Performance analysis and design of supply chains: a Petri net approach

In this paper, we investigated a dynamic modelling technique for analysing supply chain networks using generalised stochastic Petri nets (GSPNs). The customer order arrival process is assumed to be Poisson and the service processes at the various facilities of the supply chain are assumed to be exponential. Our model takes into account both the procurement process and delivery logistics that exist between any two members of the supply chain. We compare the performance of two production planning and control policies, the make-to-stock and the assemble-to-order systems in terms of total cost which is the sum of inventory carrying cost and cost incurred due to delayed deliveries. We formulate and solve the decoupling point location problem in supply chains as a total relevant cost (sum of inventory carrying cost and the delay costs) minimisation problem. We use the framework of integrated GSPN-queuing network modelling—with the GSPN at the higher level and a generalised queuing network at the lower level—to solve the decoupling point location problem.     

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

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

Revised multi-choice goal programming for multi-period,multi-stage inventory controlled supply chain model with popup stores in Guerrilla marketing

In this paper, we consider a supply chain network design problem with popup stores which can be opened for a few weeks or months before closing seasonally in a marketplace. The proposed model is multi-period and multi-stage with multi-choice goals under inventory management constraints and formulated by 0–1 mixed integer linear programming. The design tasks of the problem involve the choice of the popup stores to be opened and the distribution network design to satisfy the demand with three multi-choice goals. The first goal is minimization of the sum of transportation costs in all stages; the second is to minimization of set up costs of popup stores; and the third goal is minimization of inventory holding and backordering costs. Revised multi-choice goal programming approach is applied to solve this mixed integer linear programming model. Also, we provide a real-world industrial case to demonstrate how the proposed model works.     

Integrated location and two-echelon inventory network design under uncertainty

In this paper, we propose a two-stage stochastic model to address the design of an integrated location and two-echelon inventory network under uncertainty. The central issue in this problem is to design and operate an effective and efficient multi-echelon supply chain distribution network and to minimize the expected system-wide cost of warehouse location, the allocation of warehouses to retailers, transportation, and two-echelon inventory over an infinite planning horizon. We structure this problem as a two-stage nonlinear discrete optimization problem. The first stage decides the warehouses to open and the second decides the warehouse-retailer assignments and two-echelon inventory replenishment strategies. Our modeling strategy incorporates various probable scenarios in the integrated multi-echelon supply chain distribution network design to identify solutions that minimize the first stage costs plus the expected second stage costs. The two-echelon inventory cost considerations result in a nonlinear objective which we linearize with an exponential number of variables. We solve the problem using column generation. Our computational study indicates that our approach can solve practical problems of moderate-size with up to twenty warehouse candidate locations, eighty retailers, and ten scenarios efficiently.     

A stochastic model for risk management in global supply chain networks

With the increasing emphasis on supply chain vulnerabilities, effective mathematical tools for analyzing and understanding appropriate supply chain risk management are now attracting much attention. This paper presents a stochastic model of the multi-stage global supply chain network problem, incorporating a set of related risks, namely, supply, demand, exchange, and disruption. We provide a new solution methodology using the Moreau–Yosida regularization, and design an algorithm for treating the multi-stage global supply chain network problem with profit maximization and risk minimization objectives.     

Profit oriented supply chain network optimization

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

Financial scenario generation for stochastic multi-stage decision processes as facility location problems

The quality of multi-stage stochastic optimization models as they appear in asset liability management, energy planning, transportation, supply chain management, and other applications depends heavily on the quality of the underlying scenario model, describing the uncertain processes influencing the profit/cost function, such as asset prices and liabilities, the energy demand process, demand for transportation, and the like. A common approach to generate scenarios is based on estimating an unknown distribution and matching its moments with moments of a discrete scenario model. This paper demonstrates that the problem of finding valuable scenario approximations can be viewed as the problem of optimally approximating a given distribution with some distance function. We show that for Lipschitz continuous cost/profit functions it is best to employ the Wasserstein distance. The resulting optimization problem can be viewed as a multi-dimensional facility location problem, for which at least good heuristic algorithms exist. For multi-stage problems, a scenario tree is constructed as a nested facility location problem. Numerical convergence results for financial mean-risk portfolio selection conclude the paper.     

