Fuzzy scheduling of a build-to-order supply chain

The overwhelming majority of the literature in the area of supply chain planning and scheduling considers the traditional make-to-stock (MTS) environment. However, manufacturers of assembled products such as cars, computers, furniture, etc. adopt the build-to-order supply chain (BOSC) to become agile in a mass customization process in order to meet diversified customer requirements. In this paper we propose an integrated production–distribution planning model for a multi-echelon, multi-plant and multi-product supply chain operating in a build-to-order (BTO) environment. The uncertainties associated with estimation of the various operational cost parameters are represented by fuzzy numbers. The BOSC scheduling model is thus constructed as a mixed-integer fuzzy programming (MIFP) problem with the goal of reducing the overall operating costs related to component fabrication, procurement, assembling, inspection, logistics and inventory, while improving customer satisfaction by allowing product customization and meeting delivery promise dates at each market outlet. An efficient compromise solution approach by transforming the problem into an auxiliary multi-objective linear programming model is also suggested.     

A model for capacity planning of flexible robotic assembly systems

This paper presents a cost-based model for capacity planning of Flexible Robotic Assembly Systems capable of handling batch assembly of multiple end products. The non-linear integer programming model is based on a specific cell design procedure that considers two important aspects, such as robot selection, and cell configuration, in forming the assembly cell. The model incorporates stochastic variations in the batch arrival rate, batch size, and processing times. The solution procedure for the model is discussed and an example problem is used to demonstrate the use of the model for real world applications.     

Modelling and a tabu search solution for the slab reallocation problem in the steel industry

This paper considers a slab reallocation problem arising from operations planning in the steel industry. The problem involves reallocating steel slabs to customer orders to improve the utilisation of slabs and the level of customer satisfaction. It can be viewed as an extension of a multiple knapsack problem. We firstly formulate the problem as an integer nonlinear programming (INLP) model. With variable replacement, the INLP model is then transformed into a mixed integer linear programming (MILP) model, which can be solved to optimality by MILP optimisers for very small instances. To obtain satisfactory solutions efficiently for practical-sized instances, a heuristic algorithm based on tabu search (TS) is proposed. The algorithm employs multiple neighbourhoods including swap, insertion and ejection chain in local search, and adopts solution space decomposition to speed up computation. In the ejection chain neighbourhood, a new and more effective search method is also proposed to take advantage of the structural properties of the problem. Computational experiments on real data from an advanced iron and steel company in China show that the algorithm generates very good results within a short time. Based on the model and solution approach, a decision support system has been developed and implemented in the company.     

Fuzzy multi-objective optimisation for master planning in a ceramic supply chain

In this paper, we consider the master planning problem for a centralised replenishment, production and distribution ceramic tile supply chain. A fuzzy multi-objective linear programming (FMOLP) approach is presented which considers the maximisation of the fuzzy gross margin, the minimisation of the fuzzy idle time and the minimisation of the fuzzy backorder quantities. By using an interactive solution methodology to convert this FMOLP model into an auxiliary crisp single-objective linear model, a preferred compromise solution is obtained. For illustration purposes, an example based on modifications of real-world industrial problems is used.     

AN ASSIGNMENT METHOD FOR THE PART-MACHINE CELL FORMATION PROBLEM IN THE PRESENCE OF MULTIPLE PROCESS ROUTES

This paper considers the part-machine cell formation decision of the generalized Group Technology (GT) problem in which multiple process routes can be generated for each part. The existing p-median model and similarity coefficient algorithm can solve only small-sized or well-structured cases. An assignment method for the cell formation problem is suggested. This method uses an assignment model which is a simple linear programming. Numerical examples show that the assignment method provides good separable cell formation even for large-sized and ill-structured problems.     

