Two-echelon Supply Chain Network Research Articles

Customer segmentation, pricing, and lead time decisions: A stochastic-user-equilibrium perspective

Multiple price/lead time options are often used as a competitive tool in supply chain operations when customers have heterogeneous price and lead time preferences. We study a two-echelon supply chain network consisting of manufacturers and retailers facing customers that differ in their price- and time-sensitivity. We examine how many price/lead time options should be provided by manufacturers and retailers under decentralized and centralized supply chain management with time-cost tradeoffs. We adopt a stochastic-user-equilibrium (SUE) approach in a supply chain network by incorporating discrete choice theory and using a multinomial logit-based variational inequality to express equilibrium conditions. This is one of the first papers to study time-cost tradeoffs in a supply chain network by introducing an SUE approach. One critical part of our analysis is the establishment of concavity of profit functions, which allows for analytical derivation of the equilibrium strategies. Another critical part of our analysis is the development of SUE conditions in decentralized and centralized supply chain networks. We demonstrate that the variance of heterogeneous customers’ time-sensitivity distribution plays a crucial role in customer segmentations in a time-cost tradeoff supply chain. We find that under SUE conditions, there exists a unique equilibrium in the decentralized and centralized supply chain networks, respectively. We conduct comparative statics analyze to demonstrate the effect of SUE and UE conditions and the influence of decentralized versus centralized supply chain management paradigms. We show how the SUE approach can be applied to supply chain network management with time-cost tradeoffs. Our approach can be extended to other tradeoff decision problems in supply chain network management, especially those in which customers are heterogeneous.

A gamified teaching–learning based optimization algorithm for a three-echelon supply chain scheduling problem in a two-stage assembly flow shop environment

The supply chain scheduling problem, which is an integrated production scheduling and distribution through the batch delivery system, has been studied by researchers for more than two decades. So far, all researches in this regard have studied the two-echelon supply chain network. The first novelty of this research is that, for the first time, the three-echelon supply chain scheduling problem, including supplier, manufacturer and customer, is investigated considering two separated batch delivery systems for transportation, simultaneously. To do so, a two-stage assembly flow shop environment is used. In the first stage, there are a number of decentralized suppliers who are responsible for manufacturing components. The components are dispatched to the second stage (assembly stage) with the first batch delivery system and after assembly, the orders are dispatched to the customer through secondary batch delivery system. The purpose of this problem is to minimize the cost of total completion time plus batch delivery costs. First, a mixed integer linear programming model (MILP) is presented that is able to solve small-size instances in a logical time. The second novelty of this research is that, to solve large-size instances, a novel gamified teaching–learning based optimization (GTLBO) algorithm is developed with applying a number of dominance rules and gamification tools. The computational results indicate the superiority of the new TLBO variant over its standard form and two well-known methods, i.e. GA and PSO, especially by applying the dominance rules.

A branch and efficiency algorithm to design a sustainable two-echelon supply chain network considering traffic congestion and uncertainty.

This work aims to design a sustainable two-echelon supply chain not only based on the widely used cost perspective, but also based on the efficient use and preservation of limited resources. For this purpose, a branch and efficiency (B&E) algorithm is developed, which includes an optimization model and an evaluation model. The proposed tri-objective optimization model simultaneously minimizes the total cost of the supply chain, maximizes the sustainability score, and minimizes inequity among customers. The solutions obtained from the optimization model are then evaluated by extended data envelopment analysis (EDEA) models based on common criteria (i.e., cost and service) and traffic congestion criterion. To take into account real-world conditions, parameters related to labor and demand are assumed under uncertainty. Since the presented models consist of more than one objective function, fuzzy goal programming (FGP) method is utilized to tread the multi-objectiveness. The obtained results from tackling a case study problem demonstrate that considering sustainability issues can positively affect both the economic and social aspects of the problem. Furthermore, the developed B&E algorithm is able to reduce costs in each iteration; this is what supply chain managers are interested in. On the other hand, this algorithm can provide more services to applicants compared to one of the competing algorithms.

