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.     

Solving the heterogeneous fixed fleet open vehicle routing problem by a combined metaheuristic algorithm

The vehicle routing problem (VRP) is a well-known combinatorial optimisation problem and holds a central place in logistics management. Many exact, heuristic and metaheuristic approaches have been proposed to solve VRP. An important variant of the VRP arises when a ?eet of vehicles is fixed and characterised by different capacities for distribution activities. The problem is known as the heterogeneous fixed fleet VRP (HFFVRP). The HFFVRP is a natural generalisation of the VRP with several vehicle types, each type being defined by a capacity, a fixed cost and a cost per distance unit, and can cover more practical situations in transportation. This problem consists of determining a set of vehicle trips of minimum total length in which a set of customers is to be satisfied in the demand constraints using identical vehicles with limited capacity. If open routes instead of closed ones are considered in the HFFVRP, the problem becomes a heterogeneous fixed fleet Open VRP (HFFOVRP) which has numerous applications in industrial and service problems. In this paper, a bone route algorithm which uses the tabu search as an improved procedure is utilised to solve the HFFOVRP. The proposed algorithm was tested empirically on a 24 of generated VRPs, and compared with elite ant system and ant colony system. In all cases, the proposed algorithm finds the best-known solutions within a reasonable time.     

Implementing factory demand response via onsite renewable energy: a design-of-experiment approach

This paper proposes the implementation of demand response (DR) programmes in large manufacturing facilities featuring distributed wind and solar energy. Manufacturing facilities are high consumers of electric power. For this reason, these facilities usually pay exorbitant utility bills, which could be as much as $10–20 million per year. A high consumption of electricity also means that upstream fossil-fuelled power plants must release thousands of metric tonnes of carbon annually during the generation of electricity. DR contracts offer a lower utility rate in return for a load reduction during contingent events (i.e. peak hours). This paper covers the modelling and implementation of an interruptible/curtailable DR programme participated by a manufacturer that possesses onsite renewable generation units. These complementary energy resources allow the manufacturer to meet the curtailment requirements without causing any major electricity shortage that adversely affects the normal production schedule. We developed a stochastic programming model to determine the capacity of the wind turbine and solar panels that maximise the DR programme savings. The optimal solutions are derived based on central composite design methodology.     

An a Priori Bounded Model for Transportation Problems with Stochastic Demand and Integer Solutions

A linear approximation model is developed for transportation problems with stochastic demand where integer solutions are required. The technique reduces the stochastic integer programming problem to a deterministic linear approximating problem which can be solved as a capacitated transportation problem. Either the transportation algorithm or the primal-dual algorithm may be used thereby insuring integer solutions.     

New approach for solving intuitionistic fuzzy multi-objective transportation problem

Multi-objective transportation problem (MOTP) under intuitionistic fuzzy (IF) environment is analysed in this paper. Due to the fluctuation of market scenario, we assume that the transportation cost, the supply and the demand parameters are not always precise. Hence, the parameters are imprecise, i.e., they are IF numbers. Considering the specific cut interval, the IF transportation cost matrix is converted to interval cost matrix in our proposed problem. Again, using the same concept, the IF supply and the IF demand of the MOTP are reduced to the interval form. Then the proposed MOTP is changed into the deterministic MOTP, which includes interval form of the objective functions. Two approaches, namely intuitionistic fuzzy programming and goal programming, are used to derive the optimal solutions of our proposed problem, and then the optimal solutions are compared. A numerical example is included to illustrate the feasibility and the applicability of the proposed problem. Finally, we present the conclusions with the future scopes of our study.     

A tree-search method for solving a cutting stock assignment problem

Many production environments such as carpet or flat glass manufacturing have linked operations that perform completely different activities. In this paper, we consider a two-stage manufacturing process involving a cutting operation, followed by an assignment operation. Raw material is cut to meet product demand with minimum trim loss, and assignments are made to minimize resource requirements. This cutting stock assignment problem is formulated as a large-scale, mixed-integer nonlinear programming problem. We propose a solution methodology based on decomposition and tree search heuristic strategies. We report on extensive computational experiments on a wide range of problems, and apply statistical techniques to determine significant factors. For all small-size problems tested, our method found the exact optimal solution. For practical-size problems, our method was about two orders of magnitude faster and produced solutions that were one-third better than tabu search.     

Optimization of transit network layout and headway with a combined genetic algorithm and simulated annealing method

This article proposes a methodology for optimizing transit networks, including both route structures and headways. Given information on transit demand, transit fleet size and street network in the transit service area, the methodology seeks to minimize transfers and total user cost while maximizing service coverage. The goal is to provide an effective mathematical solution procedure with minimal reliance on heuristics to solve large-scale transit network optimization problems. This article describes the representation of the transit route network and the associated network search spaces, the representation of route network headways and the associated search spaces, the total user cost objective functions, and a stochastic global search scheme based on a combined genetic algorithm and simulated annealing search method. The methodology has been tested with published benchmark problems and applied to a large-scale realistic network optimization problem. The results show that the methodology is capable of producing improved solutions to large-scale transit network design problems.     