Polymorphic uncertain nonlinear programming approach for maximizing the capacity of V-belt driving

In this paper, a polymorphic uncertain nonlinear programming (PUNP) approach is developed to formulate the problem of maximizing the capacity in a system of V-belt driving with uncertainties. The constructed optimization model is found to consist of a nonlinear objective function and some nonlinear constraints with some parameters which are of uncertain nature. These uncertain parameters are interval parameters, random interval parameters, fuzzy parameters or fuzzy interval parameters. To find a robust solution of the problem, a deterministic equivalent formulation (DEF) is established for the polymorphic uncertain nonlinear programming model. For a given satisfaction level, this DEF turns out to be a nonlinear programming involving only interval parameters. A solution method, called a sampling based interactive method, is developed such that a robust solution of the original model with polymorphic uncertainties is obtained by using standard smooth optimization techniques. The proposed method is applied into a real-world design of V-belt driving, and the results indicate that both the PUNP approach and the developed algorithm are useful to the optimization problem with polymorphic uncertainty.     

Pattern-set generation algorithm for the one-dimensional multiple stock sizes cutting stock problem

A pattern-set generation algorithm (PSG) for the one-dimensional multiple stock sizes cutting stock problem (1DMSSCSP) is presented. The solution process contains two stages. In the first stage, the PSG solves the residual problems repeatedly to generate the patterns in the pattern set, where each residual problem is solved by the column-generation approach, and each pattern is generated by solving a single large object placement problem. In the second stage, the integer linear programming model of the 1DMSSCSP is solved using a commercial solver, where only the patterns in the pattern set are considered. The computational results of benchmark instances indicate that the PSG outperforms existing heuristic algorithms and rivals the exact algorithm in solution quality.     

A realistic multi-manned five-sided mixed-model assembly line balancing and scheduling problem with moving workers and limited workspace

The assembly line balancing problem can completely vary from one production line to the other. This paper deals with a realistic assembly line for the automotive industry inspired by Fiat Chrysler Automotive in North America and Parskhodro in Iran (both large-scale automotive companies). This problem includes some specific requirements that have not been studied in the literature. For example, the assembly line is five-sided, and workers can move along these sides. Due to the limited workspace, all the sides cannot work simultaneously at one station. First, a mixed integer linear programming model is proposed for the problem. Then, the model is improved to have a tighter linear relaxation. Moreover, an effective logic-based Benders’ decomposition algorithm is developed. After careful analysis of problem’s structure, three propositions are introduced. The master problem is well restricted by eight valid inequalities. Two different sub-problem types are defined to extract more information from the master problem’s solution. In this case, the algorithm adds effective cuts that reduce the solution space to the extent possible at each iteration. Thus, the number of iterations is significantly cut down. The performance of the model and algorithm, as well as improvement made on both, is evaluated.     

A generalized interval fuzzy mixed integer programming model for a multimodal transportation problem under uncertainty

A generalized interval fuzzy mixed integer programming model is proposed for the multimodal freight transportation problem under uncertainty, in which the optimal mode of transport and the optimal amount of each type of freight transported through each path need to be decided. For practical purposes, three mathematical methods, i.e. the interval ranking method, fuzzy linear programming method and linear weighted summation method, are applied to obtain equivalents of constraints and parameters, and then a fuzzy expected value model is presented. A heuristic algorithm based on a greedy criterion and the linear relaxation algorithm are designed to solve the model.     

Aggregate production planning in the automotive industry with special consideration of workforce flexibility

We present a new mixed integer linear programming approach for the problem of aggregate production planning of flowshop production lines in the automotive industry. Our model integrates production capacity planning and workforce flexibility planning. In contrast to traditional approaches, it considers discrete capacity adaptations which originate from technical characteristics of assembly lines as well as from work regulations and shift planning. In particular, our approach takes change costs into account and explicitly represents a working time account via a linear approximation. A solution framework containing different primal heuristics and preprocessing techniques is embedded into a decision support system. Finally, we present an illustrative case study and computational results on problem instances of practically relevant complexity.     