Optimizing the sales level of perishable goods in a two-echelon green supply chain under uncertainty in manufacturing cost and price

ABSTRACT The present study addresses a green model of vendor managed inventory policy for perishable goods in a multi-period two-echelon supply chain network. Shortage is permissible and the unsatisfied demand is considered as back order. In addition, uncertainties in prices and manufacturing costs are considered as the main contribution of this study. Two objective functions are considered to optimize simultaneously. (a) Maximizing profits and (b) minimizing the amount of carbon emissions. This problem is formulated and the effects of uncertainty in key parameters are investigated using several decision trees. The result of the study shows the efficiency of the proposed procedure in dealing with uncertainties. Accordingly, increasing backorder costs lead to a decrease in order quantity and a decrease in profit value. However, this change reduces the emission of pollutants due to the reduced need for transport. In addition, profit levels increase and carbon emissions decrease as the product lifespan increases.

Competition and coordination for supply chain networks with random yields

We consider a two-echelon supply chain network where the downstream retailers procure products from the upstream unreliable suppliers to sell in the end market. In the decentralized setting, the suppliers consider whether to enter the market and simultaneously set their wholesale prices if they enter, and then the retailers make ordering decisions and engage in quantity-based Cournot competition in the end market where each retailer can sell exactly the products purchased from the supplier. We analyze the system as a Stackelberg game where the suppliers are the leaders and the retailers are the followers. For the case where the random yields of the suppliers are independent, we derive the unique equilibrium of the game in which the suppliers with higher reliability set higher wholesale prices and obtain more profits. We then coordinate the supply chain with the spanning revenue-sharing (SRS) contract and derive the conditions under which the SRS contract achieves the win-win outcome, i.e., all the members of the supply chain network sign a single revenue-sharing contract together. Then considering the case where the random yields are correlated, we show that some suppliers may not join the game in equilibrium even if all the suppliers have the same purchasing cost. Moreover, we show that a high correlation of supplier defaults dampens suppliers’ competition, which differs from the finding in the extant literature because we consider price-sensitive demand.

Two-echelon supply chain network design with trade credit

This study considers a two-echelon supply chain that is comprised of an outside vendor, multiple distribution centers (DCs), and multiple retailers. The retailers have access to trade credit offered by upstream suppliers. We propose an integrated DC-retailer network design model that optimizes trade credit terms and safety stock levels, in addition to the decisions of DC locations, DC-retailer assignments, and inventory replenishment policies typically considered in the literature. The operating and handling cost is concave and non-decreasing to capture economies of scale whereas most existing studies simply assume that such cost is linear in demand. Trade credit financing cost is characterized in a way that preserves the important mathematical structure of the classic warehouse retailer network design model. Leveraging on the submodularity property of the cost components, we developed a polymatroid cutting-plane solution algorithm, which is effective for practically sized problem instances in numerical experiments. The results show that incorporating trade credit financing into supply chain network design may substantially reduce the total cost. Further, our study suggests a more consolidated supply chain network when either the safety stock or financing cost increases. Interestingly, as financing cost rises, a high-volume and low-frequency reorder pattern is favored, but the opposite is recommended when financing gain increases. The variation of each individual cost component is also analyzed for an in-depth understanding of the impact of operational and financial parameters on supply chain optimization.

Metaheuristics for a bi-objective green vendor managed inventory problem in a two-echelon supply chain network

A bi-objective non-linear optimization model with the goal of maximizing the profit of inventory and minimizing the carbon emissions of transportation, simultaneously, is developed. Another contribution of this work is to propose three capable metaheuristics to solve it optimality in large-scale samples. In this regard, the Non-dominated Sorting Genetic Algorithm (NSGA-II) as a well-known method as well as Multi-Objective of Keshtel Algorithm (MOKA) and Multi-Objective of Red Deer Algorithm (MORDA) are firstly applied in this research area. The results of metaheuristics are checked by the e-constraint method in a set of small-scale samples as compared with the results of literature. Finally, the outputs confirm that the allowed shortage situation along with the lack of cost reduction shows a greater amount of shipping and orders. As such, the performance of MORDA is approved in comparison with MOKA and NSGA-II through different criteria.

Determination of the optimal sales level of perishable goods in a two-echelon supply chain network

In recent years, Supply Chain Management (SCM) has been the main focus in many industries in order to decrease costs and improve efficiencies. In today’s supply chains, sale determination for a product in a specific time period and for a specific customer is highly considered. The importance of this efficiency is increased when dealing with perishable products, such as blood, vaccine, foods, etc. These products not only have various customers, but they also must be used before perishing. This paper represents a model to determine the optimal sales level of perishable products in a two-echelon supply chain, using a Vendor Managed Inventory (VMI) policy. Based on the literature most studies have considered two-echelon supply chain for perishable products with one buyer. The proposed model is formulated based on one vendor and multiple buyers. Considering buyers’ requests in various periods, this model aims to optimize the sales profit by exact and meta-heuristics methods. Three efficient meta-heuristics including GA, PSO and CPSO are utilized to solve the problem and the results showed the good consistency with the results obtained from exact method. The obtained results show that applying VMI policy on two-echelon supply chain for perishable products is an effective approach to optimize the profitability of the proposed network.

