A Note on “The Facility Location Problem with Limited Distances”

In this paper, it is shown that the polynomially bounded enumerative procedure to solve the facility location problem with limited distances, originally described by Drezner, Mehrez, and Wesolowsky [Drezner Z, Mehrez A, Wesolowsky GO (1991) The facility location problem with limited distances. Transportation Sci. 25(3):183–187.], and subsequently corrected by Aloise, Hansen, and Liberti [Aloise D, Hansen P, Liberti L (2012) An improved column generation algorithm for minimum sum-of-squares clustering. Math. Programming 131(1–2):195–220.], can still fail to optimally solve the problem. Conditions under which the procedures succeed are identified. A new modified algorithm is presented that solves the facility location problem with limited distances. It is further shown that the proposed correction is complete in that it does not require further corrections.

PENENTUAN LOKASI DISTRIBUTION CENTER DENGAN METODE P-MEDIAN DI PT PERTAMINA EP

Global energy consumption increases every year. BP Statistics Review of World Energy 2019 shows that Indonesia's energy consumption increases by 4.9% in 2018, reaching 185.5 million tons of oil equivalent (TOE). Therefore, oil and gas companies must increase production to fulfill those needs. PT Pertamina EP is a subsidiary of PT Pertamina (Persero) which focuses on the upstream oil and gas sector. One of the activities carried out in the upstream business is drilling. Drilling materials are necessary to support the dynamic of drilling process. The mechanism used when there is a shortage of stock is to send the required material from another field that has the required material, or is called Inter Unit Assistance (BAU). In 2018 the costs incurred for transportation of BAU OCTG (Oil Country Tubular Goods) material amounted to Rp 45,733,340,000. Distribution center is an alternative for cutting distribution chains. We proposed allocation of facility such distribution center location decision using p-median optimization model to reduce the BAU transportation cost. This approach is implemented using math programming using AMPL and Gurobi. Distribution center functions as a material distribution center to meet the needs of the surrounding fields. By applying the scenario of building a distribution center, transportation costs can be reduced by 13% or Rp 6,167,325,000. AbstrakKonsumsi energi global cenderung meningkat setiap tahunnya. Data BP Statistical Review of World Energy 2019 menunjukkan konsumsi energi Indonesia meningkat sebesar 4,9% pada tahun 2018 dengan nilai mencapai 185,5 juta tonnes oil equivalent (TOE). Oleh karena itu perusahaan minyak dan gas bumi (migas) harus meningkatkan produksi untuk memenuhi kebutuhan tersebut. PT Pertamina EP adalah perusahaan yang fokus pada sektor hulu migas. Salah satu kegiatan yang dilakukan pada bisnis hulu adalah pemboran. Untuk Rencana pengeboran yang dinamis dibutuhkan ketersediaan material. Mekanisme yang dilakukan saat terjadi kekurangan stock adalah mengirim material yang dibutuhkan dari field lain yang memiliki ketersediaan material yang dibutuhkan, atau disebut Bantuan Antar Unit (BAU). Biaya yang dikeluarkan pada tahun 2018 untuk transportasi BAU material OCTG (Oil Country Tubular Goods) sebesar Rp 45.733.340.000. Biaya tersebut dibutuhkan untuk mendistribusikan material pada lokasi field yang tersebar di berbagai lokasi di pulau Jawa, Sumatera, dan Kalimantan. Dalam penelitian ini diusulkan untuk memanfaatkan penggunaan distribution center (DC) sebagai upaya untuk menghemat biaya transportasi BAU. DC berfungsi sebagai pusat distribusi material untuk memenuhi kebutuhan field di sekitarnya. Model optimasi p-median digunakan memilih lokasi fasilitas DC yang memiliki biaya transportasi paling minimal dengan mempertimbangkan jarak, biaya, dan permintaan material. Diasumsikan satu DC akan ditempatkan di setiap wilayah / pulau. Solusi optimal dari model p-median dihasilkan menggunakan software pemrograman matematis AMPL dengan menggunakan solver GUROBI. Hasil eksperimen didapatkan bahwa dengan penerapan skenario adanya DC, biaya transportasi dapat dipangkas sebesar 13% atau sebesar Rp 6.167.325.000.

Optimization Modeling Exercises

The problem set contains three problems designed to help students practice their ability to build math programming models. Problem # 1 is a portfolio problem where the student is asked to find a portfolio that minimizes risk (variance) subject to a required rate of return; as such, it is nonlinear. Problem # 2 is aggregate production scheduling; hence, linear. Problem # 3 involves determining how to source a fixed quantity from a menu of vendors with differing fixed- ordering charges and per-unit prices; it is a mixed integer model. All are sufficiently small that they can be easily optimized with standard math programming software (such as Excel's standard Solver).

Linear Programming Formulation of Idle Times for Single-Server Discrete-Event Simulation Models

Mathematical programming representations (MPRs) are discrete-event simulation models represented using math programming. In this paper, we first introduce an MPR formulation for single-server queueing systems based on idle times. We use this formulation to conduct a perturbation analysis to study the effect of imposing a constraint on idle times. We apply the formulation to obtain a linear programming-based gradient estimator for idle times. We demonstrate the integration of optimization into MRP and identify properties of the optimal solution to facilitate finding the optimal solution.

A competency-based bachelor’s degree in applied math programming model

The article aims – to find out what is competence, how to develop those elements must reflect the competency-based training program for the preparation of undergraduate Applied Mathematics.

On generalized Newton method for solving operator inclusions

In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ? 0, where F is a Fr?chet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and the generalized Newton method, Math. Programming 73 (1996) 251-268].