A robust optimization model for multi-product two-stage capacitated production planning under uncertainty

Production planning (PP) is one of the most important issues carried out in manufacturing environments which seeks efficient planning, scheduling and coordination of all production activities that optimizes the company’s objectives. In this paper, we studied a two-stage real world capacitated production system with lead time and setup decisions in which some parameters such as production costs and customer demand are uncertain. A robust optimization model is developed to formulate the problem in which minimization of the total costs including the setup costs, production costs, labor costs, inventory costs, and workforce changing costs is considered as performance measure. The robust approach is used to reduce the effects of fluctuations of the uncertain parameters with regards to all the possible future scenarios. A mixed-integer programming (MIP) model is developed to formulate the related robust production planning problem. In fact the robust proposed model is presented to generate an initial robust schedule. The performance of this schedule could be improved against of any possible occurrences of uncertain parameters. A case from an Iran refrigerator factory is studied and the characteristics of factory and its products are discussed. The computational results display the robustness and effectiveness of the model and highlight the importance of using robust optimization approach in generating more robust production plans in the uncertain environments. The tradeoff between solution robustness and model robustness is also analyzed.     

Design and planning of supply chains with integration of reverse logistics activities under demand uncertainty

In this paper, a mixed integer linear programming (MILP) formulation is developed for the design and planning of supply chains with reverse flows while considering simultaneously production, distribution and reverse logistics activities. It is also considered products’ demand uncertainty using a scenario tree approach. As main goal the model defines the maximization of the expected net present value and the results provide details on sizing and location of plants, warehouses and retailers, definition of processes to install, establishment of forward and reverse flows and inventory levels to attain. The model is applied to a representative European supply chain case study and its applicability is demonstrated.     

A robust optimization approach to closed-loop supply chain network design under uncertainty

The concern about significant changes in the business environment (such as customer demands and transportation costs) has spurred an interest in designing scalable and robust supply chains. This paper proposes a robust optimization model for handling the inherent uncertainty of input data in a closed-loop supply chain network design problem. First, a deterministic mixed-integer linear programming model is developed for designing a closed-loop supply chain network. Then, the robust counterpart of the proposed mixed-integer linear programming model is presented by using the recent extensions in robust optimization theory. Finally, to assess the robustness of the solutions obtained by the novel robust optimization model, they are compared to those generated by the deterministic mixed-integer linear programming model in a number of realizations under different test problems.     

Optimisation of integrated reverse logistics networks with different product recovery routes

The awareness of importance of product recovery has grown swiftly in the past few decades. This paper focuses on a problem of inventory control and production planning optimisation of a generic type of an integrated Reverse Logistics (RL) network which consists of a traditional forward production route, two alternative recovery routes, including repair and remanufacturing and a disposal route. It is assumed that demand and return quantities are uncertain. A quality level is assigned to each of the returned products. Due to uncertainty in the return quantity, quantity of returned products of a certain quality level is uncertain too. The uncertainties are modelled using fuzzy trapezoidal numbers. Quality thresholds are used to segregate the returned products into repair, remanufacturing or disposal routes. A two phase fuzzy mixed integer optimisation algorithm is developed to provide a solution to the inventory control and production planning problem. In Phase 1, uncertainties in quantity of product returns and quality of returns are considered to calculate the quantities to be sent to different recovery routes. These outputs are inputs into Phase 2 which generates decisions on component procurement, production, repair and disassembly. Finally, numerical experiments and sensitivity analysis are carried out to better understand the effects of quality of returns and RL network parameters on the network performance. These parameters include quantity of returned products, unit repair costs, unit production cost, setup costs and unit disposal cost.     

An integrated model for logistics network design

In this paper we introduce a new formulation of the logistics network design problem encountered in deterministic, single-country, single-period contexts. Our formulation is flexible and integrates location and capacity choices for plants and warehouses with supplier and transportation mode selection, product range assignment and product flows. We next describe two approaches for solving the problem---a simplex-based branch-and-bound and a Benders decomposition approach. We then propose valid inequalities to strengthen the LP relaxation of the model and improve both algorithms. The computational experiments we conducted on realistic randomly generated data sets show that Benders decomposition is somewhat more advantageous on the more difficult problems. They also highlight the considerable performance improvement that the valid inequalities produce in both solution methods. Furthermore, when these constraints are incorporated in the Benders decomposition algorithm, this offers outstanding reoptimization capabilities.     