A mixed-integer program and a Lagrangian-based decomposition algorithm for the supply chain network design with quantity discount and transportation modes

We study the design of a two-echelon supply chain network in the presence of suppliers’ all-unit quantity discount and transportation mode selection. The problem involves determining the best location for plants and the allocation of customers to open plants. The problem additionally entails making decisions for the order quantity from each supplier for each plant and accordingly selecting the best transportation mode that can accommodate these order quantities among echelons. The objective is to minimize the total cost associated with fixed opening and operating costs of plants, fixed and variable costs of transportation modes, and purchasing costs of raw materials. To characterize and solve this problem, we develop a mixed-integer programming (MIP) model. We demonstrate that the MIP model has a special mathematical structure that makes it amenable to decomposition techniques. We, therefore, exploit this decomposable structure and develop an effective Lagrangian-based decomposition for solving the MIP. Our Lagrangian Relaxation (LR) method relaxes the complicating constraints associated with commodity flow conservation among echelons in the MIP, yielding more tractable subproblems, one for each echelon. Solutions obtained from the relaxed problem may be infeasible, e.g., the demand for some of the customers may not be satisfied. We remedy these subproblems’ infeasibilities using novel feasibility algorithms and appropriate Lagrangian multipliers that penalize constraints’ violations in the subproblems, leading the algorithm towards global feasibility/optimality. We appraise the performance of the MIP model and the LR algorithm on instances of varying sizes. We show that the MIP model solved via CPLEX finds integer feasible solutions for 42% of large problem instances and its average optimality gap for these solved instances is 64.56%. The LR algorithm significantly improves the solvability and optimality gap of the MIP model and finds integer feasible solutions for 100% of problem instances and achieves an average optimality gap of 1.78%. We investigate the robustness of our algorithm by conducting sensitivity analyses on the model parameters. We demonstrate that the LR technique remains robust and tractable with respect to various parameters’ values.

Effects of Preservation Technology Investment on Waste Generation in a Two-Echelon Supply Chain Model

This study develops an integrated production-inventory model for a two-echelon supply chain network with controllable probabilistic deterioration. The investment in preservation technology is considered a decision variable to control the deteriorated quantity of an integrated system. The objective of the study is to optimize preservation investment, the number of shipments and shipment quantity, so that the total cost per unit of time of the supply chain is minimized. The study proposes a solution method, and the results show that investment in preservation technology reduces the total supply chain cost by 13%. Additionally, preservation increases the lot size, thus increasing the production cycle length, which reduces the ordering cost of the system. Furthermore, this study shows that preservation leads to a reduction of solid waste from deteriorated products. Total deteriorated products reduced to 8 units from 235 units, hence, preservation generates positive environmental benefits along with economic impacts. The robustness of the proposed model is illustrated with a numerical example, sensitivity analysis, and graphical representations. Moreover, comparative study and managerial insights are given to extract significant insights from the model.

Fuzzy multi-objective optimization for multi-site integrated production and distribution planning in two echelon supply chain

This paper addresses an integrated production and distribution planning problem for a two-echelon supply chain network comprising of multiple manufacturers serving multiple selling locations. A novel fuzzy multi-objective mixed integer programming model is formulated considering multi-product, multi-period, and multi-site manufacturing environment. Minimization of total cost, delivery time, and backorder level are the three fuzzy objectives represented by piecewise linear membership function. Three important production and distribution aspects viz. capacity of the heterogeneous transportation, backordering for unfulfilled demand, and set-up cost/time for different products at manufacturing site are incorporated in an integrated manner to represent closeness to the real-life problem. An illustrative example inspired from a real-world case of an automobile industry is taken to demonstrate analytical results of the proposed approach. The outcome of the research indicates the practical applicability of the approach. Sensitivity analysis on objective function values is conducted for analyzing the effect of change in aspiration levels of objective function values on decision maker’s satisfaction level.

