This paper presents the formulation and solution of the Combinatorial MULTI-MODE RESOURCE CONSTRAINED MULTI-PROJECT SCHEDULING PROBLEM. The focus of the proposed method is not on finding a single optimal solution, instead on presenting multiple feasible solutions, with cost and duration information to the PROJECT manager. The motivation for developing such an approach is due in part to practical situations where the definition of optimal changes on a regular basis. The proposed approach empowers the PROJECT manager to determine what is optimal, on a given day, under the current constraints, such as, change of priorities, lack of skilled worker. The proposed method utilizes a simulation approach to determine feasible solutions, under the current constraints. RESOURCEs can be non-consumable, consumable, or doubly CONSTRAINED. The paper also presents a real-life case study dealing with SCHEDULING of ship repair activities.

The MULTI-MODE RESOURCE Constrains PROJECT SCHEDULING PROBLEM (MRCPSP) tries to find the best sequence of activities in a manner that involves more than one type of operating MODE and in the presence of RESOURCE constraints, PROJECT’s precedence constraints must be satisfied. In each execution MODE, the amount of RESOURCEs and execution time are specified and different. In The Preemptive MULTI-MODE RESOURCE Constraints PROJECT SCHEDULING PROBLEM (P-MRCPSP), each operating MODE activity can be interrupted and restarted at any time without any extra cost. In this paper, minimizing the completion time along with maximizing the current net value of the PROJECT in the P-MRCPSP are considered. After solving the PROBLEM by using Epsilon limits method, according to NP-hard PROBLEM and MULTI-objective MODEl, MULTI-objective particle swarm optimization (MOPSO) has been developed to achieve optimum SCHEDULING. In order to evaluate the proposed method’s efficiency, results have been compared to non-dominance genetic algorithm sorting (NSGAII) based on designed indicators. The Taguchi method has been used in experimental design, to adjust these two algorithms’ parameters. The results of the MODEl solution show the strength of MOPSO algorithm.

PROJECT SCHEDULING is an important process in PROJECT planning. In PROJECT SCHEDULING, precedence relations and RESOURCE constraints must be considered. In this study, a MULTI-MODE RESOURCE CONSTRAINED PROJECT SCHEDULING PROBLEM (MRCPSP), as a main PROBLEM of PROJECT SCHEDULING, is investigated. Exact methods, heuristic procedures and meta-heuristic approaches are different methods for solving the MRCPSP. However, with respect to the fact that exact methods are unable to solve PROBLEMs with more than 20 activities in acceptable computational time, in recent years, heuristic and metaheuristic approaches have been further investigated by researchers. On the other hand, it has been proven that the meta-heuristic approach outperforms heuristic methods.In this study, an improved genetic algorithm (GA) is presented for solving MRCPSP, with minimization of the PROJECT makespan, as the objective, subject to RESOURCE and precedence constraints. Before starting with GA, the preprocessing procedure is employed to reduce the search space and computational effort. For solving this PROBLEM, a random key and a related MODE list (ML) representation scheme are used as encoding schemes and the MULTI-MODE serial schedule generation scheme (MSSGS) is considered as the decoding procedure. In this paper, a new fitness function is proposed for reducing computational effort and average deviation from optimality. A new mutation operator is also defined for improving the solution quality.The well-known benchmark sets, J10, J12, J14, J16, J18, J20 and J30, in PSPLIB are used for testing the proposed GA. Comparison of the results of the proposed GA with other approaches validates the effectiveness of the proposed algorithm to solve the MRCPSP. It is worth mentioning that average deviation from the optimal makespans (in the case of set J30, from the lower bounds), the percentage of optimally solved instances, and the average CPU time, in seconds, are used for comparison.

Surgical theater is one of the most expensive hospital RESOURCEs which accounts for a high percentage of hospital receptions. Therefore, efficient planning and SCHEDULING of the operating rooms (ORs) is necessary to improving the efficiency of any healthcare system. In this paper, weekly OR planning and SCHEDULING PROBLEM was addressed to minimize waiting time of elective patients, overutilization and underutilization costs of ORs, and the total completion time of surgeries. In our MODEl, the available hours of ORs, recovery beds, the surgeons, legal constraints and job qualification of surgeons, and priority of patients were taken into account. A real-life example was provided to demonstrate the effectiveness and applicability of the MODEl and was solved using ε-constraint method in GAMS software. Then, data envelopment analysis (DEA) was employed to obtain the best solution among the Pareto solutions obtained by ε-constraint method. Finally, the best Pareto solution was compared with the schedule used in the hospitals. The results indicated that the best Pareto solution outperforms the schedule offered by the OR director.

