A multi-objective bi-level location planning problem for stone industrial parks

This paper focuses on a stone industrial park location problem with a hierarchical structure consisting of a local government and several stone enterprises under a random environment. In contrast to previous studies, conflicts between the local authority and the stone enterprises are considered. The local government, being the leader in the hierarchy, aims to minimize both total pollution emissions and total development and operating costs. The stone enterprises, as the followers in the hierarchy, only aim to minimize total costs. In addition, unit production cost and unit transportation cost are considered random variables. This complicated multi-objective bi-level optimization problem poses several challenges, including randomness, two-level decision making, conflicting objectives, and difficulty in searching for the optimal solutions. Various approaches are employed to tackle these challenges. In order to make the model trackable, expected value operator is used to deal with the random variables in the objective functions and a chance constraint-checking method is employed to deal with such variables in the constraints. The problem is solved using a bi-level interactive method based on a satisfactory solution and Adaptive Chaotic Particle Swarm Optimization (ACPSO). Finally, a case study is conducted to demonstrate the practicality and efficiency of the proposed model and solution algorithm. The performance of the proposed bi-level model and ACPSO algorithm was highlighted by comparing to a single-level model and basic PSO and GA algorithms.     

A stochastic production planning problem with nonlinear cost

Most production planning models are deterministic and often assume a linear relation between production volume and production cost. In this paper, we investigate a production planning problem in a steel production process considering the energy consumption cost which is a nonlinear function of the production quantity. Due to the uncertain environment, the production demands are stochastic. Taking a scenario-based approach to express the stochastic demands according to the knowledge of planners on the demand distributions, we formulate the stochastic production planning problem as a mixed integer nonlinear programming (MINLP) model.Approximated with the piecewise linear functions, the MINLP model is transformed into a mixed integer linear programming model. The approximation error can be improved by adjusting the linearization ranges repeatedly. Based on the piecewise linearization, a stepwise Lagrangian relaxation (SLR) heuristic for the problem is proposed where variable splitting is introduced during Lagrangian relaxation (LR). After decomposition, one subproblem is solved by linear programming and the other is solved by an effective polynomial time algorithm. The SLR heuristic is tested on a large set of problem instances and the results show that the algorithm generates solutions very close to optimums in an acceptable time. The impact of demand uncertainty on the solution is studied by a computational discussion on scenario generation.     

A path planning algorithm for industrial robots

Instead of using the tedious process of robot teaching, an off-line path planning algorithm has been developed for industrial robots to improve their accuracy and efficiency. Collision avoidance is the primary concept to achieve such goal. By use of the distance maps, the inspection of obstacle collision is completed and transformed to the configuration space in terms of the robot joint angles. On this configuration map, the relation between the obstacles and the robot arms is obvious. By checking the interference conditions, the collision points are indicated with marks and collected into the database. The path planning is obtained based on the assigned marked number of the passable region via wave expansion method. Depth-first search method is another approach to obtain minimum sequences to pass through. The proposed algorithm is experimented on a 6-DOF industrial robot. From the simulation results, not only the algorithm can achieve the goal of collision avoidance, but also save the manipulation steps.     

Task scheduling and motion planning for an industrial manipulator

In many robotic industrial applications, a manipulator should move among obstacles and reach a set of task-points in order to perform a pre-defined task. It is quite important as well as very complicated to determine the time-optimum sequence of the task-points visited by the end-effector's tip only once assuring that the manipulator's motion through the successive task-points is collision-free.     

A planning and scheduling problem for an operating theatre using an open scheduling strategy

The objective of this paper is to design a weekly surgery schedule in an operating theatre where time blocks are reserved for surgeons rather than specialities. Both operating rooms and places in the recovery room are assumed to be multifunctional, and the objectives are to maximise the utilisation of the operating rooms, to minimise the overtime cost in the operating theatre, and to minimise the unexpected idle time between surgical cases. This weekly operating theatre planning and scheduling problem is solved in two phases. First, the planning problem is solved to give the date of surgery for each patient, allowing for the availability of operating rooms and surgeons. Then a daily scheduling problem is devised to determine the sequence of operations in each operating room in each day, taking into account the availability of recovery beds. The planning problem is described as a set-partitioning integer-programming model and is solved by a column-generation-based heuristic (CGBH) procedure. The daily scheduling problem, based on the results obtained in the planning phase, is treated as a two-stage hybrid flow-shop problem and solved by a hybrid genetic algorithm (HGA). Our results are compared with several actual surgery schedules in a Belgian university hospital, where time blocks have been assigned to either specific surgeons or specialities several months in advance. According to the comparison results, surgery schedules obtained by the proposed method have less idle time between surgical cases, much higher utilisation of operating rooms and produce less overtime.     

