Supply chain network downsizing with product line pruning using a new demand substitution

This paper presents an optimization model for downsizing a multi-product supply chain facing bankruptcy risk, where multi-functional production facilities are shared for producing a group of substitutable products. In order to determine the potential demand after discontinuation of certain product types, the proposed mixed integer programming model incorporates a new general formulation of demand substitution, which allows arbitrary demand diversion and arbitrary replacement rates between products under investigation. The new substitution formulation enables considering uneven substitutions for supply chain network design and therefore it extends currently used substitution approaches. A series of systematically generated downsizing cases confirm the validity of the here proposed approach, and illustrate how downsized chains can successfully adopt to the new circumstances.     

An optimization model for the design of a capacitated multi-product reverse logistics network with uncertainty

In this work the design of a reverse distribution network is studied. Most of the proposed models on the subject are case based and, for that reason, they lack generality. In this paper we try to overcome this limitation and a generalized model is proposed. It contemplates the design of a generic reverse logistics network where capacity limits, multi-product management and uncertainty on product demands and returns are considered. A mixed integer formulation is developed which is solved using standard B&B techniques. The model is applied to an illustrative case.     

On the mixed integer signomial programming problems

This paper proposes an approximate method to solve the mixed integer signomial programming problem, for which the objective function and the constraints may contain product terms with exponents and decision variables, which could be continuous or integral. A linear programming relaxation is derived for the problem based on piecewise linearization techniques, which first convert a signomial term into the sum of absolute terms; these absolute terms are then linearized by linearization strategies. In addition, a novel approach is included for solving integer and undefined problems in the logarithmic piecewise technique, which leads to more usefulness of the proposed method. The proposed method could reach a solution as close as possible to the global optimum.     

On the inventory model with variable lead time and price–quantity discount

In this paper, we propose a mixed integer optimization approach for solving the inventory problem with variable lead time, crashing cost, and price–quantity discount. A linear programming relaxation based on piecewise linearization techniques is derived for the problem. It first converts non-linear terms into the sum of absolute terms, which are then linearized by goal programming techniques and linearization approaches. The proposed method can eliminate the complicated multiple-step solution process used in the traditional inventory models. In addition, the proposed model allows constraints to be added by the inventory decision-maker as deemed appropriate in real-world situations.     

A continuous DC programming approach to the strategic supply chain design problem from qualified partner set

We present a new continuous approach based on the DC (difference of convex functions) programming and DC algorithms (DCA) to the problem of supply chain design at the strategic level when production of a new market opportunity has to be launched among a set of qualified partners. A well known formulation of this problem is the mixed integer linear program. In this paper, we reformulate this problem as a DC program by using an exact penalty technique. The proposed algorithm is a combination of DCA and Branch and Bound scheme. It works in a continuous domain but provides mixed integer solutions. Numerical simulations on many empirical data sets show the efficiency of our approach with respect to the standard Branch and Bound algorithm.     

Optimal solution of cellular manufacturing system design: Benders' decomposition approach

In this paper, a mathematical model for cellular manufacturing system (CMS) design which incorporates three critical aspects - resource utilization, alternate routings, and practical constraints, is presented. The model is shown to be NP-complete. A linear, mixed-integer version of the model which not only has fewer integer variables compared to most other models in the literature, but one that also permits us to solve it optimally using Benders' decomposition approach is presented. Some results that allow us to solve the problem efficiently as well as computational results with Benders' decomposition algorithm and a modified version are presented.     

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.     

A partitioning algorithm for the network loading problem

This paper proposes a Benders-like partitioning algorithm to solve the network loading problem. The approach is an iterative method in which the integer programming solver is not used to produce the best integer point in the polyhedral relaxation of the set of feasible capacities. Rather, it selects an integer solution that is closest to the best known integer solution. Contrary to previous approaches, the method does not exploit the original mixed integer programming formulation of the problem. The effort of computing integer solutions is entirely left to a pure integer programming solver while valid inequalities are generated by solving standard nonlinear multicommodity flow problems. The method is compared to alternative approaches proposed in the literature and appears to be efficient for computing good upper bounds.     