Batching deteriorating items with applications in computer communication and reverse logistics

We study two deterministic scheduling problems that combine batching and deterioration features. In both problems, there is a certain demand for identical good quality items to be produced in batches. In the first problem, each batch is assigned an individual machine that requires a cost and a time to be activated. All the machines are identical, work in parallel, and always produce good quality items. All the items are available at time zero and they deteriorate while waiting for production. Deterioration results in a linear increase of time and cost of production. In the second problem, there is a single machine that produces good quality as well as defective items in batches. Each batch is preceded by a setup time and requires a setup cost. Defective items have to be reworked on the same machine. They deteriorate while waiting for rework. At a time to be decided, the machine switches from production to rework defective items of the current batch. After rework, every defective item has the required good quality. In both problems, the objective is to find batch partitioning such that a linear combination of the production cost and production completion time is minimized. The two problems are observed at computer service providers and also reverse logistics. In computer service providers, machines and items correspond to communication service channels and information transfer tasks, respectively. We reduce both problems to minimizing a function of one variable representing the number of batches. In an optimal solution of either problem, there are at most two different batch sizes. Linear time algorithms are proposed for both problems.     

Combined location and routing problems for designing the quality-dependent and multi-product reverse logistics network

With a growing awareness of carbon footprints and their impact on environmental degradation, many firms hope to streamline their reverse logistics (RL) operations involving end-of-use products. However, managing end-of-use products can be extremely challenging due to inherent complexity involved in the collection, sorting, transhipment, and processing of these products. Despite numerous challenges, the efficient handling of these products can be a source of competitive advantages. In this regard, a plastic recycling industry in Southern India is no exception. This industry often copes with the problem of picking up recyclable plastic bottles using private collecting agents, transferring those bottles to the initial collection points (ICPs), and then transhipping and consolidating them at the centralized return centres (CRCs) for final shipments to the processing centres where these bottles were treated for recycling. This problem can be further complicated with the dilemma of finding the most ideal locations of ICPs and CRCs and the optimal routing of vehicles serving ICPs and CRCs such that the total RL cost is minimized. To aid the industry in dealing with such RL problems, we developed a mathematical model and then evaluated the performances of that model with the actual data obtained from a case study of the Indian company. Given a lack of efforts in combining the location-routing problem with the balanced allocation problem in the closed-loop supply chain network, the main contribution of this paper includes the simultaneous consideration of location, allocation, and routing decisions. In addition, this paper is one of the first to consider incentive payments, the quality level of products, and multiple types of products.     

Selective capacitated location-routing problem with incentive-dependent returns in designing used products collection network

This paper addresses a generalization of the capacitated location-routing problem (CLRP) arising in the design of a collection network for a company engaged in collecting used products from customer zones. The company offers customers a financial incentive per unit of used products. This incentive determines the quantity of used products which are returned by customers. Moreover, it is not necessary for the company to visit all customer zones or to collect all returns in each visited customer zone. The objective is to simultaneously find the location of collection centers, the routes of vehicles, the value of incentive offered and the amount of used products collected from customer zones, so as to maximize the company's overall profit. We develop two mixed integer linear programming formulations of the problem and a heuristic algorithm based on iterated local search. Extensive computational experiments on this problem demonstrate the effectiveness of the proposed algorithm.     

Reliable design of a logistics network under uncertainty: A fuzzy possibilistic-queuing model

This paper proposes a bi-objective model for designing a reliable network of bi-directional facilities in logistics network under uncertainties. For this purpose, the model utilizes an effective reliability approach to find a robust logistics network design. The objectives of the model are to minimize the total costs and the expected transportation costs after failures of bi-directional facilities of the logistics network. To solve the model, a new solution approach is proposed by combining queuing theory, fuzzy possibilistic programming and fuzzy multi-objective programming. Finally, the computational experiments are provided to illustrate the effectiveness of the proposed model and solution approach.     

A capacity scaling heuristic for the multicommodity capacitated network design problem

In this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem.     

A dynamic pricing approach for returned products in integrated forward/reverse logistics network design

During the last decade, the stringent pressures from environmental and social requirements have spurred an interest in designing a reverse logistics network. In this paper, we address the problem of designing and planning a multi-echelon, multi-period, multi-commodity and capacitated integrated forward/reverse logistics network. Returned products are categorized with respect to their quality levels, and a different acquisition price is offered for each return type. Furthermore, the reservation incentive of customers, the expected price of customers for one unit of used product described by uniform distribution, is applied to model the customers’ return willingness. Due to the fact that the remaining worthwhile value in the used products is the corporation’s key motivation for buying them from customers, a dynamic pricing approach is developed to determine the acquisition price for these products and based on it determine the percentage of returned products collected from customer zones. The used products’ acquisition prices at each time period are determined based on the customers’ return willingness by each collection center.     

An optimal solution to a three echelon supply chain network with multi-product and multi-period

Recently, Kadadevaramath et al. (2012) [1] presented a mathematical model for optimizing a three echelon supply chain network. Their model is an integer linear programming (ILP) model. In order to solve it, they developed five algorithms; four of them are based on a particle swarm optimization (PSO) method and the other is a genetic algorithm (GA). In this paper, we develop a more general mathematical model that contains the model developed by Kadadevaramath et al. (2012) [1]. Furthermore, we show that all instances proved in Kadadevaramath et al. (2012) [1] can easily be solved optimally by any integer linear programming solver.     