Bi-level programming for supplier selection under quantity discount policy

This paper proposes two models to formulate a Supplier Selection Problem (SSP) in a single-buyer, multi-supplier two-echelon supply chain network. The model coordinates order allocation and supplier selection problems under all-unit quantity discount policy. In this way, bi-level programming is employed to obtain two models: 1) The model with buyer as a leader; 2) The model with vendor as a leader. The resulted nonlinearbi-level programming problems are hard to solve. Therefore, Particle Swarm Optimization (PSO) algorithm is used to deal with the complexity of the model and makes it solvable. Numerical results show that the proposed model is ecient for SSP in compliance with order allocation decision making.

A decentralized supply chain planning model: a case study of hardboard industry

This paper presents a new decentralized/distributed decision-making (DDM) supply chain planning model. A supply chain is called decentralized when various decisions are made in different companies trying to optimize their own objectives. The proposed approach is applied to plan a wood supply chain network called Puya Wood Company. The supply chain network design problem discussed in this paper is an integrated multi-echelon, multi-product problem considering total costs of purchasing raw materials/returned product, transportation of raw materials, and inventory holding of raw materials. A coordination mechanism is designed to share information between the retailer model and the manufacturer model called centralized planning. The main contributions of this paper are summarized as follows: (1) presenting a decentralized (distributed) approach in order to address the production and distribution problem in supply chain including manufacturer and retailers and (2) proposing a coordination mechanism in order to handle problems related to production and distribution in a two-echelon supply chain network through a decentralized approach. The proposed model is tested using real case study. Sensitivity analysis is accomplished to find the effects of changing the parameter on the results. The proposed coordination mechanism provides high-quality solutions in reasonable number of iterations for the case study. This coordination mechanism can be applied in other supply chains such as natural gas and oil, water resource management, and crisis and disaster planning.

Inventory Management for One Warehouse Multi-Port Systems with Free Storage Periods

We consider a two-echelon supply chain network with one centralized warehouse and a set of ports, in which the sea cargo ports offer such kind of service that allows the in-transit inventory to stay in their ports for free for a certain time period. In the replenishment of the warehouse and ports, we take into account of the free storage period to minimize the two-echelon inventory cost. Focusing on stationary and integer-ratio policies, we formulate this problem as a mathematical model with a convex objective function and a set of integer-ratio constraints. We present an algorithm to solve the corresponding relaxed problem in () time, and prove that the objective function value of the relaxed problem (relaxing the integer-ratio constraints) is a lower bound on the average cost of all feasible policies (containing dynamic policies).Then we construct a stationary and integer-ratio inventory policy, i.e., the power-of-two policy, via the solution of the relaxed problem, and we also prove the optimality of the power-of-two policy.

Outsourcing optimization in two-echelon supply chain network under integrated production-maintenance constraints

In this paper, we study a two-echelon supply chain network consisting of multi-outsourcers and multi-subcontractors. Each one is composed of a failure-prone production unit that produces a single product to fulfil market demands with variable production rates. Sometimes the manufacturing systems are not able to satisfy demand; in this case, outsourcing option is adopted to improve the limited in-house production capacity. The outsourcing is not justified by the production lack of manufacturing systems, but is also considered for the costs minimization issues. In the considered problem, we assume that the failure rate is dependent on the time and production rate. Preventive maintenance activities can be conducted to mitigate the deterioration effects, and minimal repairs are performed when unplanned failures occurs. We consider that the production cost depends on the rate of the machine utilization. The aim of this research is to propose a joint policy based on a mixed integer programming formulation to balance the trade-off between two-echelon of supply chain. We seek to assist outsourcers to determine the integrated in-house/ outsourcing, and maintenance plans, and the subcontractors to determine the integrated production-maintenance plans so that the benefit of the supply chain is maximized over a finite planning horizon. We develop an improved optimization procedure based on the genetic algorithms, and we discuss and conduct computational experiments to study the managerial insights for the developed framework.

