A two-phase ant colony algorithm for multi-echelon defective supply chain network design

Supply chain system is an integrated production system of a product. In the past researches, this system was often assumed to be an equilibrium structure, but in real production process, some members in this system usually cannot effectively complete their production task because of the losses of production, which will reduce the performance of the whole supply chain production system. This supply chain with the losses of production is called the defective supply chain (DSC) system. This research will discuss the partner selection and the production–distribution planning in this DSC network system. Besides the cost of production and transportation, the reliability of the structure and the unbalance of this system caused by the losses of production are considered. Then a germane mathematical programming model is developed for solving this problem. Due to the complex problem and in order to get a satisfactory near-optimal solution with great speed, this research proposes seeking the solution with the solving model based on ant colony algorithm. The application results in real cases show that the solving model presented by this research can quickly and effectively plan the most suitable type of the DSC network and decision-making of the production–distribution. Finally, a comparative numerical experiment is performed by using the proposed approach and the common single-phase ant colony algorithm (SAC) to demonstrate the performance of the proposed approach. The analysis results show that the proposed approach can outperform the SAC in partner selection and production–distribution planning for DSC network design.     

A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem – A case study on supply chain model

The main goal of supply chain management is to coordinate and collaborate the supply chain partners seamlessly. On the other hand, bi-level linear programming is a technique for modeling decentralized decision. It consists of the upper level and lower level objectives. Thus, this paper intends to apply bi-level linear programming to supply chain distribution problem and develop an efficient method based on hybrid of genetic algorithm (GA) and particle swarm optimization (PSO). The performance of the proposed method is ascertained by comparing the results with GA and PSO using four problems in the literature and a supply chain distribution model.     

An analysis of production-inventory models with deteriorating items in a two-echelon supply chain

This paper revisits two previous studies that addressed the integrated production–inventory problem for deteriorating items in a two-echelon supply chain, where the item’s deterioration rate is a constant or follows a continuous probability distribution function. The aim of this study is to present an improved solution procedure to determine the delivery lot size and the number of deliveries per production batch cycle that minimizes the total cost of the entire supply chain. The performance of the proposed methodology is illustrated analytically and numerically.     

Capacitated location allocation problem with stochastic location and fuzzy demand: A hybrid algorithm

In this article, a capacitated location allocation problem is considered in which the demands and the locations of the customers are uncertain. The demands are assumed fuzzy, the locations follow a normal probability distribution, and the distances between the locations and the customers are taken Euclidean and squared Euclidean. The fuzzy expected cost programming, the fuzzy β-cost minimization model, and the credibility maximization model are three types of fuzzy programming that are developed to model the problem. Moreover, two closed-form Euclidean and squared Euclidean expressions are used to evaluate the expected distance between customers and facilities. In order to solve the problem at hand, a hybrid intelligent algorithm is applied in which the simplex algorithm, fuzzy simulation, and a modified genetic algorithm are integrated. Finally, in order to illustrate the efficiency of the proposed hybrid algorithm, some numerical examples are presented.     

Multiple-buyer multiple-vendor multi-product multi-constraint supply chain problem with stochastic demand and variable lead-time: A harmony search algorithm

In this paper, a multi-buyer multi-vendor supply chain problem is considered in which there are several products, each buyer has limited capacity to purchase products, and each vendor has warehouse limitation to store products. In this chain, the demand of each product is stochastic and follows a uniform distribution. The lead-time of receiving products from a vendor to a buyer is assumed to vary linearly with respect to the order quantity of the buyer and the production rate of the vendor. For each product, a fraction of the shortage is backordered and the rest are lost. The ordered product quantities are placed in multiple of pre-defined packets and there are service rate constraints for the buyers. The goal is to determine the reorder points, the safety stocks, and the numbers of shipments and packets in each shipment of the products such that the total cost of the supply chain is minimized. We show that the model of this problem is of an integer nonlinear programming type and in order to solve it a harmony search algorithm is employed. To validate the solution and to compare the performance of the proposed algorithm, a genetic algorithm is utilized as well. A numerical illustration and sensitivity analysis are given at the end to show the applicability of the proposed methodology in real-world supply chain problems.     