Hierarchical facility network planning model for global logistics network configurations

This paper presents a novel hierarchical network planning model for global logistics (GLs) network configurations. The proposed method, which is based on the fundamentals of integer programming and hierarchical cluster analysis methods, determines the corresponding locations, number and scope of service areas and facilities in the proposed GLs network. Therein, a multi-objective planning model is formulated that systematically minimizes network configuration cost and maximizes both operational profit and the customer satisfaction rate. Particularly, potential risk-oriented costs, such as macro-environmental-risk and micro-operational-risk costs are considered in the proposed model. Numerical results indicate that the overall system performance can be improved by up to 11.52% using the proposed approach.     

Modeling reverse logistics process in the agro-industrial sector: The case of the palm oil supply chain

As today’s consumers are more and more concerned with the environmental impacts of products and services they buy, enterprises have been more and more concerned with “green operations”. One of the key aspects of green logistics management is reverse logistics. This paper shows how the potential of managing reverse logistics flows can be implemented in the agro-industrial sector. As an example, the palm oil supply chain is considered. This study is carried out under the focus of the “closed-loop supply chain (CLSC) framework” in which forward and backward product flows are considered simultaneously. A mathematical model is proposed in order to represent the dynamic interaction between flows. The objective function considers energy, cost and economic profits. Different implementation scenarios of recovery processes are proposed and interactions between direct and reverse flows in the chain are evaluated. Results are analyzed using proper statistical tools, showing that the simultaneous analysis of direct and reverse flows positively impact the net economic profits in this complex supply chain of the agro-industrial sector.     

An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty

Planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities, where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist. With the purpose of tackling such difficulties, this paper presents the development of an interval-fuzzy nonlinear programming (IFNP) model for water quality management under uncertainty. Methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left- and right-hand sides of the nonlinear constraints. Uncertainties in water quality, pollutant loading, and the system objective were reflected through the developed IFNP model. The method of piecewise linearization was developed for dealing with the nonlinearity of the objective function. A case study for water quality management planning in the Changsha section of the Xiangjiang River was then conducted for demonstrating applicability of the developed IFNP model. The results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels. It was also indicated that the proposed linearization method was effective in dealing with IFNP problems; uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives; the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals. It also suggested that the linearized method should be used under detailed error analysis in tackling IFNP problems.     

Fuzzy chance-constrained programming model for a multi-echelon reverse logistics network for household appliances

Efficient planning and design of an appropriate reverse logistics network is crucial to the economical collection and disposal of scrapped household appliances and electrical products. Such systems are commonly modelled as mixed-integer programs, whose solutions will determine the location of individual facilities that optimize material flow. One of the major drawbacks of current models is that they do not adequately address the important issue of uncertainty in demand and supply. Another deficiency in current models is that they are restricted to a two-echelon system. This study addresses these deficiencies by embodying such uncertainties in the model using the technique of fuzzy-chance constrained programming, and by extending the model to a three-echelon system. A heuristic in the form of a hybrid genetic algorithm is then employed to generate low-cost solutions. The overall objective is to find economical solutions to the general problem of determining the volume of appliances to be moved between the three echelons of customer base to collection sites, collection sites to disposal centres and disposal centre to landfill centre/remanufacturing centre; and to the problems of positioning the disposal centres and the landfill centre/remanufacturing centres within the problem domain. A case example in China is presented and the quality and robustness of the solutions are explored through sensitivity analysis.     

An integrated approach for collection network design,capacity planning and vehicle routing in reverse logistics

This study considers network design, capacity planning and vehicle routing for collection systems in reverse logistics. The network design and capacity planning problems are to determine the static locations and capacities of collection points as well as the dynamic allocations of demand points to the opened collection points over a planning horizon, and the vehicle routing problem is to determine the number and routes of vehicles in such a way that each collection point must be visited exactly once by one vehicle starting and terminating at the depot while satisfying the return demands at collection points and the vehicle capacity. The objective is to minimize the sum of fixed costs to open collection points and to acquire vehicles as well as variable costs to transport returns at demand points to the opened collection points and travel the opened collection points by vehicles. Unlike the location-routing problems, the integrated problem considered in this study has several features: multi-period dynamic model, capacity planning for collection points, maximum allowable collection distances, etc. To solve the integrated problem, two types of tabu search algorithms, hierarchical and integrated ones, are suggested, and their test results are reported. In particular, the efficiency of the integrated approach is shown by comparing the two algorithm types.     

The value of information in a capacitated closed loop supply chain

We explore the value of information in the context of a firm that faces uncertainty with respect to demand, product returns, recovery yield, and capacity utilization. Capacity is finite and shared between new production and recovery operations. The operational decisions of interest are the quantity of new product to produce, the quantity of returns to recover, and the quantity of returns to dispose. Product recovery is uncertain in that each returned unit can be successfully recovered with a known probability, and otherwise it is discarded at a cost. Demand in a period is satisfied with new production, recovered returns, or a mix of both types.