Integer and constraint programming models for the straight and U-shaped assembly line balancing with hierarchical worker assignment problem

It may be very difficult to achieve the optimal shift schedule in call centers which have highly uncertain and peaked demand during short time periods. Overlapping shift systems are usually designed for such cases. This paper studies shift scheduling and rostering problems for inbound call centers where overlapping shift systems are used. An integer programming model that determines which shifts to be opened and how many operators to be assigned to these shifts is proposed for the shift scheduling problem. For the rostering problem both integer programming and constraint programming models are developed to determine assignments of operators to all shifts, weekly days-off, and meal and relief break times of the operators. The proposed models are tested on real data supplied by an outsource call center and optimal results are found in an acceptable computation time. An improvement of 15% in the objective function compared to the current situation is observed with the proposed model for the shift scheduling problem. The computational performances of the proposed integer and constraint programming models for the rostering problem are compared using real data observed at a call center and simulated test instances. In addition, benchmark instances are used to compare our Constraint Programming (CP) approach with the existing models. The results of the comprehensive computational study indicate that the constraint programming model runs more efficiently than the integer programming model for the rostering problem. The originality of this research can be attributed to two contributions: (a) a model for shift scheduling problem and two models for rostering problem are presented in detail and compared using real data and (b) the rostering problem is considered as a task-resource allocation and considerably shorter computation times are obtained by modeling this new problem via CP.

Integration of balancing and preventive maintenance in straight and U-shaped resource-dependent assembly lines: MILP model and memetic algorithm

U-shaped Line (UL) utilizes many manufacturing industries. It applies the just-in-time principle, the lean manufacture, and the quality improvement. It reduces the waste in the manufacturing operation. This paper presents two UL models which consist of eight certain tasks and three uncertain tasks. Two UL models include UL No.1 and UL No.2. The uncertain tasks assume the time distribution that is discrete. The uncertain task time of UL No.1 classifies to three types. The uncertain task time of UL No.2 classifies to five types. The objective function of two UL models is the minimum workstations. Two UL models formulate on a zero-one integer linear programming. This academic work applies MATLAB R2014a which solves the solution of two models. The procedure is run by INTLINPROG toolbox. The solution of the uncertain tasks for UL No.1 is the optimistic time. The solution of the uncertain tasks for UL No.2 is the most optimistic time. The number of workstations of UL No.2 is less than the number of workstations of UL No.1. The most early finish tasks which assign along the UL line affect the minimum workstations.

Collaborative robots are progressively employed to support human workers in assembly tasks or independently assigned to one station to complete assembly tasks in U-shaped assembly lines. This study develops two exact methods, based on constraint programming (CP) model and Combinatorial Benders’ decomposition algorithm (CBDA), to tackle the U-shaped assembly line balancing problem with collaborative robots. The CBDA is based on distinct decomposition strategies that address the master problem and the subproblem, formulated by a mixed integer linear programming (MILP) model and a CP model, which is designed to obtain a real objective value and generate cuts that refine the master problem. Additionally, MILP-based and CP-based local search techniques are proposed to improve the algorithm's performance. The computational study demonstrates that both the proposed methods, namely CP and CBDA, outperform the current state-of-the-art methods (the MILP model and simulated annealing algorithm). Furthermore, the CP outperforms the CBDA in terms of the number of optimal solutions, achieving the optimal solutions for 574 out of 1500 test instances, and might be regarded as the new state-of-the-art methodology.

Effective methods for solving the Bi-criteria p-Center and p-Dispersion problem

A comparison of integer and constraint programming models for the deficiency problem

Manufacturing industries these days are more concerned about the energy consumption due to the increasing energy cost. It is observed that industries can achieve significant savings in the energy cost even when a small percentage of energy consumption is reduced. In a manufacturing industry, assembly lines are equipped with robots to perform the assembly tasks and there is a need for efficiently balancing the assembly line by reducing the energy consumption during the production phase. The authors could not find any research on optimizing energy consumption in U-shaped robotic assembly line systems to date. The objective of this paper is to propose an optimization models with an objective of minimizing the energy consumption in a U-shaped robotic assembly line when the number of workstations are fixed. Since the assembly line balancing problems falls under the category of NP-hard, an efficient bio inspired algorithm is implemented to solve the problem. The model proposed is very well applicable for automobile assembly line where robots are employed. The energy consumption is evaluated on the benchmark data and energy consumption obtained by the U-shaped robotic assembly line is compared with the energy consumption obtained with straight robotic assembly line. The cycle time of the layouts are also compared. The results obtained using this proposed model can be used for the decision making process in the industry. The paper also proposes an optimization model for minimizing the cycle time. The energy consumption of the assembly line when the cycle time is minimized is evaluated and presented.