A hybrid genetic algorithm for the finite horizon economic lot and delivery scheduling in supply chains

In this paper, we investigate the lot and delivery scheduling problem in a simple supply chain where a single supplier produces multiple components on a flexible flow line (FFL) and delivers them directly to an assembly facility (AF). It is assumed that all of parameters such as demand rates for the components are deterministic and constant over a finite planning horizon. The main objective is to find a lot and delivery schedule that would minimize the average of holding, setup, and transportation costs per unit time for the supply chain. We develop a new mixed integer nonlinear program (MINLP) and an optimal enumeration method to solve the problem. Due to difficulty of obtaining the optimal solution in medium and large-scaled problems, a hybrid genetic algorithm (HGA) is also developed. The proposed HGA incorporates a neighborhood search (NS) into a basic genetic algorithm that enables the algorithm to perform genetic search over the subspace of local optima. The two proposed solution methods are compared on randomly generated problems, and computational results show that the performance of HGA is very promising because it is able to find an optimal or near-optimal solution for majority of the test problems.     

Generating artificial chromosomes with probability control in genetic algorithm for machine scheduling problems

In this paper, a novel genetic algorithm is developed by generating artificial chromosomes with probability control to solve the machine scheduling problems. Generating artificial chromosomes for Genetic Algorithm (ACGA) is closely related to Evolutionary Algorithms Based on Probabilistic Models (EAPM). The artificial chromosomes are generated by a probability model that extracts the gene information from current population. ACGA is considered as a hybrid algorithm because both the conventional genetic operators and a probability model are integrated. The ACGA proposed in this paper, further employs the “evaporation concept” applied in Ant Colony Optimization (ACO) to solve the permutation flowshop problem. The “evaporation concept” is used to reduce the effect of past experience and to explore new alternative solutions. In this paper, we propose three different methods for the probability of evaporation. This probability of evaporation is applied as soon as a job is assigned to a position in the permutation flowshop problem. Experimental results show that our ACGA with the evaporation concept gives better performance than some algorithms in the literature.     

Time-dependent optimization of a multi-item uncertain supply chain network: A hybrid approximation algorithm

We consider the uncertain least cost shipping problem. The input is a multi-item supply chain network with time-evolving uncertain costs and capacities. Exploiting the operational law of uncertainty theory, a mathematical model of the problem is established and the indeterminacy factors are tackled. We use the scaling idea together with transformation approach and uncertainty programming to develop a hybrid algorithm to optimize and obtain the uncertainty distribution of the total shipping cost. We analyze the practical performance of the algorithm and present an illustrative example.     

Incorporating inventory and routing costs in strategic location models

We consider a supply chain design problem where the decision maker needs to decide the number and locations of the distribution centers (DCs). Customers face random demand, and each DC maintains a certain amount of safety stock in order to achieve a certain service level for the customers it serves. The objective is to minimize the total cost that includes location costs and inventory costs at the DCs, and distribution costs in the supply chain. We show that this problem can be formulated as a nonlinear integer programming model, for which we propose a Lagrangian relaxation based solution algorithm. By exploring the structure of the problem, we find a low-order polynomial algorithm for the nonlinear integer programming problem that must be solved in solving the Lagrangian relaxation sub-problems. We present computational results for several instances of the problem with sizes ranging from 40 to 320 customers. Our results show the benefits of having an integrated supply chain design framework that includes location, inventory, and routing decisions in the same optimization model.     

Estimation of Transit Origin–Destination Matrices from Passenger Counts Using a Frequency-Based Approach

This paper investigates the transit passenger origin–destination (O–D) estimation problem in congested transit networks where updated passenger counts and outdated O–D matrices are available. The bi-level programming approach is used for the transit passenger O–D estimation problem. The upper level minimizes the sum of error measurements in passenger counts and O–D matrices, and the lower level is a new frequency-based stochastic user equilibrium (SUE) assignment model that can determine simultaneously the passenger overload delays and passenger route choices in congested transit network together with the resultant transit line frequencies. The lower-level problem can be formulated as either a logit-type or probit-type SUE transit assignment problem. A heuristic solution algorithm is developed for solving the proposed bi-level programming model which is applicable to congested transit networks. Finally, a case study on a simplified transit network connecting Kowloon urban area and the Hong Kong International Airport is provided to illustrate the applications of the proposed bi-level programming model and solution algorithm. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.     