Optimization procedures for simultaneous road rehabilitation and bridge replacement decisions in highway networks

A road-bridge rehabilitation model is formulated as a mixed non-linear programming problem with linear constraints. The purpose of the model is to minimize user travel costs under limited availability of funds. Two constraints are related to budget availability for road rehabilitation and bridge replacement (or rehabilitation). For a given set of replaced bridges, the problem is reduced to a continuous non-linear programming problem that can be further decomposed into a traffic assignment problem (TAP) and a road rehabilitation budget allocation problem (RBAP). The solution to the non-linear problem is found by iteratively solving the TAP and the RBAP. Since the TAP has a non-convex objective function, its solution is only guaranteed to be a local optimum. Several local optima are obtained at each branch of the search tree to estimate a lower confidence limit on the user cost of a global solution.     

A scheduling problem in glass manufacturing

In this paper, a production scheduling problem in glass manufacturing is studied. The production facility consists of multiple identical production lines and each production line includes a number of serially arranged machines. The production is characterized by semi-ordered processing times in each product family, and the last machine in each production line is a bottleneck machine. Significant changeover times are required when products of different families are produced on a production line. The scheduling problem was modeled as a parallel no-delay flowshop scheduling problem (PNDFSP). The PNDFSP combines the parallel machine scheduling problem (PMSP) with the no-delay flowshop scheduling problem (NDFSP). While PMSP and NDFSP have received considerable attention in the literature, PNDFSP has not been well studied. A mixed-integer programming formulation is developed and an efficient heuristic algorithm is proposed. The sequential heuristic algorithm considers simultaneously the line changeover time, no-delay effect, and line utilization in assigning product families to the production lines. The computational results are reported.     

Application of simulated annealing to a linear model forthe formulation of machine cells ingroup technology

The central issue in group technology is the cell formation problem, which involves the grouping of parts into families and machines into cells, so that parts with similar manufacturing (and design) attributes are identified and processed by dedicated cells of machines. In the present work, the cell formation problem is modelled as a linear integer programming problem with the objective of minimizing the number of intercellular moves subject to cell-size constraints and taking into account the machine operation sequence of each part. An interesting feature of the proposed formulation is that there is no need of specifying a priori the number of cells to be used, which is automatically adjusted within the solution procedure. A very efficient random search heuristic algorithm, based on the simulated annealing method, is adopted for its solution. The heuristic is tested on a number of problems and its performance is evaluated. Subsequently, a straight forward model is presented to identify the families of parts which are to be processed by the corresponding machine cells.     

A manufacturing network design model based on processor and worker capabilities

This paper presents an optimization methodology to design networks of manufacturing facilities producing several products under deterministic demand. The bill of materials and the operations for each product are taken into account through the use of a product-state graph. Starting from the current state of the manufacturing network, the approach considers a multi-period planning horizon. For each period it specifies the facilities to open within the set of current and potential facilities, the mission for each of the centres in the selected facilities, the equipment to be used for producing the goods, and the structure of the network. Taking human resource competencies into account, the approach selects the type of workers to use for executing the manufacturing tasks. The transfer of resources between plants is also considered. A multi-period mixed integer linear programming model is formulated, a solution method based on the addition of specialized cuts is proposed and computational results are presented.     

Mathematical model and solution algorithms for selective disassembly sequencing with multiple target components and sequence-dependent setups

This study considers selective disassembly sequencing under the sequential disassembly environment in which one component is obtained at each disassembly operation. The problem is to determine the sequence of disassembly operations to obtain multiple target components of a used or end-of-life product for the purpose of repair, reuse, remanufacturing, disposal, etc. In particular, we consider sequence-dependent setups in which setup costs depend on the disassembly operation just completed and on the operation to be processed. The problem is represented as a disassembly precedence graph and then a new integer programming model is suggested for the objective of minimising the total disassembly cost. After it is proved that the problem is NP-hard, we suggest two types of heuristics: (1) branch and fathoming algorithm for small-to-medium-sized instances; and (2) priority-rule-based algorithm for large-sized instances. A series of computational experiments, i.e., effectiveness of the new integer programming model and performances of the two heuristic types, were done on various test instances, and the results are reported. In addition, to show the applicability of the mathematical model and the solution algorithms, a case study is reported on an end-of-life electronic calculator.     

