An Integrated Approach for Shift Scheduling and Rostering Problems with Break Times for Inbound Call Centers

ABSTRACTThe solution to the assembly line balancing with the hierarchical worker assignment problem (ALBHWP) provides the optimal allocation of workers and tasks to the stations that minimise the total worker cost. In the ALBHWP, tasks differ in terms of the qualification requirements of workers, and the qualification levels of workers are hierarchical. In the hierarchical workforce structure, a lower qualified worker can be replaced by higher qualified ones with higher costs, while the vice versa is not applicable. This problem has only been studied for straight assembly lines so far. In this paper, we introduce the ALBHWP for U-shaped assembly lines. We developed integer and constraint programming models for solving the ALBHWP and compared their effectiveness using an extensive set of benchmark instances. We solved the ALBHWP for straight and U-shaped assembly lines comparatively. Constraint programming models have been statistically proven to provide better quality solutions faster than integer programming models. Besides, the CP model outperforms the only available metaheuristic in the literature for the S-ALBHWP in almost all problem sizes. Another observation is that a U-shaped line design is more cost-effective than a straight line design, but solving the ALBHWP for U-shaped lines is more difficult regarding computational complexity.

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

Cell formation deals with grouping of machines and parts in manufacturing systems according to their compatibility. Manufacturing processes are surrounded with an abundance of complex constraints which should be considered carefully and represented clearly for obtaining high efficiency and productivity. Constraint programming is a new approach to combinatorial optimization and provides a rich language to represent complex constraints easily. However, the cell formation problems are well suited to be solved by constraint programming approach since the problem has many constraints such as part-machine requirements, availabilities in the system in terms of capacity, machine and worker abilities. In this study, the cell formation problem is modeled using machine, part processing and worker flexibilities via resource element–based representation. Resource elements define the processing requirements of parts and processing capabilities of machines and workers, which are resource-independent capability units. A total of 12 case problems are generated, and different search phases of constraint programming are defined for the solution procedure. The cell formation problem is modeled in both constraint programming and integer programming, and a comparative analysis of constraint programming and integer programming model solutions is done. The results indicate that both the models are effective and efficient in the solution of the cell formation problem.

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.

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.

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

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.

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

Traditional vehicle routing problems implicitly assume that only one crew operates a vehicle for the entirety of its journey. However, this assumption is violated in many applications arising in humanitarian and military logistics. This paper considers a joint vehicle and crew routing and scheduling problem in which crews are able to interchange vehicles, resulting in space and time interdependencies between vehicle routes and crew routes. The problem is formulated as a mixed integer programming (MIP) model and a constraint programming (CP) model that overlay crew routing constraints over a standard vehicle routing problem. The constraint program uses a novel optimization constraint to detect infeasibility and to bound crew objectives. This paper also explores methods using large neighborhood search over the MIP and CP models. Experimental results indicate that modeling the vehicle and crew routing problems jointly and supporting vehicle interchanges for crews may bring significant benefits in cost reduction compared with a method that sequentializes these decisions.

This paper compares two shift patterns of nurse scheduling, APN and ABC, which are widely used in Chinese intensive care units (ICUs). Two binary integer programming (IP) models for the nurse scheduling problems with APN and ABC patterns are presented, respectively. A general heuristic solution procedure, which considers the equity of nurse schedules and reduction in shift changes, is proposed to solve these problems. A case study of nurse scheduling based on given nurse demands is performed. Two schedules with APN and ABC patterns are constructed. It shows that ABC pattern generally needs fewer nurses and meanwhile is more apt to achieve equity in nurse scheduling, while APN pattern is more likely to reduce shift changes.

In this study, the U-type assembly line balancing problem (UALBP) with assignment restrictions (AR-UALBP) is considered. Linked and incompatible distance and station restrictions are taken into account. New mathematical programming (MP) and constraint programming (CP) models are proposed. The objective function of the models is minimizing the cycle time for a given number of workstations. In addition to this objective, line efficiency and CPU time are also considered as other performance measurements. Numerical experiments on some problems from the literature are performed to evaluate the effectiveness of the proposed models. The results are compared with the results of the CP model of the straight ALBP with assignment restrictions and also the results from MP and CP models are compared with each other. The numerical results indicate that the proposed CP and MP models are more effective in obtaining better and optimal results when solving the AR-UALBP.

A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery

TDRS (Tracking and Data Relay Satellite) can be seen as a bridge between user spacecrafts and ground station. The TDRSS (Tracking and Data Relay Satellite System) single access link scheduling problem is an important application field of TDRSS. The important character of the scheduling problem lies in that there is time windows constraint between TDRS and user spacecrafts. Tasks can be completed only within given time windows. The paper builds the CP (constraint programming) model of the scheduling problem based on reasonable assumption. The CP model is solved with improved GA (genetic algorithm) based on path representation of valid genes. Computational experiments indicate that it is quite good to solve the scheduling problem by building the CP model and solving it with improved GA

This chapter concentrates on compact and cyclic compact open shop scheduling. Compact scheduling is motivated by timetabling and cyclic compact scheduling by just-in-time systems. A compact schedule requires each job to be processed in a no-wait fashion and each machine to process operations without idle time. Compact schedules do not always exist. The chapter presents smallest instances for which compact schedules do not exist and tests to determine whether compact schedules exist for a given degree Δ. Such tests run in polynomial time for open shop instances with Δ ≤ 4 but become NP-complete for Δ = 5. The minimization of makespan over all compact schedules has polynomial-time solution only for Δ ≤ 3, and it is open even for (3, 4)-biregular open shops where every job has length equal 3 and each machine workload equal 4. Deficiency has been proposed as a measure of deviation from compactness. However, the problem of minimizing deficiency is not only NP-hard in the strong sense but also the existing integer programming (IP) and constraint programming (CP) models can hardly solve problems of size n + m = 10 in reasonable time.

A hybrid integer and constraint programming approach to solve nurse rostering problems