Multi-mode resource availability cost problem with recruitment and release dates for resources

This paper investigates the multi-mode resource availability cost problem with recruitment and release dates for resources. This problem is a more realistic model and extended case of the resource availability cost problem. The project contains activities interrelated by finish–start precedence relations with zero time lags, which require a set of renewable resources. First, a mixed integer programming formulation is proposed for the problem. Then, simulated annealing (SA) algorithm is proposed to obtain a satisfying solution for this NP-hard problem. The effectiveness of the proposed algorithm is demonstrated through comprehensive experimentation based on 300 test problems. The results are analyzed and discussed.     

An improved local branching approach for train formation planning

The train formation plan (TFP) determines routing and frequency of trains, and assigns the demands to trains. In this paper, an improved local branching algorithm is proposed for the TFP model in Iranian railway. This solution strategy is exact in nature, although it is designed to improve the heuristic behavior of the mixed integer programming (MIP) solver at hand. In the local branching algorithm, additional constraints are built in the model for the binary variables, but in the improved local branching algorithm, the additional constraints are built in the model for integer variables. A state-of-the-art method is applied for parameter tuning using design of experiments approach. To evaluate the proposed solution method, we have simulated and solved twenty test problems. The results show the efficiency and effectiveness of the proposed approach. The proposed algorithm is implemented for Iranian Railway network as a case study.     

Fair transfer price and inventory holding policies in two-enterprise supply chains

A key issue in supply chain optimisation involving multiple enterprises is the determination of policies that optimise the performance of the supply chain as a whole while ensuring adequate rewards for each participant.In this paper, we present a mathematical programming formulation for fair, optimised profit distribution between echelons in a general multi-enterprise supply chain. The proposed formulation is based on an approach applying the Nash bargaining solution for finding optimal multi-partner profit levels subject to given minimum echelon profit requirements.The overall problem is first formulated as a mixed integer non-linear programming (MINLP) model. A spatial and binary variable branch-and-bound algorithm is then applied to the above problem based on exact and approximate linearisations of the bilinear terms involved in the model, while at each node of the search tree, a mixed integer linear programming (MILP) problem is solved. The solution comprises inter-firm transfer prices, production and inventory levels, flows of products between echelons, and sales profiles.The applicability of the proposed approach is demonstrated by a number of illustrative examples based on industrial processes.     

Identification of switched linear systems using subspace and integer programming techniques

We consider the identification of a switched linear system which consists of linear sub-models, with a rule that orchestrates the switching mechanism between the sub-models. Taking a set of switched linear systems and using a state space framework, we show that it is possible to combine subspace methods with mixed integer programming for system identification. The states of the system are first extracted from input–output data using sub-space methods. Once the state variables are known, the switched system is re-written as a mixed logical dynamical (MLD) system and the model parameters are calculated for via mixed integer programming. We report an example at the end of this paper together with simulation results in the presence of noise.     

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.     

Minimising total average cycle stock subject to practical constraints

Silver and Moon (J Opl Res Soc 50(8) (1999) 789–796) address the problem of minimising total average cycle stock subject to two practical constraints. They provide a dynamic programming formulation for obtaining an optimal solution and propose a simple and efficient heuristic algorithm. Hsieh (J Opl Res Soc 52(4) (2001) 463–470) proposes a 0–1 linear programming approach to the problem and a simple heuristic based on the relaxed 0–1 programming formulation. We show in this paper that the formulation of Hsieh can be improved for solving very large size instances of this inventory problem. So the mathematical approach is interesting for several reasons: the definition of the model is simple, its implementation is immediate by using a mathematical programming language together with a mixed integer programming software and the performance of the approach is excellent. Computational experiments carried out on the set of realistic examples considered in the above references are reported. We also show that the general framework for modelling given by mixed integer programming allows the initial model to be extended in several interesting directions.     

