On the inventory model with continuous and discrete lead time,backorders and lost sales

A well-established global supply chain system plays an important role in an enterprise’s strategic management, and an effective just-in-time system is a critical success factor for a global supply chain system. The advantages and benefits of just-in-time are associated with controlling the lead time. In this paper, we propose an approach to overcome the drawback of traditional methods for improving the continuous and discrete lead time with mixture of backorders and lost sales, by which only a local optimal solution can be obtained. In addition, the proposed model allows decision-makers to add suitable constraints to their model in accordance with their actual business environments. Finally, in order to demonstrate the accuracy and effectiveness of the suggested model, a real-life case, some numerical examples and sensitivity analysis are also included.     

A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge

This paper considers a two-stage distribution problem of a supply chain that is associated with a fixed charge. Two kinds of cost are involved in this problem: a continuous cost that linearly increases with the amount transported between a source and a destination, and secondly, a fixed charge, that incurs whenever there exists a transportation of a non-zero quantity between a source and a destination. The objective criterion is the minimisation of the total cost of distribution. A genetic algorithm (GA) that belongs to evolutionary search heuristics is proposed and illustrated. The proposed methodology is evaluated for its solution quality by comparing it with the approximate and lower bound solutions. Thus, the comparison reveals that the GA generates better solution than the approximation method and is capable of providing solution either equal or closer to the lower bound solution of the problem.     

A profit-maximizing supply chain network design model with demand choice flexibility

We present a profit-maximizing supply chain design model in which a company has flexibility in determining which customers to serve. The company may lose a customer to competition if the price it charges is too high. We show the problem formulation and solution algorithm, and discuss computational results.     

Network design problem with relays: A genetic algorithm with a path-based crossover and a set covering formulation

The network design problem with relays arises in telecommunications and distribution systems where the payload must be reprocessed at intermediate stations called relays on the route from its origin to its destination. In fiber-optic networks, for example, optical signals may be regenerated several times to overcome signal degradation because of attenuation and other factors. Given a network and a set of commodities, the network design problem with relays involves selecting network edges, determining a route for each commodity, and locating relays to minimize the network design cost. This paper presents a new formulation to the problem based on set covering constraints. The new formulation is used to design a genetic algorithm with a specialized crossover/mutation operator which generates a feasible path for each commodity, and the locations of relays on these paths are determined by solving the corresponding set covering problem. Computational experiments show that the proposed approach can outperform other approaches, particularly on large size problems.     

A possibilistic decision model for new product supply chain design

This paper models supply chain (SC) uncertainties by fuzzy sets and develops a possibilistic SC configuration model for new products with unreliable or unavailable SC statistical data. The supply chain is modeled as a network of stages. Each stage may have one or more options characterized by the cost and lead-time required to fulfill required functions and may hold safety stock to prevent an inventory shortage. The objective is to determine the option and inventory policy for each stage to minimize the total SC cost and maximize the possibility of fulfilling the target service level. A fuzzy SC model is developed to evaluate the performance of the entire SC and a genetic algorithm approach is applied to determine near-optimal solutions. The results obtained show that the proposed approach allows decision makers to perform trade-off analysis among customer service levels, product cost, and inventory investment depending on their risk attitude. It also provides an alternative tool to evaluate and improve SC configuration decisions in an uncertain SC environment.     

A genetic algorithm for optimizing defective goods supply chain costs using JIT logistics and each-cycle lengths

The competitive environment of global markets has forced many manufacturers to select the most appropriate supply chain network (SCN) for reduction of total costs and wasted time. Cost reduction and selection of the appropriate length of each period are two important factors in the competitive market that are often not addressed comprehensively by researchers. In our study, we proposed genetic algorithms (GAs) for optimising a novel mathematical model of the defective goods supply chain network (DGSCN). In the proposed model, we assumed that all imperfect-quality products are not repairable, whereas those considered as scrap are directly sold to customers at a low price. The objective of the proposed model is to minimise the costs of production, distribution, holding and backorder. In addition to minimising the costs, the model can determine the economic production quantity (EPQ), the appropriate length of each cycle (ALOEC) and the quantities of defective products, scrap products and retailer shortages using Just-In-Time logistics (JIT-L). We used the GAs and a Cplex solver with probability parameters and various dimensions for validation of the studied model in real-life situations, and we compared the outputs to demonstrate the performance of the model. Additionally, to identify the appropriate length of each cycle (ALOEC), we needed to solve the model using exact parameters and same dimensions and prefer to use Lingo for this application.     