A Scheduling Algorithm for the Unbalanced Production Line

This paper presents procedures for obtaining feasible fractional and integer assignments which can be used to schedule manpower for the unbalanced production line. The objective is to minimize the cost of the total in-process inventory. A mathematical model is formulated and then used to calculate fractional assignments using linear programming and integer assignments using integer programming. An algorithm is then developed which provides the equivalent fractional solution as obtained from linear programming followed by a heuristic algorithm which converts these fractional assignments to feasible integer assignments. Sample problems and their solutions are provided to illustrate the assignment procedures.     

A robust optimization approach for the capacitated vehicle routing problem with demand uncertainty

In this paper we introduce a robust optimization approach to solve the Vehicle Routing Problem (VRP) with demand uncertainty. This approach yields routes that minimize transportation costs while satisfying all demands in a given bounded uncertainty set. We show that for the Miller-Tucker-Zemlin formulation of the VRP and specific uncertainty sets, solving for the robust solution is no more difficult than solving a single deterministic VRP. Our computational results on benchmark instances and on families of clustered instances show that the robust solution can protect from unmet demand while incurring a small additional cost over deterministic optimal routes. This is most pronounced for clustered instances under moderate uncertainty, where remaining vehicle capacity is used to protect against variations within each cluster at a small additional cost. We compare the robust optimization model with classic stochastic VRP models for this problem to illustrate the differences and similarities between them. We also observe that the robust solution amounts to a clever management of the remaining vehicle capacity compared to uniformly and non-uniformly distributing this slack over the vehicles.     

The Uncapacitated Facility Location Problem With Primary and Secondary Facility Requirements

We consider the problem of locating uncapacitated facilities among a set of potential sites to minimize cost of serving a number of demand points each requiring service from two different facilities. This problem has many potential applications. One such application is location of emergency service facilities where it is desirable to have a primary and back-up service facility wthin a certain distance from every district An efficient solution procedure is developed. This procedure is tested on a number of problems and computational results are reported. It is compared to a state of the art commercial linear/integer programming package and found to be around two orders of magnitude faster than this package. It is also compared to a state of the art special purpose agorithm for the simple uncapacitated facility location problem to investigate the computational implications of introducing secondary service requirements. The model is used to illustrate the effect of considering secondary service on the spatial characteristics of the optimal set of locations. The model is further demonstrated on a “real life” example with 625 demand points and 30 potential facility locations.     

Multi-scale reliability analysis and updating of complex systems by use of linear programming

Complex systems are characterized by large numbers of components, cut sets or link sets, or by statistical dependence between the component states. These measures of complexity render the computation of system reliability a challenging task. In this paper, a decomposition approach is described, which, together with a linear programming formulation, allows determination of bounds on the reliability of complex systems with manageable computational effort. The approach also facilitates multi-scale modeling and analysis of a system, whereby varying degrees of detail can be considered in the decomposed system. The paper also describes a method for computing bounds on conditional probabilities by use of linear programming, which can be used to update the system reliability for any given event. Applications to a power network demonstrate the methodology.     

A Lagrangean heuristic for integrated production and transportation planning problems in a dynamic, multi-item, two-layer supply chain

We present a Lagrangean-based decomposition that is used to generate solutions for an integrated production and transportation planning problem in a two-stage supply chain. This supply chain consists of a number of facilities, each capable of producing the final products, and a number of retailers. It is assumed that the retailers' demands are known and deterministic, and that there are production capacity constraints. The problem is formulated as a multi-commodity network flow problem with fixed charge costs which is a NP-hard problem. An alternative formulation is provided whose linear programming relaxation gives tighter lower bounds. The quality of the lower and upper bounds from the Lagrangean decomposition is tested on a large set of randomly generated problems.     

Route-reduction-based dynamic programming for large-scale satellite range scheduling problem

Satellites offer many services through communication with stations, such as tracking, navigation, telecommand uplink, earth observation, etc. How to coordinate these services is referred to as the satellite range scheduling problem (SRSP). In the research, it is found that only the resources (referring to time slots of stations) requested by more than one satellite simultaneously influence scheduling results. These resources are called critical resources and selected as scheduling elements, which makes some jobs optimally served in advance and the problem be decomposable into a multi-stage decision process, so dynamic programming is suitable to be employed. For large-scale SRSPs, a route-reduction-based dynamic programming (RR-DP) is presented, wherein a multi-level route reduction strategy is adopted to alleviate ‘the curse of dimensionality’. Experimental results reveal that RR-DP can find optimal solutions for small-to-medium sized problems and outperforms state-of-the-art methods for large-scale problems.     