In this work, it is presented an exact method to solve the Single Container Loading Problem, which aims at deciding which items should be packed into the container in order to attain the maximum loaded value. The method is derived from the resolution of integer and constraint programming models. One of the integer programming models is a relaxation for the three-dimensional packing problem related to arranging items into the container. Besides that, it is measured how constraints related to priority conditions and vertical and horizontal load cargo stability can impact on the solution. Instances from the literature are solved in order to assess the method behavior in relation to the occupied volume and runtime. It has been observed that the highest volume losses have happened when the priority conditions are taken into consideration, while the runtime has increased when the vertical and horizontal stability constraints are considered.

This paper investigates the skiving and cutting stock problem (SCSP) encountered in the paper and plastic film industries, in which a set of nonstandard reels generated from previous cutting processes are used to produce finished rolls through the skiving and cutting process. First, reels are skived together lengthwise to form a reel‐pyramid (a polygon), and then the reel‐pyramid is cut into finished rolls of small widths. Depending on if a reel can be divided lengthwise into subreels to form the reel‐pyramid, the problem can be classified into divisible SCSP (DSCSP) and indivisible SCSP (ISCSP). In this paper, two integer programming (IP) models are proposed for DSCSP and ISCSP, respectively. A sequential value correction procedure combined with the two IP models (SVCTIP) is developed to solve the two SCSPs. The effectiveness of the SVCTIP is demonstrated through extensive computational tests.

Evaluating the solution performance of IP and CP for berth allocation with time-varying water depth

Decision-making is a complex problem in all fields of production, because decision makers have to find the most suitable solution alternative among the numerous, while the solution of the problem is limited by multiple, usually conflicting constraints. In the Industry 4.0 era, one of the most widely used production lines are the U-shaped production lines, which focus on the elimination of waste through a high utilization of workers. It means, that worker-machine assignment plays a significant role in the optimization of production processes in a U-shaped production line. The current investigation proposes a novel absorbing Markov chain (AMC) optimization approach to support the decision making regarding worker selection and assignment. The proposed approach integrates the AMC and the performance analysis of the production process. The numerical results validated the decision making model and showed that optimal worker-machine assignment can lead to about 20% production cost reduction, while the key performance indicators (KPI) of the U-shaped production line are significantly increased. The sensitivity analysis of influencing factors made it possible to identify the critical factors of this decision making problem, such as the qualification of operators, time of technological and logistics operations, and maintenance policy.

Facing the increasingly competitive market environment, assembly lines are gained attention because of the assembly process expenditure consumes more than 20 % of the manufacturing cost, and also improve its products to meet demand. In this paper, an attempt has been made to develop worker-task assigned to workstation heuristic (W-TAWH) approach for solving mixed-model assembly line balancing problem (M-MALBP), in which the assembly tasks have to be assigned to workstations, and each workstation needs to select only one of the available operators to perform the assigned tasks corresponding to the straight and U-shaped assembly lines with the objective minimum cycle time. The performance of the developed approach was evaluated and validated through applying the practical case in the Dayla State Company for Electrical Industries (DSCEI) particularly in the electric transformer factory (ETF). Taguchi method was used to evaluate the contribution of each one of the considerations in the assembly line are solution approach, layout, sequence vector (SV), and workstation numbers. All results proved the stated considerations have impact significant in any trying to re-balance the assembly line.

Integer programming models for logical layout design of modular machining lines

Balancing U-shaped assembly lines with resource dependent task times: A Simulated Annealing approach

A resource-constrained identical parallel machine scheduling problem with machine eligibility restrictions is investigated in this study. For the considered problem, three optimization models; an integer programming (IP) model, a constraint programming (CP) model and a combined IP/CP model are developed. A problem-based search procedure to be used in CP and IP/CP combined models is also proposed to give quick and efficient results. All three optimization models are constructed and solved in OPL Studio 3.7™ setting 1000 second run-time limit. Computational results show that the combined IP/CP OPL™ model with the proposed problem-based search procedure not only achieves magnitude reduction in computational time but also gives optimal results in 174 out of 200 test problems, while IP and CP models prove optimality in only 47 and 6 problems, respectively. Finally, computational results are also analysed and discussed in terms of various problem parameters.