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 multi-stage and multi-supplier inventory model allowing different order quantities

This paper addresses a multi-stage inventory model that allows different order quantities among the selected suppliers to obtain the optimal solutions. To achieve the objective of the study, the single-objective and multi-objective methods are adopted for suitable real-world applications. With respect to a single-objective method, this paper aims to minimize the total ordering costs, holding costs, and purchasing costs, subject to the price, quality, and capacity. With respect to a multi-objective method, it focuses on cost minimization, as well as quality and capacity maximization. The proposed model not only considers the allocation of different order quantities among the selected suppliers, but also incorporates the multi-stage inventory problem. Furthermore, a numerical example is provided to illustrate the usefulness of the proposed model and a comparative understanding of various methods. In addition, a simulation test is performed to effectively validate the proposed model which outperforms the previous works. Finally, a sensitivity analysis is carried out to investigate the impact of supply chain cost.     

A multi-stage supply chain network design problem with in-house production and partial product outsourcing

We propose a mixed-integer linear programming model for a novel multi-stage supply chain network design problem. Our model integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, and the distribution of multiple products through the network. The aim is to identify the network configuration with the least total cost subject to side constraints related to resource availability, technological conditions, and customer service level requirements. In addition to in-house manufacturing, end products may also be purchased from external sources and consolidated in warehouses. Therefore, our model identifies the best mix between in-house production and product outsourcing. To measure the impact of this strategy, we further present two additional formulations for alternative network design approaches that do not include partial product outsourcing. Several classes of valid inequalities tailored to the problems at hand are also proposed. We test our models on randomly generated instances and analyze the trade-offs achieved by integrating partial outsourcing into the design of a supply chain network against a pure in-house manufacturing strategy, and the extent to which it may not be economically attractive to provide full demand coverage.     

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 stochastic programming approach for supply chain network design under uncertainty

This paper proposes a stochastic programming model and solution algorithm for solving supply chain network design problems of a realistic scale. Existing approaches for these problems are either restricted to deterministic environments or can only address a modest number of scenarios for the uncertain problem parameters. Our solution methodology integrates a recently proposed sampling strategy, the sample average approximation (SAA) scheme, with an accelerated Benders decomposition algorithm to quickly compute high quality solutions to large-scale stochastic supply chain design problems with a huge (potentially infinite) number of scenarios. A computational study involving two real supply chain networks are presented to highlight the significance of the stochastic model as well as the efficiency of the proposed solution strategy.     

Supply chain scheduling in a collaborative manufacturing mode: model construction and algorithm design

In collaborative manufacturing, the supply chain scheduling problem becomes more complex according to both multiple product demands and multiple production modes. Aiming to obtain a reasonable solution to this complexity, we analyze the characteristics of collaborative manufacturing and design some elements, including production parameters, order parameters, and network parameters. We propose four general types of collaborative manufacturing networks and then construct a supply chain scheduling model composed of the processing costs, inventory costs, and two penalty costs of the early completion costs and tardiness costs. In our model, by considering the urgency of different orders, we design a delivery time window based on the least production time and slack time. Additionally, due to the merit of continuously processing orders belonging to the same product type, we design a production cost function by using a piecewise function. To solve our model efficiently, we present a hybrid ant colony optimization (HACO) algorithm. More specifically, the Monte Carlo algorithm is incorporated into our HACO algorithm to improve the solution quality. We also design a moving window award mechanism and dynamic pheromone update strategy to improve the search efficiency and solution performance. Computational tests are conducted to evaluate the performance of the proposed method.

     

Collaborative production planning of supply chain under price and demand uncertainty

This research is motivated by an automobile manufacturing supply chain network. It involves a multi-echelon production system with material supply, component fabrication, manufacturing, and final product distribution activities. We address the production planning issue by considering bill of materials and the trade-offs between inventories, production costs and customer service level. Due to its complexity, an integrated solution framework which combines scatter evolutionary algorithm, fuzzy programming and stochastic chance-constrained programming are combined to jointly take up the issue. We conduct a computational study to evaluate the model. Numerical results using the proposed algorithm confirm the advantage of the integrated planning approach. Compared with other solution methodologies, the supply chain profits from the proposed approach consistently outperform, in some cases up to 13% better. The impacts of uncertainty in demand, material price, and other parameters on the performance of the supply chain are studied through sensitivity analysis. We found the proposed model is effective in developing robust production plans under various market conditions.     

Node Features Adjusted Stochastic Block Model

Stochastic block model (SBM) and its variants are popular models used in community detection for network data. In this article, we propose a feature-adjusted stochastic block model (FASBM) to capture the impact of node features on the network links as well as to detect the residual community structure beyond that explained by the node features. The proposed model can accommodate multiple node features and estimate the form of feature impacts from the data. Moreover, unlike many existing algorithms that are limited to binary-valued interactions, the proposed FASBM model and inference approaches are easily applied to relational data that generate from any exponential family distribution. We illustrate the methods on simulated networks and on two real-world networks: a brain network and an US air-transportation network.     