A comparison of two methods for solving 0–1 integer programs using a general purpose simulated annealing algorithm

0–1 problems are often difficult to solve. Although special purpose algorithms (exact as well as heuristic) exist for solving particular problem classes or problem instances, there are few general purpose algorithms for solving practical-sized instances of 0–1 problems. This paper deals with a general purpose heuristic algorithm for 0–1 problems. In this paper, we compare two methods based on simulated annealing for solving general 0–1 integer programming problems. The two methods differe in the scheme used for neighbourhood transitions in the simulated annealing framework. We compare the performance of the two methods on the set partitioning problem.     

Accumulating Jacobians as chained sparse matrix products

 The chain rule – fundamental to any kind of analytical differentiation - can be applied in various ways to computational graphs representing vector functions. These variants result in different operations counts for the calculation of the corresponding Jacobian matrices. The minimization of the number of arithmetic operations required for the calculation of the complete Jacobian leads to a hard combinatorial optimization problem. We will describe an approach to the solution of this problem that builds on the idea of optimizing chained matrix products using dynamic programming techniques. Reductions by a factor of 3 and more are possible regarding the operations count for the Jacobian accumulation. After discussing the mathematical basics of Automatic Differentiation we will show how to compute Jacobians by chained sparse matrix products. These matrix chains can be reordered, must be pruned, and are finally subject to a dynamic programming algorithm to reduce the number of scalar multiplications performed. Received: January 17, 2002 / Accepted: May 29, 2002 Published online: February 14, 2003 Key words. chained matrix product – combinatorial optimization – dynamic programming – edge elimination in computational graphs     

智能制造环境下的备件生产与运输协同调度问题研究

智能制造和即时配送环境下的备件生产与运输协同调度问题是目前国内研究的一大热点,这是因为备件供应链响应速度已成为当前备件制造企业赢得客户的关键因素。为了提高客户满意度,尽可能缩短从客户下达定制化生产订单到订单配送完成的时间,本文建立了以所有客户总等待时间最短为目标的混合整数规划模型和集合覆盖模型,推导了最优解性质,并设计改进的分支定价算法求得最优解。通过将小规模算例结果与CPLEX进行对比,验证了模型和算法的有效性。多组算例测试结果表明,所提出的模型和算法可以有效提升智能制造环境下的备件供应链运作效率。     

Solving Problems with Semidefinite and Related Constraints Using Interior-Point Methods for Nonlinear Programming

 In this paper, we describe how to reformulate a problem that has second-order cone and/or semidefiniteness constraints in order to solve it using a general-purpose interior-point algorithm for nonlinear programming. The resulting problems are smooth and convex, and numerical results from the DIMACS Implementation Challenge problems and SDPLib are provided. Received: March 10, 2001 / Accepted: January 18, 2002 Published online: September 27, 2002 Key Words. semidefinite programming – second-order cone programming – interior-point methods – nonlinear programming Mathematics Subject Classification (2000): 20E28, 20G40, 20C20     

Optimizing the supply chain configuration for make-to-order manufacturing

We consider a make-to-order (MTO) manufacturer who has won multiple contracts with specified quantities to be delivered by certain due dates. Before production starts, the company must configure its supply chain and make sourcing decisions. It also needs to plan the starting time for each production task under limited availability of resources such as machines and workforce. We develop a model for simultaneously optimizing such sourcing and planning decisions while exploiting their tradeoffs. The resulting multi-mode resource-constrained project scheduling problem (MMRCPSP) with a nonlinear objective function is NP-complete. To efficiently solve it, a hybrid Benders decomposition (HBD) algorithm combining the strengths of both mathematical programming and constraint programming is developed. The HBD exploits the structure of the model formulation and decomposes it into a relaxed master problem handled by mixed-integer nonlinear programming (MINLP), and a scheduling feasibility sub-problem handled by constraint programming (CP). Cuts are iteratively generated by solving the feasibility sub-problem and added back to the relaxed master problem, until an optimal solution is found or infeasibility is proved. Computational experiments are conducted to examine performance of the model and algorithm. Insights about optimal configuration of MTO supply chains are drawn and discussed.     