A knapsack problem as a tool to solve the production planning problem in small foundries

According to recent research carried out in the foundry sector, one of the most important concerns of the industries is to improve their production planning. A foundry production plan involves two dependent stages: (1) determining the alloys to be merged and (2) determining the lots that will be produced. The purpose of this study is to draw up plans of minimum production cost for the lot-sizing problem for small foundries. As suggested in the literature, the proposed heuristic addresses the problem stages in a hierarchical way. Firstly, the alloys are determined and, subsequently, the items that are produced from them. In this study, a knapsack problem as a tool to determine the items to be produced from furnace loading was proposed. Moreover, we proposed a genetic algorithm to explore some possible sets of alloys and to determine the production planning for a small foundry. Our method attempts to overcome the difficulties in finding good production planning presented by the method proposed in the literature. The computational experiments show that the proposed methods presented better results than the literature. Furthermore, the proposed methods do not need commercial software, which is favorable for small foundries.     

Cross-facility management of production and transportation planning problem

This paper studies 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 product, and a number of retailers. We assume that retailers’ demands are known deterministically and there are no production or transportation capacity constraints. We formulate the problem as a network flow problem with fixed charge costs. This is an NP  -hard problem. To solve the problem we propose a primal-dual based heuristic that generates upper and lower bounds and runs in O(FRT²)$O({\mathit{FRT}}^2)$. The quality of the upper and lower bounds is tested on a large set of randomly generated problems. The maximum error reported for these problems is 4.36% and the maximum running time is 7.65 cpu seconds.     

Method for solving multiobjective aggregate production planning problem with fuzzy parameters

We propose an efficient method that transforms a fuzzy multiple objective linear programming (MOLP) problem model to crisp MOLP model, and an interactive solution procedure that suggest the best compromise aggregate production plans for the multi-period fuzzy multiple objective aggregate production planning (APP) problem.     

Experimental comparison of the switching heuristics for aggregate production planning problem

Two improved versions of the production switching heuristic(PSH), Dominant PSH and Inventory-Ratio-Based PSH are proposed. Extensive computer experiments are performed to evaluated the proposed rules. Both linear and quadratic cost functions are adopted for the comparison study. Also. the influence of seasonality is investigated on the effectiveness of each rule. The results show that the proposed rules outperform the PSH in terms of the total cost, especially when seasonality factor is significant or the unit inventory carrying cost is high.     

A branch-and-price algorithm for an integrated production and inventory routing problem

With globalization, the need to better integrate production and distribution decisions has become ever more pressing for manufacturers trying to streamline their supply chain. This paper investigates a previously developed mixed-integer programming (MIP) model aimed at minimizing production, inventory, and delivery costs across the various stages of the system. The problem being modeled includes a single production facility, a set of customers with time varying demand, a finite planning horizon, and a fleet of homogeneous vehicles. Demand can be satisfied from either inventory held at a customer site or from daily product distribution. Whether a customer is visited on a particular day is determined by an implicit tradeoff between inventory and distribution costs. Once the decision is made, a vehicle routing problem must be solved for those customers who are scheduled for a delivery.A hybrid methodology that combines exact and heuristic procedures within a branch-and-price framework is developed to solve the underlying MIP. The approach takes advantage of the efficiency of heuristics and the precision of branch and price. Implementation required devising a new branching strategy to accommodate the unique degeneracy characteristics of the master problem, and a new procedure for handling symmetry. A novel column generation heuristic and a rounding heuristic were also implemented to improve algorithmic efficiency. Computational testing on standard data sets showed that the hybrid scheme can solve instances with up to 50 customers and 8 time periods within 1 h. This level of performance could not be matched by either CPLEX or standard branch and price alone.     