Measurement and optimization of responsiveness in supply chain networks with queueing structures

In this paper we consider supply chains with multiple stages of serial or network structure. The supply chains are endogenous in the sense that they involve queues because each order’s lead-time is dependent on the orders already in the system. We define supply chain responsiveness as the probability of fulfilling customer orders within a promised lead-time and study the problems of measuring and optimizing supply chain responsiveness using queueing network models. We first consider a single-server multi-stage serial supply chain and find a closed form expression for the fulfilment time distribution. For the multi-server multi-stage problem, the closed form evaluation of the fulfilment time distribution becomes intractable due to the dependency of the lead-times in different stages. We circumvent this difficulty by proposing a novel FCFS discipline which enables a closed-form analysis. For the multi-server multi-stage Jackson-type supply chain network, to enable analysis, we convert the system into an equivalent single server single stage system with state-dependent rates. For each case, we present detailed numerical examples for both measurement and the optimization of supply chain responsiveness.     

Improved approximations for the Erlang loss model

Stochastic loss networks are often very effective models for studying the random dynamics of systems requiring simultaneous resource possession. Given a stochastic network and a multi-class customer workload, the classical Erlang model renders the stationary probability that a customer will be lost due to insufficient capacity for at least one required resource type. Recently a novel family of slice methods has been proposed by Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) to approximate the stationary loss probabilities in the Erlang model, and has been shown to provide better performance than the classical Erlang fixed point approximation in many regimes of interest. In this paper, we propose some new methods for loss probability calculation. We propose a refinement of the 3-point slice method of Jung et al. (Proceedings of ACM SIGMETRICS conference on measurement and modeling of computer systems, pp. 407–418, 2008) which exhibits improved accuracy, especially when heavily loaded networks are considered, at comparable computational cost. Next we exploit the structure of the stationary distribution to propose randomized algorithms to approximate both the stationary distribution and the loss probabilities. Whereas our refined slice method is exact in a certain scaling regime and is therefore ideally suited to the asymptotic analysis of large networks, the latter algorithms borrow from volume computation methods for convex polytopes to provide approximations for the unscaled network with error bounds as a function of the computational costs.     

Dynamic Capacity Acquisition and Assignment under Uncertainty

Given a set of m resources and n tasks, the dynamic capacity acquisition and assignment problem seeks a minimum cost schedule of capacity acquisitions for the resources and the assignment of resources to tasks, over a given planning horizon of T periods. This problem arises, for example, in the integrated planning of locations and capacities of distribution centers (DCs), and the assignment of customers to the DCs, in supply chain applications. We consider the dynamic capacity acquisition and assignment problem in an environment where the assignment costs and the processing requirements for the tasks are uncertain. Using a scenario based approach, we develop a stochastic integer programming model for this problem. The highly non-convex nature of this model prevents the application of standard stochastic programming decomposition algorithms. We use a recently developed decomposition based branch-and-bound strategy for the problem. Encouraging preliminary computational results are provided.     

Goodwill hunting and profit sharing: Decision-making in a newspaper chain

A generalised equilibrium solution to the stochastic two-echelon newsvendor problem is achievable when formulated in the context of some cooperation and coordination between the primal (retailer) and dual (manufacturer) operators. We build on previous work detailing this equilibrium solution and apply it to the newspaper business. The solution incorporates changes in variability encountered due to promotional activity which extends the efficient frontier. We also consider consequences for profit and goodwill costs of identifying an equilibrium solution when additional income is generated from a source outside of the supply chain, such as advertising. We generalise to the supply chain network where there is some knowledge of demand or supply distributions further up or down the supply chain. We find that the primal–dual formulation and equilibrium solution apply to interactions between components of supply chain networks and illustrate with the transition to the direct distribution of newspapers.     

The research on optimization of auto supply chain network robust model under macroeconomic fluctuations

Considering the uncertainty of the macroeconomic environment, the robust optimization method is studied for constructing and designing the automotive supply chain network, and based on the definition of robust solution a robust optimization model is built for integrated supply chain network design that consists of supplier selection problem and facility location–distribution problem. The tabu search algorithm is proposed for supply chain node configuration, analyzing the influence of the level of uncertainty on robust results, and by comparing the performance of supply chain network design through the stochastic programming model and robustness optimize model, on this basis, determining the rational layout of supply chain network under macroeconomic fluctuations. At last the contrastive test result validates that the performance of tabu search algorithm is outstanding on convergence and computational time. Meanwhile it is indicated that the robust optimization model can reduce investment risks effectively when it is applied to supply chain network design.