Genetic algorithms for supply-chain scheduling: A case study in the distribution of ready-mixed concrete

The coordination of just-in-time production and transportation in a network of partially independent facilities to guarantee timely delivery to distributed customers is one of the most challenging aspect of supply chain management. From a theoretical perspective, the timely production/distribution can be viewed as a hybrid combination of planning, scheduling and routing problems, each notoriously affected by nearly prohibitive combinatorial complexity. From a practical viewpoint, the problem calls for a trade-off between risks and profits. This paper focuses on the ready-mixed concrete delivery: in addition to the mentioned complexity, strict time-constraints forbid both earliness and lateness of the supply. After developing a detailed model of the considered problem, we propose a novel meta-heuristic approach based on a hybrid genetic algorithm combined with constructive heuristics. A detailed case study derived from industrial data is used to illustrate the potential of the proposed approach.     

Combining Metaheuristics and Exact Methods for Solving Exactly Multi-objective Problems on the Grid

This paper presents a parallel hybrid exact multi-objective approach which combines two metaheuristics – a genetic algorithm (GA) and a memetic algorithm (MA), with an exact method – a branch and bound (B&B) algorithm. Such approach profits from both the exploration power of the GA, the intensification capability of the MA and the ability of the B&B to provide optimal solutions with proof of optimality. To fully exploit the resources of a computational grid, the hybrid method is parallelized according to three well-known parallel models – the island model for the GA, the multi-start model for the MA and the parallel tree exploration model for the B&B. The obtained method has been experimented and validated on a bi-objective flow-shop scheduling problem. The approach allowed to solve exactly for the first time an instance of the problem – 50 jobs on 5 machines. More than 400 processors belonging to 4 different administrative domains have contributed to the resolution process during more than 6 days.      

Optimal selection of retailers for a manufacturing vendor in a vendor managed inventory system

A Vendor Managed Inventory (VMI) system consists of a manufacturing vendor and a number of retailers. In such a system, it is essential for the vendor to optimally determine retailer selection and other related decisions, such as the product’s replenishment cycle time and the wholesale price, in order to maximize his profit. Meanwhile, each retailer’s decisions on her willingness to enter the system and retail price are simultaneously considered in the retailer selection process. However, the above interactive decision making is complex and the available studies on interactive retailer selection are scarce. In this study, we formulate the retailer selection problem as a Stackelberg game model to help the manufacturer, as a vendor, optimally select his retailers to form a VMI system. This model is non-linear, mixed-integer, game-theoretic, and analytically intractable. Therefore, we further develop a hybrid algorithm for effectively and efficiently solving the developed model. The hybrid algorithm combines dynamic programming (DP), genetic algorithm (GA) and analytical methods. As demonstrated by our numerical studies, the optimal retailer selection can increase the manufacturer’s profit by up to 90% and the selected retailers’ profits significantly compared to non-selection strategy. The proposed hybrid algorithm can solve the model within a minute for a problem with 100 candidate retailers, whereas a pure GA has to take more than 1 h to solve a small sized problem of 20 candidate retailers achieving an objective value no worse than that obtained by the hybrid algorithm.     

Global Optimization Versus Integer Programming in Portfolio Optimization under Nonconvex Transaction Costs

This paper is concerned with a portfolio optimization problem under concave and piecewise constant transaction cost. We formulate the problem as nonconcave maximization problem under linear constraints using absolute deviation as a measure of risk and solve it by a branch and bound algorithm developed in the field of global optimization. Also, we compare it with a more standard 0–1 integer programming approach. We will show that a branch and bound method elaborating the special structure of the problem can solve the problem much faster than the state-of-the integer programming code.