P-Median based formulations with backbone facility locations

Two new continuous-time MILP (Mixed Integer Linear Programming) models are developed for resource constrained project scheduling problems in which activities can be conducted in different (multi) modes. There are efficient and flexible MILP models for this problem in which time is represented by a number of discrete time intervals. However, they require to use large numbers of binary variables as the number of activities increases and time horizon stretches. Hence efforts have been made to formulate MILP models based on continuous-time representation and therefore to speed up the solution process. We propose two novel MILP models based on the event and resource flow concepts. The models are verified by solving benchmark problems in the literature.

Let G V , E be a simple undirected complete graph with vertex and edge sets V and E , respectively. In this paper, we consider the degree-constrained k -minimum spanning tree (DC k MST) problem which consists of finding a minimum cost subtree of G formed with at least k vertices of V where the degree of each vertex is less than or equal to an integer value d ≤ k − 2 . In particular, in this paper, we consider degree values of d ∈ 2,3 . Notice that DC k MST generalizes both the classical degree-constrained and k -minimum spanning tree problems simultaneously. In particular, when d = 2 , it reduces to a k -Hamiltonian path problem. Application domains where DC k MST can be adapted or directly utilized include backbone network structures in telecommunications, facility location, and transportation networks, to name a few. It is easy to see from the literature that the DC k MST problem has not been studied in depth so far. Thus, our main contributions in this paper can be highlighted as follows. We propose three mixed-integer linear programming (MILP) models for the DC k MST problem and derive for each one an equivalent counterpart by using the handshaking lemma. Then, we further propose ant colony optimization (ACO) and variable neighborhood search (VNS) algorithms. Each proposed ACO and VNS method is also compared with another variant of it which is obtained while embedding a Q-learning strategy. We also propose a pure Q-learning algorithm that is competitive with the ACO ones. Finally, we conduct substantial numerical experiments using benchmark input graph instances from TSPLIB and randomly generated ones with uniform and Euclidean distance costs with up to 400 nodes. Our numerical results indicate that the proposed models and algorithms allow obtaining optimal and near-optimal solutions, respectively. Moreover, we report better solutions than CPLEX for the large-size instances. Ultimately, the empirical evidence shows that the proposed Q-learning strategies can bring considerable improvements.

MILP and MINLP models for the optimal scheduling of multi-energy systems accounting for delivery temperature of units, topology and non-isothermal mixing

Passive Optical Network (PON) deployments have recently been aiming to combine the capacity of metro and access networks in the last mile of the Internet service provisioning. Deployment of PONs by running fiber to the premises introduces the advantage of huge capacity but at the same time, it calls for a robust design in order to avoid long service outage durations in case of network failures where survivable network design is mostly limited to the deployment budget. In this paper, we propose three mixed integer linear programming (MILP) models for various survivability policies to deploy reliable long-reach PONs under the budget limitations. Each MILP model aims to place the ONUs in optimal locations so that the covered area is maximized while availability requirements of the users are satisfied within the deployment budget. We solve the MILP models under the uniform and heterogeneous availability requirement scenarios and show that service availability and coverage introduce a trade-off so as the coverage and deployment cost do. Two out of the three survivability policies can guarantee 99.99% service availability while the third one is able to guarantee 99.999% by running the proposed MILP models. However, the first two schemes are able to cover larger area when compared to the third scheme which is the most reliable protection policy.

Purpose: The main purpose of the paper is to evaluate the impact of diverse personnel policies around personnel promotion in the design of the strategic staff plan for a public university. The strategic staff planning consists in the determination of the size and composition of the workforce for an organization.Design/methodology/approach: The staff planning is solved using a Mixed Integer Linear Programming (MILP) model. The MILP model represents the organizational structure of the university, the personnel categories and capacity decisions, the demand requirements, the required service level and budget restrictions. All these aspects are translated into a set of data, as well as the parameters and constraints building up the mathematical model for optimization. The required data for the model is adopted from a Spanish public university.Findings: The development of appropriate policies for personnel promotion can effectively reduce the number of dismissals while proposing a transition towards different preferable workforce structures in the university.Research limitations/implications: The long term staff plan for the university is solved by the MILP model considering a time horizon of 8 years. For this time horizon, the required input data is derived from current data of the university. Different scenarios are proposed considering different temporal trends for input data, such as in demand and admissible promotional ratios for workers.Originality/value: The literature review reports a lack of formalized procedures for staff planning in universities taking into account, at the same time, the regulations on hiring, dismissals, promotions and the workforce heterogeneity, all considered to optimize workforce size and composition addressing not only an economic criteria, but also the required workforce expertise and the quality in the service offered. This paper adopts a formalized procedure developed by the authors in previous works, and exploits it to assess the impact of various personnel policies in the staff planning for a particular university case, and this is the principal contribution of the paper.