A genetic algorithm for optimal operating parameters of VMI system in a two-echelon supply chain

This paper deals with the operational issues of a two-echelon single vendor–multiple buyers supply chain (TSVMBSC) model under vendor managed inventory (VMI) mode of operation. The operational parameters to the above model are: sales quantity and sales price that determine the channel profit of the supply chain, and contract price between the vendor and the buyer, which depends upon the understanding between the partners on their revenue sharing. In order to find out the optimal sales quantity for each buyer in TSVMBSC problem, a mathematical model is formulated. Optimal sales price and acceptable contract price at different revenue share are subsequently derived with the optimal sales quantity. A genetic algorithm (GA) based heuristic is proposed to solve this TSVMBSC problem, which belongs to nonlinear integer programming problem (NIP). The proposed methodology is evaluated for its solution quality. Furthermore, the robustness of the model with its parameters, which fluctuate frequently and are sensitive to operational features, is analysed.     

A Benders decomposition approach for a distribution network design problem with consolidation and capacity considerations

We develop a model for a strategic freight-forwarding network design problem in which the design decisions involve the locations and capacities of consolidation and deconsolidation centers, and capacities on linehaul linkages as well as the shipment routes from origins to destinations through centers. We devise a solution approach based on Benders decomposition and conduct a computational study that illustrates the efficiency and the effectiveness of the approach.     

An efficient approximation algorithm for the survivable network design problem

The survivable network design problem (SNDP) is to construct a minimum-cost subgraph satisfying certain given edge-connectivity requirements. The first polynomial-time approximation algorithm was given by Williamson et al. (Combinatorica 15 (1995) 435–454). This paper gives an improved version that is more efficient. Consider a graph ofn vertices and connectivity requirements that are at mostk. Both algorithms find a solution that is within a factor 2k – 1 of optimal fork 2 and a factor 2 of optimal fork = 1. Our algorithm improves the time from O(k ³n⁴) to O ). Our algorithm shares features with those of Williamson et al. (Combinatorica 15 (1995) 435–454) but also differs from it at a high level, necessitating a different analysis of correctness and accuracy; our analysis is based on a combinatorial characterization of the redundant edges. Several other ideas are introduced to gain efficiency. These include a generalization of Padberg and Rao's characterization of minimum odd cuts, use of a representation of all minimum (s, t) cuts in a network, and a new priority queue system. The latter also improves the efficiency of the approximation algorithm of Goemans and Williamson (SIAM Journal on Computing 24 (1995) 296–317) for constrained forest problems such as minimum-weight matching, generalized Steiner trees and others. © 1998 The Mathematical Programming Society, Inc. Published by Elsevier Science B.V.A preliminary version of this paper has appeared in the Proceedings of the Third Mathematical Programming Society Conference on Integer Programming and Combinatorial Optimization, 1993, pp. 57–74.Research supported in part by NSF Grant No. CCR-9215199 and AT & T Bell Laboratories.Research supported in part by Air Force contracts AFOSR-89-0271 and F49620-92-J-0125 and DARPA contracts N00014-89-J-1988 and N00014-92-1799.This research was performed while the author was a graduate student at MIT. Research supported by an NSF Graduate Fellowship, Air Force contract F49620-92-J-0125, DARPA contracts N00014-89-J-1988 and N00014-92-J-1799, and AT & T Bell Laboratories.     

A polynomial time primal network simplex algorithm for minimum cost flows

Developing a polynomial time primal network simplex algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n ²m lognC, n ²m² logn)) time, wheren is the number of nodes in the network,m is the number of arcs, andC denotes the maximum absolute arc costs if arc costs are integer and ∞ otherwise. We first introduce a pseudopolynomial variant of the network simplex algorithm called the “premultiplier algorithm”. We then develop a cost-scaling version of the premultiplier algorithm that solves the minimum cost flow problem in O(min(nm lognC, nm ² logn)) pivots. With certain simple data structures, the average time per pivot can be shown to be O(n). We also show that the diameter of the network polytope is O(nm logn).     

A seasonal demand inventory model with variable lead time and resource constraints

In this paper, two new methods are proposed for solving a seasonal demand problem with variable lead-time and resource constraints. Despite its significance, no study has been done on such problem to obtain the best policy. First, in order to solve the variable lead time, a linear programming relaxation using piecewise linearization techniques is derived. Then, a mixed integer program with linearization techniques is constructed for the seasonal demand problem. Finally, some illustrative examples are included to demonstrate the applicability of the proposed models.     