Filter allocation and replacement strategies in fluid power system under uncertainty: a fuzzy robust nonlinear programming approach

A fuzzy robust nonlinear programming model is developed for the assessment of filter allocation and replacement strategies in hydraulic systems under uncertainty. It integrates the methods of fuzzy mathematic programming (FMP) and robust programming (RP) within the mixed integer nonlinear programming framework, and can facilitate dynamic analysis and optimization of filters allocation and replacement planning where the uncertainties are expressed as fuzzy membership functions. In modeling formulation, theory of contamination wear of typical hydraulic components is introduced to strengthen the presentation of relationship between system contamination and work performance. The fuzzy decision space is delimited into a more robust one by specifying the uncertainties through dimensional enlargement of the original fuzzy constraints. The piecewise linearization approach is employed to handle the nonlinearities of problem. The developed method has been applied to a case of planning filter allocation and replacement strategies under uncertainty and the generated optimal solution will help to reduce the total system cost and failure-risk level of the FPS.     

Multi-degree cyclic hoist scheduling with time window constraints

This paper deals with the multi-degree cyclic single-hoist scheduling problem with time window constraints, in which multiple identical parts enter and leave the system during each cycle. We propose an analytical mathematical model and a branch-and-bound algorithm so as to find a cyclic sequence of hoist moves that maximises the throughput. The branch-and-bound algorithm implicitly enumerates the sequence of hoist moves and requires the solution of a specific set of linear programming problems (LPPs). Computational results on benchmark instances and randomly generated test instances are presented.     

The equipment maintenance scheduling problem in a coal production system

This paper addresses an equipment maintenance scheduling problem in a coal production system which includes three consecutive stages: the coal mining stage, the coal washing stage and the coal loading stage. Each stage is composed of different equipment that needs maintenance each day. There exists intermediate storage with finite capacities and the finished products are transported by train. Moreover, some equipment has a different preference for (aversion to) the start time of maintenance (STOM). The objective is to minimise the weighted sum of aversion about STOM, changeover times and train waiting time. We first formulate this problem into a mixed integer linear programming (MILP) model, then a hybrid genetic algorithm (HGA) is proposed to solve it. The proposed method has been tested on a practical coal enterprise in China and some randomly generated instances. Computational results indicate that our algorithm can produce near-optimal solutions efficiently.     

A Branch-and-price algorithm for placement routing for a multi-head beam-type component placement tool

We develop a branch-and-price procedure for a placement routing problem for a multi-head beam-type component placement tool. The problem is modelled as an integer programming model with a huge number of variables, each of which corresponds to a placement route. Its linear programming relaxation is solved by a column generation method. For the column generation subproblem to determine the columns to be added, we develop a dynamic programming procedure. We also propose an effective branching rule to partition the current solution space to eliminate the current fractional solution. Through experiments using real tool data, we observe that the LP relaxation solution value is noticeably close to an integer optimal solution value and hence the integer program formulation and the column generation approach are effective.     

DSS approach for heterogeneous parallel machines scheduling considering proximate supply chain constraints

This paper describes the basis of a Decision Support System (DSS) designed to schedule fertiliser production orders to be delivered within time windows, in plants made up of multiple heterogeneous parallel processors (production lines), considering that fertiliser production rates and nomenclatures depend on lines, that setup times depend on sequence and lines, and taking into account downtime constraints (preventive maintenance?…). A mixed linear programming model is encapsulated in the DSS which considers the schedule’s impacts, immediately upstream and downstream of plants in the supply chain. These side-effects may make the proposed solution unfeasible and the DSS helps redefining the problem to avoid them.