Optimizing a location allocation-inventory problem in a two-echelon supply chain network: A modified fruit fly optimization algorithm

In this paper, a design of the supply chain distributer–retailer network for a seasonal multiple-product location allocation-inventory control problem in a planning horizon consisting of multiple periods is modeled. The distance between the distributers and retailers are assumed to be Euclidean and square Euclidean while retailers purchase the products from the distributers under all-unit and incremental quantity discount policies. Furthermore, the products are delivered in packets of known size of items and in case of shortage, a fraction of demand is considered backorder and a fraction lost sale. Besides, the distributers store the manufactured products in their warehouses before delivering them to the retailers since the total warehouse spaces and the total available budget are limited. Capacity constraints are also taken into account when planning inventory levels. It is considered that the distributers manufacture the products under some production limitations. The aim of the problem is to find the optimal number of packets of the products purchased by the retailers from the distributers in different periods and determine the coordinates of the distributers’ locations to minimize the total inventory cost. As the mixed integer nonlinear model of the problem is complicated to solve using exact methods, a modified fruit fly optimization algorithm (MFOA) is proposed to find the optimal solution. Due to the nonlinear nature of the original formulation and noticing that there is no benchmark available in the literature to justify and validate the results, particle swarm optimization (PSO) and simulated annealing (SA) algorithms are represented as well. Some numerical examples are generated to show the performance and application of the algorithms for both Euclidean and square Euclidean distances where the MFOA has a better performance than the PSO and SA.

A modified particle swarm optimization for solving the integrated location and inventory control problems in a two-echelon supply chain network

In this study, the design of a two-echelon distribution supply chain network for the seasonal products with multiple vendors (manufacturers) and buyers (retailers), and a set of warehouses for each vendor are considered. The locations of the buyers are known and the capacity of the warehouses is restricted while the buyers purchase different products from the vendors under all unit discount policy. The main objective of this research is to find out the optimal locations of the potential vendors in addition to the quantity ordered (allocation) by the buyers so that the total inventory cost including ordering (transportation), holding and the purchasing costs is minimized. Besides, the distance from the buyers to the vendors is considered as the Euclidean distance. The total budget to buy the products is limited and the production capacity of each vendor is also restricted. To solve the problem, a modified particle swarm optimization (MPSO) algorithm is applied where the results are validated using a genetic algorithm (GA). Finally, some computational examples are generated to assess the algorithms' performance where MPSO shows a better efficiency in comparison with the GA.

Comparing classical performance measures for a multi-period, two-echelon supply chain network design problem with sizing decisions

This paper addresses a new problem to design a two-echelon supply chain network over a multi-period horizon. Strategic decisions are subject to a given budget and concern the location of new facilities in the upper and intermediate echelons of the network as well as the installation of storage areas to handle different product families. A finite set of capacity levels for each product family is available at each potential location. Further decisions concern the quantities of products to be shipped through the network. Two mixed-integer linear programming models are proposed that differ in the type of performance measure that is adopted to design the supply chain. Under a cost minimization objective, the network configuration with the least total cost is to be determined. In contrast, under a profit maximization goal the aim is to design the network so as to maximize the difference between total revenue and total cost. In this case, it may not always be attractive to completely satisfy demand requirements. To investigate the implications that the choice of these performance measures have on network design, an extensive computational study is conducted with randomly generated instances that are solved using CPLEX.

Two-echelon, multi-commodity supply chain network design with mode selection, lead-times and inventory costs

Designing distribution networks – as one of the most important strategic issues in supply chain management – has become the focus of research attention in recent years. This paper deals with a two-echelon supply chain network design problem in deterministic, single-period, multi-commodity contexts. The problem involves both strategic and tactical levels of supply chain planning including locating and sizing manufacturing plants and distribution warehouses, assigning the retailers' demands to the warehouses, and the warehouses to the plants, as well as selecting transportation modes.We have formulated the problem as a mixed integer programming model, which integrates the above mentioned decisions and intends to minimize total costs of the network including transportation, lead-times, and inventory holding costs for products, as well as opening and operating costs for facilities. Moreover, we have developed an efficient Lagrangian based heuristic solution algorithm for solving the real-sized problems in reasonable computational time.

Integrating customer responsiveness and distribution cost in designing a two-echelon supply chain network with considering capacity level and piecewise linear cost

When designing supply chains, firms are often faced with the competing demands of improved customer responsiveness and reduced cost. In this paper, we present a two echelon distribution network design problem in supply chain system which includes location, transportation and customer responsiveness decisions. Customer responsiveness is measured by the delivery delay cost. Unlike most of past research, our model allows for multiple levels of capacities available to the distribution centers and piecewise linear transportation cost between suppliers and distribution centers for obtaining economic of scale. A hybrid heuristic combining Tabu search with Simulated Annealing (SA) sharing the same tabu list is developed for solving the problem. We comprise the hybrid algorithm with the optimal solution, Simulated Annealing algorithm and Tabu search algorithm. The results indicate that the method is efficient for a wide variety of problem sizes.