A Dynamic Programming Approach to a Bidder Selection Problem

This paper deals with a set of combinatorial decision problems that arise in large-scale governmental or military procurement operations. After stating the problems, they are then mathematically formulated as linear integer programming problems. However, because a specified sensitivity analysis is required, a dynamic programming approach is shown to give all solutions needed after one pass through the DP tableaus. A model has been implemented and is currently being used by a large buying activity of the Department of the Army.     

MODELING THE EVOLUTION OF DEMAND FORECASTS ITH APPLICATION TO SAFETY STOCK ANALYSIS IN PRODUCTION/DISTRIBUTION SYSTEMS

In this paper, we propose a general probabilistic model for modeling the evolution of demand forecasts, referred to as the Martingale Model of Forecast Evolution (MMFE). We combine the MMFE with a linear programming model of production and distribution planning implemented in a rolling horizon fashion. The resulting simulation methodology is used to analyze safety stock levels for a multi-product/multi-plant production/distribution system with seasonal stochastic demand. In the context of this application we demonstrate the importance of good forecasting.     

Heuristic for two-dimensional homogeneous two-segment cutting patterns

This article deals with the guillotine-constrained two-dimensional cutting problem, where a guillotine is used to cut the stock plate into rectangular pieces, such that the pattern value (the total value of the pieces produced) is maximized, observing the constraint that the frequency of each piece type should not exceed the demand. Homogeneous two-segment (HTS) cutting patterns are considered to simplify the cutting process. Each HTS pattern includes two segments, each segment contains homogeneous strips of the same direction, and each homogeneous strip contains pieces of the same type. A heuristic is presented for generating HTS patterns. It is based on dynamic programming and branch-and-bound techniques. The computational results indicate that the heuristic is able to generate solutions close to optimal, and is adequate for solving large-scale instances.     

Optimization models for the dynamic facility location and allocation problem

The design of logistic distribution systems is one of the most critical and strategic issues in industrial facility management. The aim of this study is to develop and apply innovative mixed integer programming optimization models to design and manage dynamic (i.e. multi-period) multi-stage and multi-commodity location allocation problems (LAP). LAP belong to the NP-hard complexity class of decision problems, and the generic occurrence requires simultaneous determination of the number of logistic facilities (e.g. production plants, warehousing systems, distribution centres), their locations, and assignment of customer demand to them. The proposed models use a mixed integer linear programming solver to find solutions in complex industrial applications even when several entities are involved (production plants, distribution centres, customers, etc.). Lastly, the application of the proposed models to a significant case study is presented and discussed.     

Active demand management for substitute products through price optimisation

This paper presents a systematic mathematical programming approach for active demand management in process industries. The proposed methodology aims to determine optimal pricing policies as well as output levels for substitute products, while taking into consideration manufacturing costs, resource availability, customer demand elasticity, outsourcing and market competition. First, profit maximisation analytical formulae are derived for determining Nash equilibrium in prices for a duopolistic market environment where each company produces only one product. An iterative algorithm is then proposed so as to determine the decision-making process by solving a series of non-linear mathematical programming (NLP) models before determining the Nash equilibrium in prices for the competing companies. The proposed algorithm is extended in order to accommodate the case of multi-product companies, each one selling a set of substitute products at different prices. The applicability of the proposed methodology is demonstrated by a number of illustrative examples.     

GENERATING A LAYOUT FROM A DESIGN SKELETON

In the past, researchers have proposed several types of design skeletons from which a human designer can generate good facilities layouts. Examples are flow graphs, SLP space relationships, bubble diagrams, planar adjacency graphs, matching based adjacency graphs, centroid locations, and cut trees. In this paper, we introduce a linear programming model which efficiently generates a layout from a graphical representation of any design skeleton. We demonstrate how the model can be used to enhance most design skeleton based layout approaches.     

Practical solution approaches to solve a hierarchical stochastic production planning problem in a flexible automated workshop in China

This paper deals with a Hierarchical Stochastic Production Planning (HSPP) problem of Flexible Automated Workshops (FAWs), each with a number of Flexible Manufacturing Systems (FMSs). The problem includes not only the standard (demand, capacity and material supply) uncertainties but also uncertainties in processing times, necessity for rework and scrap. In contrast to most work that only considers either single period or infinite horizons, we also considers multiple time periods and multiple products. One objective of this paper is to determine a cost minimizing production plan for each FMS taking into consideration work-inprocess inventory, work centers overload and underload, cumulative over- and under-production of finished products over a finite time horizon. The HSPP problem is formulated as a stochastic nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. To facilitate the solution procedure, the model is first transformed into a deterministic nonlinear programming model and then into a linear programming model. For medium- or small-scale problems, Karmarkar's algorithm is applied to obtain the solution. For large-scale problem, an interaction/prediction algorithm is used. The effectiveness of these approaches is benchmarked against the linear programming method in Matlab 5.0 in various HSPP settings.