In this paper, two different sub-PROBLEMs are considered to solve a RESOURCE CONSTRAINED PROJECT SCHEDULING PROBLEM (RCPSP), namely i) assignment of MODEs to tasks and ii) SCHEDULING of these tasks in order to minimize the make span of the PROJECT. The modified electromagnetism-like algorithm deals with the first PROBLEM to create an assignment of MODEs to activities. This list is used to generate a PROJECT schedule. When a new assignment is made, it is necessary to fix all MODE dependent requirements of the PROJECT activities and to generate a random schedule with the serial SGS method. A local search will optimize the sequence of the activities. Also in this paper, a new penalty function has been proposed for solutions which are infeasible with respect to non-renewable RESOURCEs. Performance of the proposed algorithm has been compared with the best algorithms published so far on the basis of CPU time and number of generated schedules stopping criteria. Reported results indicate excellent performance of the algorithm.

This paper presents a mathematical MODEl for the MULTI-MODE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM with maximizing the net present value of PROJECT. The proposed MODEl is inspired by MRCPSP-GPR. Firstly, we presented an exact MODEl solving MRCPSP_GPR then we expanded the MODEl to estimate other cost-related options, penalty-related expenditure is a case in point. As a result of estimating different factors which impact on PROJECT SCHEDULING such as reward and penalty of finishing the PROJECT, managers can efficiently make a better decision. For better adaptation with real conditions, we consider two payment methods in two objective functions. The adjusted schedule by proposed MODEl and solving time was logical. Moreover, to verify the proposed MODEl, a numerical example is solved in small size and the related computational results are illustrated in terms of schedules. In addition, computational results with a set of 36 test PROBLEMs in various sizes are reported and the results analyzed.

MultiMODE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM (MRCPSP) is a type of RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM (RCPSP). In this PROBLEM the PROJECTs involves activities that condition each other and there is constraint of RESOURCEs, both renewable and non-renewable. Each activity can be executed in more than one MODE, each MODE requiring a different RESOURCE. This PROBLEM is among the NP-Hard ones; therefore, scholars have always been eager to find a solution for it. In this study bee colony algorithm has been proposed as a solution. No other research has used bee colony algorithm for this PROBLEM before, and the present article is innovating this solution. We have solved the standard PROBLEMs in the existing literature via this algorithm and have compared our results with the results created by the best and newest algorithms which are usually used for these PROBLEMs in order to testify the strength of bee colony algorithm in this regard. The results demonstrate successful performance of bee colony algorithm for solving MRCPSP.

The aim of a MULTI-MODE RESOURCE-CONSTRAINED PROJECT SCHEDULING PROBLEM (MRCPSP) is to assign RESOURCE (s) with the restricted capacity to an execution MODE of activities by considering relationship constraints to achieve pre-determined objective (s). These goals vary with managers or decision makers of any organization who should determine suitable objective (s) considering organization strategies. Also, we introduce the preemptive extension of the PROBLEM which allows for activity splitting. In this paper, the preemptive MULTI-MODE RESOURCE CONSTRAINED PROJECT SCHEDULING PROBLEM (P-MMRCPSP) with Minimum makespan and the maximization of net present value (NPV) has been considered. Since the considered MODEl is NP-Hard, the performance of our proposed MODEl is evaluated by comparison with two well-known algorithms: non-dominated sorting genetic algorithm (NSGA II) and MULTI-objective imperialist competitive algorithm (MOICA). These meta heuristics have been compared on the basis of a computational experiment performed on a set of instances obtained from standard test PROBLEMs constructed by the ProGen PROJECT generator, where, additionally, cash flows were generated randomly with the uniform distribution. Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method (DOE) was applied to set and estimate the proper values of GAs parameters for improving their performances. The computational results show that the proposed MOICA outperforms the NSGA-II.