A curve-fitting genetic algorithm for a styling application

Fitting curves in computer-aided geometric design is generally regarded as an optimisation problem. Depending on the application, the conditions to be satisfied can make the problem difficult to solve using classic methods, and for this reason, stochastic methods, such as genetic algorithms appear to be appropriate. This article considers a curve fitting problem, with the objective of generating shapes with specific curvature variations for use in the design of car bodies. To this end, a particular curve model was developed and implemented within a genetic algorithm. The main characteristics of this algorithm are described and its promising results are presented. The conclusion will show that this technique can be used as an alternative method in the design of car bodies.     

A polynomial time algorithm for a chance-constrained single machine scheduling problem

This paper gives an O(n√nlog³n) time algorithm for the chance-constrained sequencing problem on a single machine, where n is the number of jobs and the objective is to minimize the number of jobs which are early with probability not smaller than α (a given constant) against the common due time d.     

Calculating safety stocks for assembly systems with random component procurement lead times: A branch and bound algorithm

In this paper, a discrete single-level multi-component inventory control model for assembly systems with random component procurement lead times is considered. The economic order quantity (EOQ) policy is used for a type of finished product. The requirements of the components are constant and cyclic (periodic), and their values per period are deduced from the EOQ for the finished product. The paper focuses on the components safety stock calculation. The objective is to minimise the average holding cost of the components while keeping the desired service level for the finished product. For this, an upper bound, two lower bounds, two dominance properties and an efficient branch and bound algorithm are suggested. Several tests are executed and conclusions are drawn. The proposed model provides a substantial saving for assembly systems with a large number and unreliable delivery of components as in semi-conductor and automotive industries.     

Minimizing flow time variance in a single machine system using genetic algorithms

In this paper, we address an n-job, single machine scheduling problem with an objective to minimize the flow time variance. We propose heuristic procedure based on genetic algorithms with the potential to address more generalized objective function such as weighted flow time variance. The development and implementation of the algorithm is supported with literature review and statistical analysis of the results. Some general guidelines to select the parameter values of the genetic algorithm are also developed using an experimental design approach.     

Solving the response time variability problem by means of a genetic algorithm

The response time variability problem (RTVP) is a hard scheduling problem that has recently been defined in the literature and has a wide range of real-world applications in mixed-model assembly lines, multithreaded computer systems, network environments and others. The RTVP arises whenever products, clients or jobs need to be sequenced in such a way that the variability in the time between the points at which they receive the necessary resources is minimized. Since the RTVP is a complex problem, heuristic and metaheuristic techniques are needed to solve it. The best results in the literature for the RTVP have been obtained with a psychoclonal algorithm. We propose a genetic algorithm (GA) that is adapted to solve the RTVP. A computational experiment is carried out and it is shown that, on average, the GA produces better results than the psychoclonal algorithm.     

A hybrid genetic algorithm with dominance properties for single machine scheduling with dependent penalties

In this paper, a hybrid genetic algorithm is developed to solve the single machine scheduling problem with the objective to minimize the weighted sum of earliness and tardiness costs. First, dominance properties of (the conditions on) the optimal schedule are developed based on the switching of two adjacent jobs i and j. These dominance properties are only necessary conditions and not sufficient conditions for any given schedule to be optimal. Therefore, these dominance properties are further embedded in the genetic algorithm and we call it genetic algorithm with dominance properties (GADP). This GADP is a hybrid genetic algorithm. The initial populations of schedules in the genetic algorithm are generated using these dominance properties. GA can further improve the performance of these initial solutions after the evolving procedures. The performances of hybrid genetic algorithm (GADP) have been compared with simple genetic algorithm (SGA) using benchmark instances. It is shown that this hybrid genetic algorithm (GADP) performs very well when compared with DP or SGA alone.     

Supply chain coordination with controllable lead time and asymmetric information

This paper considers coordinated decisions in a decentralized supply chain consisting of a vendor and a buyer with controllable lead time. We analyze two supply chain inventory models. In the first model we assume the vendor has complete information about the buyer’s cost structure. By taking both the vendor and the buyer’s individual rationalities into consideration, a side payment coordination mechanism is designed to realize supply chain Pareto dominance. In the second model we consider a setting where the buyer possesses private cost information. We design the coordination mechanism by using principal-agent model to induce the buyer to report his true cost structure. The solution procedures are also developed to get the optimal solutions of these two models. The results of numerical examples show that shortening lead time to certain extent can reduce inventory cost and the coordination mechanisms designed for both symmetric and asymmetric information situations are effective.     

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).     

An approximation algorithm for network design problems with downwards-monotone demand functions

Building on an existing 2-approximate algorithm for the class of network design problems with downwards-monotone demand functions, many of which are NP-hard, we present an algorithm that produces solutions that are at least as good as and typically better than solutions produced by the existing algorithm.