With the rapid development of computer technology and related softwares for mathematical models, mathematical modelling of scheduling problems is receiving growing attention from researchers. In this work, the hybrid flow shop scheduling problem with unrelated parallel machines (HFSP-UPM) with the objective aimed to minimise the makespan is studied. According to the characteristics of the HFSP-UPM, eight mixed integer linear programming (MILP) models are formulated in order to obtain optimal solutions based on different modelling ideas. Then, these models are extended to solve HFSP-UPM with sequence-dependent setup times (HFSP-UPM-SDST), no-wait HFSP-UPM (HFSP-UPM-NW) and HFSP-UPM with blocking (HFSP-UPM-B). All the proposed models and the existing model are detailedly compared and evaluated under three aspects namely modelling process, size complexity and computational complexity. Numerical experiments show that MILP models dependent on diverse modelling ideas perform very differently. The model developed based on stage precedence is the best one and should be given preference in future applications. In addition, the proposed models of HFSP-UPM-NW and HFSP-UPM-B improve several best known solutions for the test instances in the existing literature.

The Capacitated Multiple Traveling Repairmen Problem (CmTRP) is an extension of the Multiple Traveling Repairmen Problem (mTRP). In the CmTRP, the number of vehicles is dispatched to serve a set of customers, while each vehicle’s capacity is limited by a predefined-value as well as each customer is visited exactly once. The goal is to find a tour that minimizes the sum of waiting times. The problem is NP-hard because it is harder than the mTRP. Even finding a feasible solution is also NP-hard problem. To solve medium and large size instances, a metaheuristic algorithm is proposed. The first phase constructs a feasible solution by combining between the Nearest Neighborhood Search (NNS) and Variable Neighborhood Search (VNS), while the optimization phase develops the feasible solution by the General Variable Neighborhood Search (GVNS). The combination maintains the balance between intensification and diversification to escape local optima. The proposed algorithm is implemented on benchmark instances from the literature. The results indicate that the developed algorithm obtains good feasible solutions in a short time, even for the cases with up to 200 vertices.

Simultaneous product family and supply chain design: An optimization approach

This paper addresses the dual-resource constrained flexible job shop scheduling problem (DRCFJSP) with minimizing energy consumption. It is the first to study the energy-conscious DRCFJSP with turn OFF/ ON strategy. Different from the classical FJSP, the worker flexibility is considered in DRCFJSP. First, in order to solve this problem, we propose two mixed integer linear programming (MILP) models based on two modeling ideas, namely, idle time and idle energy. Because DRCFJSP is NP-hard, then we propose an efficient variable neighborhood search (VNS) algorithm. In the proposed VNS algorithm, eight neighborhood structures are designed to generate neighboring solutions. In addition, four energy-saving decoding approaches are specifically designed, in which two energy-saving strategies, namely, postponing strategy and turn OFF/ ON strategy are designed. Finally, the MILP model, the energy-conscious decoding methods, and the VNS are evaluated on numerical tests, whose effectiveness is shown by the experimental results. The experimental results show that the MILP model based on idle energy performs better than the model based on idle time idea, and the greedy hybrid decoding method outperforms the other three decoding methods. Moreover, the proposed VNS with eight neighborhood structures is a very competitive algorithm for the energy-conscious DRCFJSP.

Mixed integer linear programming for the design of solar thermal energy systems with short-term storage

To support the selection of food items for FFQs in such a way that the amount of information on all relevant nutrients is maximised while the food list is as short as possible. Selection of the most informative food items to be included in FFQs was modelled as a Mixed Integer Linear Programming (MILP) model. The methodology was demonstrated for an FFQ with interest in energy, total protein, total fat, saturated fat, monounsaturated fat, polyunsaturated fat, total carbohydrates, mono- and disaccharides, dietary fibre and potassium. The food lists generated by the MILP model have good performance in terms of length, coverage and R 2 (explained variance) of all nutrients. MILP-generated food lists were 32-40 % shorter than a benchmark food list, whereas their quality in terms of R 2 was similar to that of the benchmark. The results suggest that the MILP model makes the selection process faster, more standardised and transparent, and is especially helpful in coping with multiple nutrients. The complexity of the method does not increase with increasing number of nutrients. The generated food lists appear either shorter or provide more information than a food list generated without the MILP model.

Modeling side slopes in vertical alignment resource road construction using convex optimization

To improve the utilization of port resources and reduce the consumption of resources due to vessel waiting and delays, this paper investigates the Berth Allocation and Quay Crane Assignment Problem (BACAP) in container ports, focusing on the Quay Crane (QC) profile. The objective is to assign berths, berthing times, and QC profiles to vessels arriving at the port within a given planning horizon, thereby extending the traditional BACAP framework. To minimize the sum of idle time costs caused by vessel waiting and delay time costs due to late vessel departures, a mixed-integer linear programming (MILP) model is proposed. Additionally, a variable neighborhood search (VNS) algorithm is designed to solve the model, tailored to the specific characteristics of the problem. The proposed MILP model and VNS algorithm are evaluated using two sets of BACAP instances. The numerical results demonstrate the effectiveness of both the model and the algorithm, showing that VNS efficiently and reliably solves instances of various sizes. Furthermore, each neighborhood structure contributes uniquely to the iterative process. This study also analyzes the impact of different idle and delay costs on BACAP, providing valuable managerial insights. The proposed framework contributes to enhancing operational efficiency and supports sustainable port management.

An improved MILP model for scheduling crude oil unloading, storage and processing

A new MILP model and fast heuristics for the variable-sized bin packing problem with time windows