Robust optimization for interactive multiobjective programming with imprecise information applied to R&D project portfolio selection

A multiobjective binary integer programming model for R&D project portfolio selection with competing objectives is developed when problem coefficients in both objective functions and constraints are uncertain. Robust optimization is used in dealing with uncertainty while an interactive procedure is used in making tradeoffs among the multiple objectives. Robust nondominated solutions are generated by solving the linearized counterpart of the robust augmented weighted Tchebycheff programs. A decision maker’s most preferred solution is identified in the interactive robust weighted Tchebycheff procedure by progressively eliciting and incorporating the decision maker’s preference information into the solution process. An example is presented to illustrate the solution approach and performance. The developed approach can also be applied to general multiobjective mixed integer programming problems.     

A Metaheuristic to Solve a Location-Routing Problem with Non-Linear Costs

The paper deals with a location-routing problem with non-linear cost functions. To the best of our knowledge, a mixed integer linear programming formulation for the addressed problem is proposed here for the first time. Since the problem is NP-hard exact algorithms are able to solve only particular cases, thus to solve more general versions heuristics are needed. The algorithm proposed in this paper is a combination of a p-median approach to find an initial feasible solution and a metaheuristic to improve the solution. It is a hybrid metaheuristic merging Variable Neighborhood Search (VNS) and Tabu Search (TS) principles and exploiting the synergies between the two. Computational results and conclusions close the paper.     

An integrated fuzzy DEA–Fuzzy simulation approach for optimization of operator allocation with learning effects in multi products CMS

This paper presents an integrated fuzzy data envelopment analysis (FDEA) and fuzzy computer simulation approach for optimization of operator allocation in multi product cellular manufacturing systems (CMS) with learning effects. Operator allocation with learning effects is a challenging issue in flexible manufacturing systems in general and in CMS in particular. The main contribution of this work is taking into consideration various operators layouts and learning effects using fuzzy simulation and fuzzy DEA. FDEA is utilized to assess simulation alternatives in various levels of uncertainty. Previous studies consider only one type of product with crisp inputs, whereas this study considers multi-products and fuzzy set up times and processing times for CMS modeling. In addition, this study considers and integrates learning effects for optimum operators’ allocation. Moreover, more robust CMS assessment indicators are used in the proposed model. A case study illustrates the practicability, effectiveness and superiority of the proposed methodology.     

Design of a recovery network for WEEE collection: the case of Galicia,Spain

This research aims to optimize the design of the reverse logistic network for the collection of Waste of Electric and Electronic Equipment (WEEE), in the Spanish region of Galicia. As a basis for our study a three-phase hierarchical approach is proposed. In the first phase a facility location problem is formulated and solved by means of a mixed integer linear programming; in the second phase a new integer programming formulation for the corresponding heterogeneous fleet vehicle routing problem is presented, and a savings-based heuristic algorithm is developed to efficiently solve the related collection routing problems; in the third phase a simulation study is performed on the collection routes in order to assess the overall performance of the recovery system. The results show a good performance of the proposed procedure, and an improved configuration of the recovery network compared to the one currently in use (particularly transportation costs are reduced by 29.2%).     

Solving a capacitated hub location problem

In this paper we address a problem consisting of determining the routes and the hubs to be used in order to send, at minimum cost, a set of commodities from sources to destinations in a given capacitated network. The capacities and costs of the arcs and hubs are given, and the arcs connecting the hubs are not assumed to create a complete graph. We present a mixed integer linear programming formulation and describe two branch-and-cut algorithms based on decomposition techniques. We evaluate and compare these algorithms on instances with up to 25 commodities and 10 potential hubs. One of the contributions of this paper is to show that a Double Benders’ Decomposition approach outperforms the standard Benders’ Decomposition, which has been widely used in recent articles on similar problems. For larger instances we propose a heuristic approach based on a linear programming relaxation of the mixed integer model. The heuristic turns out to be very effective and the results of our computational experiments show that near-optimal solutions can be derived rapidly.