resilience while focusing on critical suppliers and order (re)-allocation that will have a more significant impact on the performance of the SC when disrupted.

A hybrid MCDM-FMOO approach for sustainable supplier selection and order allocation

The growing interest in sustainability increases the challenges for decision makers in selecting the sustainable suppliers in which consider economic, environmental and social aspects. Particularly, decision makers are being increasingly motivated to improve their supply chain activities in coping efficiently with the objectives of sustainable development. Where the era of sustainability threatens the current supply chain partners to either cope with the new regulations of sustainability or leave the field for new players. Notwithstanding, most of the recent studies considered economic and green criteria in handling sustainable supplier selection and order allocation (SSS/OA) problems overlooking the social criteria which represents the third pillar of sustainability. This work aims at putting forward a hybrid Multi Criteria Decision-Making (MCDM)-Fuzzy Multi-Objective Optimization (FMOO) approach for a sustainable supplier selection and order allocation problem by considering economic, environmental and social criteria. Thus, an integrated Fuzzy AHP-Fuzzy TOPSIS is proposed to assess and rank suppliers according to three sets of criteria (i.e. conventional, green and social). A Multi-Objective Optimization Model (MOOM) is developed for choosing suppliers and allocating the optimal order quantities. To cope with the multiple uncertainties in the input data, the MOOM is reformulated into a Fuzzy Multi-Objective Optimization Model. The ε-constraint and LP-metrics approaches are used to reveal two sets of Pareto solutions based on the developed FMOOmodel. Finally, TOPSIS is applied to select the final Pareto solution that is closest to the ideal solution and furthest from the nadir solution. The effectiveness and the applicability of the developed hybrid MCDM-FMOO approach is demonstrated through a case study.

Sustainability in supplier selection and order allocation: Combining integer variables with Markowitz portfolio theory

This research presents a decision support methodology for the multi-criteria supplier selection and order allocation problem. The proposed approach supports purchasing managers in assembling mid-term supplier portfolios while making them aware of the trade-offs between the supplier sustainability, the purchasing costs, and the overall supply risk. First, we propose a multi-objective optimization model with three objectives: to maximize the supplier sustainability, to select the supplier portfolio with the lowest purchasing costs, and to minimize the supply risk. Our model extends existing mathematical approaches that follow the portfolio theory fathered by H. Markowitz by integrating the aspect ‘risk’ into the supplier selection problem. Secondly, since we allow for integer variables in our model—in contrast to the classical Markowitz portfolio theory—we use the ε-constraint method to visualize the efficient surface. The possibility of considering the non-dominated set of supplier portfolios is advantageous for purchasing managers as they gain a picture of the different optimal supplier portfolios and are able to analyze the trade-offs between the different purchasing goals before making a decision. Finally, we illustrate the applicability of the proposed methodology in a real-world supplier selection and order allocation case from the automotive industry. In the example case, we identify 1754 optimal supplier portfolios that may be assembled based on the eight available suppliers. Our analyses show that each optimal portfolio consists of two suppliers, with one specific supplier being included in each portfolio. Furthermore, four suppliers are not part of any optimal solution.

A resilient supply portfolio considering political and disruption risks

The need of accounting for resilience in global supply chains has been growing from practical and academic points of view. However, there is still the need for developing quantitative decision support models on this issue. In the present work, we propose a novel multi-objective mixed possibilistic, two-stage scenario-based stochastic programming model to handle supplier selection and order allocation problem in a global supply chain under operational and disruption risks. The model minimises cost and political risk, while, maximising resilience of the supply portfolio. Various risk mitigation approaches including: contracting with backup suppliers, fortification of suppliers and procurement of emergency inventory, are considered in the model. In addition, the proposed model determines recovery plans. Reservation level driven Tchebycheff procedure is incorporated in the solution procedure to find Pareto-optimal solutions. The validation of the model via computational experiments demonstrates the applicability of the proposed model and solution method in building a resilient supply portfolio under consideration of operational and disruption risks.

A resilient supply portfolio considering political and disruption risks

The need of accounting for resilience in global supply chains has been growing from practical and academic points of view. However, there is still the need for developing quantitative decision support models on this issue. In the present work, we propose a novel multi-objective mixed possibilistic, two-stage scenario-based stochastic programming model to handle supplier selection and order allocation problem in a global supply chain under operational and disruption risks. The model minimises cost and political risk, while, maximising resilience of the supply portfolio. Various risk mitigation approaches including: contracting with backup suppliers, fortification of suppliers and procurement of emergency inventory, are considered in the model. In addition, the proposed model determines recovery plans. Reservation level driven Tchebycheff procedure is incorporated in the solution procedure to find Pareto-optimal solutions. The validation of the model via computational experiments demonstrates the applicability of the proposed model and solution method in building a resilient supply portfolio under consideration of operational and disruption risks.