A study on production planning for CIM

As for the conventional study of CIM system, the critical ratio rule has taken the remaining time until due date into consideration has been commonly utilized for a characteristic of the operational priority rule. In this paper, a characteristic of new priority rule was proposed in order to remove the defect of the critical ratio rule. To put it concretelt, both of backorders and outstandings were introduced into this priority rule as a substitution for considering the due date. The superiority of the proposed rule over the critical ratio rule was proved by the use of the model experiments.     

Dynamic optimization of production planning problem with periodic operation

This paper considers the production planning problem of a firm that produces an item during a repetitive period over an infinite planning horizon. The problem is to determine simultaneously the optimal production policy and the length of the planning period that minimizes a discounted total cost, under the assumption that the initial and final inventory levels are identical. Using optimal control theory, the necessary conditions for optimality are found and transformed into a second-order differential equation. The production time path rate is derived in closed form, and the behaviour of the optimal solution is studied.     

Optimization of production planning problem with continuously distributed time-lags

This paper considers a production and inventory problem in which the utility or potential of an item gradually reduces with the passage of time, such as grain, photographic film and electronic component. The aim of this paper is to determine the production rate of the decaying item in a way that minimizes the current value of total cost using optimal control theory. For the model developed, a computational procedure of finding an optimal solution is developed. The steady-state solution and the properties of the optimal solution for the case of constant rate of decay are discussed.     

Computer simulation of a parametric optimization problem for an industrial process

Results in functional analysis are applied to the computation of the optimal control of a parabolic distributed parameter system. The control term is a coefficient of the state equation, and is computed by the steepest descent method. An a-priori feedback is determined in the case of a constant control on the optimization interval. Numerical results are discussed.     

A robust hierarchical production planning for a capacitated two-stage production system

In this paper, we propose a robust hierarchical production planning approach for a two-stage real world capacitated production system operating in an uncertain environment. The first stage of the system produces a set of semi-finished products having relatively stable annual demands, and the second finishing stage produces finished products having highly variable weekly demands. The fixed production setup costs incurred at the first stage are considerably high. Fixed production setup costs incurred at the second stage are fairly small compared to those of the first stage. We propose an integrated hierarchical planning model, where semi-finished products from the first stage (i.e. the aggregate level) are disaggregated into finished products to be produced in the second stage (i.e. the operational level). As a result of the relatively stable demands and the high setup costs experienced at the first stage, a cyclical aggregate planning model is proposed for production planning at the upper level of the hierarchical plan. Based on this aggregate plan, a modified periodic review policy is then proposed for production planning at the lower level. Finally, a coupling plan, linking the two planning levels, is proposed to ensure the feasibility of the disaggregation process at every period.     

A hybrid genetic approach for solving an integrated multi-objective operating room planning and scheduling problem

In this paper, we propose a multi-objective integer linear programming model aiming at efficiently planning and managing hospital operating room suites. By effectively exploiting a novel hybrid genetic solution approach, the devised optimization model is able to determine, in an integrated way, (i) the operating room time assigned to each surgical specialty, (ii) the operating room time assigned to each surgical team, (iii) the surgery admission planning and (iv) the surgery scheduling. The resulting Pareto frontiers provide a set of “optimal” solutions able to support hospital managers in efficiently orchestrating the involved resources and planning surgeons and surgeries. On this basis, the proposed solution framework could represent a suitable engine for the development of advanced and effective health care management decision support systems.     

Hybrid genetic algorithms and line search method for industrial production planning with non-linear fitness function

Many engineering, science, information technology and management optimization problems can be considered as non-linear programming real-world problems where all or some of the parameters and variables involved are uncertain in nature. These can only be quantified using intelligent computational techniques such as evolutionary computation and fuzzy logic. The main objective of this research paper is to solve non-linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers, which was represented by logistic membership functions using the hybrid evolutionary optimization approach. To explore the applicability of the present study, a numerical example is considered to determine the production planning for the decision variables and profit of the company.     

Laboratory analysis planning system for industrial enterprises

An algorithm for industrial laboratory analysis scheduling is considered. A system of its software implementation intended for scheduling of continuous analyses of raw materials, intermediate and final products at chemical plants is examined.