Optimal staffing under an annualized hours regime using Cross-Entropy optimization

This paper discusses staffing under annualized hours. Staffing is the selection of the most cost-efficient workforce to cover workforce demand. Annualized hours measure working time per year instead of per week, relaxing the restriction for employees to work the same number of hours every week. To solve the underlying combinatorial optimization problem this paper develops a Cross-Entropy optimization implementation that includes a penalty function and a repair function to guarantee feasible solutions. Our experimental results show Cross-Entropy optimization is efficient across a broad range of instances, where real-life sized instances are solved in seconds, which significantly outperforms an MILP formulation solved with CPLEX. In addition, the solution quality of Cross-Entropy closely approaches the optimal solutions obtained by CPLEX. Our Cross-Entropy implementation offers an outstanding method for real-time decision making, for example in response to unexpected staff illnesses, and scenario analysis

Hibridisasi Genetic-tabu Search Algorithm Untuk Penjadwalan Job Terhadap Beberapa Resource Di Dalam Komputasi Grid

Permasalahan penjadwalan job terhadap beberapa mesin (scheduling jobs on multiple machines / SJMM) merupakan salah satu permasalahan penjadwalan klasik yang dapat ditemui pada proses komputasi terlebihjika komputasi dilakukan secara terdistribusi. Beberapa metode penyelesaian permasalahan tersebut telah dikembangkan baik dengan pendekatan eksak maupun heuristik/metaheuristik. Tabu Search sebagai salah satu metode metaheuristik yang relatif baru dapat menjadi alternatif metode untuk mendapatkan pendekatan penyelesaian permasalahan tersebut. Metode ini sudah diaplikasikan pada permasalahan optimasi kombinatorial, optimasi multi ekstermal, serta rare event simulation, dengan hasil penyelesaian yang cukup optimal dengan waktu yang relative singkat. Penelitian ini mengimplementasikan metode Tabu Search yang digabungkan dengan algoritma genetika (Incorporation Genetic-Tabu Search Algorithm / IGTS) dalam permasalahan SJMM pada komputasi grid, serta membandingkan kelebihan dan kekurangan antara metode IGTS tersebut dengan metode lain pada permasalahan yang sama. Hasil yang diharapkan dari penelitian ini adalah pengembangan algoritma IGTS pada permasalahan SJMM, untuk mendapatkan hasil makespan yang lebih baik

A Cross Entropy-Based Heuristic for the Capacitated Multi-Source Weber Problem with Facility Fixed Cost: Cross entropy for continuous location problems

This paper investigates a capacitated planar location-allocation problem with facility fixed cost. A zone-based fixed cost which consists of production and installation costs is considered. A nonlinear and mixed integer formulation is first presented. A powerful three stage Cross Entropy meta-heuristic with novel density functions is proposed. In the first stage a covering location problem providing a multivariate normal density function for the associated stochastic problem is solved. The allocation values considering a multinomial density function are obtained in the second stage. In the third stage, single facility continuous location problems are solved. Several instances of various sizes are used to assess the performance of the proposed meta-heuristic. Our approach performs well when compared with the optimizer GAMS which is used to provide the optimal solution for small size instances and lower/upper bounds for some of the larger ones

Penjadwalan Flow Shop untuk Meminimasi Total Tardiness Menggunakan Algoritma Cross Entropy–Algoritma Genetika

Flow shop scheduling problems much studied by several researchers. One problem with scheduling is the tardiness. Total tardiness is the performance to minimize tardiness jobs. it is the right performance if there is a due date. This study proposes the Cross-Entropy Genetic Algorithm (CEGA) method to minimize the mean tardiness in the flow shop problem. In some literature, the CEGA algorithm is used in the case of minimizing the makespan. However, CEGA not used in the case of minimizing total tardiness. CEGA algorithm is a combination of the Cross-Entropy Algorithm which has a function to provide optimal sampling distribution and Genetic Algorithms that have functions to get new solutions. In some numeric experiments, the proposed algorithm provides better performance than some algorithms. For computing time, it is affected by the number of iterations. The higher the iteration, computing requires high time

How green is a lean supply chain?

This article presents a supply chain planning model that can be used to investigate tradeoffs between cost and environmental degradation including carbon emissions, energy consumption and waste generation. The model also incorporates other aspects of real world supply chains such as multiple transport lot sizing and flexible holding capacity of warehouses. The application of the model and solution method is investigated in an actual case problem. Our analysis of the numerical results focuses on investigating relationship between lean practices and green outcomes. We find that (1) not all lean interventions at the tactical supply chain planning level result in green benefits, and (2) an agile supply chain is the greenest and most efficient alternative when compared to strictly lean and centralized situations

Knapsack Problems with Side Constraints

The thesis considers a specific class of resource allocation problems in Combinatorial Optimization: the Knapsack Problems. These are paradigmatic NP-hard problems where a set of items with given profits and weights is available. The aim is to select a subset of the items in order to maximize the total profit without exceeding a known knapsack capacity. In the classical 0-1 Knapsack Problem (KP), each item can be picked at most once. The focus of the thesis is on four generalizations of KP involving side constraints beyond the capacity bound. More precisely, we provide solution approaches and insights for the following problems: The Knapsack Problem with Setups; the Collapsing Knapsack Problem; the Penalized Knapsack Problem; the Incremental Knapsack Problem. These problems reveal challenging research topics with many real-life applications. The scientific contributions we provide are both from a theoretical and a practical perspective. On the one hand, we give insights into structural elements and properties of the problems and derive a series of approximation results for some of them. On the other hand, we offer valuable solution approaches for direct applications of practical interest or when the problems considered arise as sub-problems in broader contexts