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"Many engineering, operations, and scientific applications include a mixture of discrete and continuous decision variables and nonlinear relationships involving the decision variables that have a pronounced effect on the set of feasible and optimal solutions. Mixed-integer nonlinear programming (MINLP) problems combine the numerical difficulties of handling nonlinear functions with the challenge of optimizing in the context of nonconvex functions and discrete variables. MINLP is one of the most flexible modeling paradigms available for optimization."

"A reprint of the original volume, which won the Lanchester Prize awarded by the Operations Research Society of America for the best work of 1968. Although out of print for nearly 15 years, it remains one of the most referenced volumes in the field of mathematical programming. Recent interest in interior point methods generated by Karmarkar's Projective Scaling Algorithm has created a new demand for this book because the methods that have followed from Karmarkar's bear a close resemblance to those described. There is no other source for the theoretical background of the logarithmic barrier function and other classical penalty functions. Analyzes in detail the "central" or "dual" trajectory used by modern path following and primal/dual methods for convex and general linear programming. As researchers begin to extend these methods to convex and general nonlinear programming problems, this book will become indispensable to them."

"Pertumbuhan industri otomotif yang semakin meningkat di Indonesia belum diimbangi dengan jumlah pemasok bahan baku lokal dan membuat industri otomotif bergantung pada aktivitas impor. Seiring dengan banyaknya kebutuhan aktivitas impor ini, maka dibutuhkan pula aktivitas logistik yang lebih besar. Namun dengan biaya logistik yang tinggi, membuat perusahaan harus meningkatkan efisiensi untuk dapat terus bersaing dalam industri nasional. Oleh karena itu, perlu adanya perencanaan aktivitas inbound logistik yang mengatur pergerakan material dari pemasok hingga sampai ke pabrik. Pada penelitian ini, dikembangkan sebuah model optimasi menggunakan pendekatan pemrograman non linier integer campuran yang diselesaikan dengan algoritma branch and bound. Hasil dari penelitian ini, yaitu didapatkan total biaya inbound logistik yang optimal mencakup biaya material, biaya transportasi, dan biaya pelabuhan. Model ini juga dapat digunakan sebagai alat bantu perusahaan dalam pengambilan keputusan mengenai tipe kontainer dan jumlah kontainer yang digunakan beserta total muatan yang optimal dalam setiap kontainer, sehingga didapatkan nilai utilasi kontainer yang tinggi.

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The increasing growth of automotive industry in Indonesia has not been matched by the number of local suppliers and makes the automotive industry too dependent on imported raw materials. Along with the needs of import activities, it is also required a greater logistics activities. However, with high logistics costs, the manufacturer must increase efficiency to be able compete in the global market. This can be accomplished by planning inbound logistics activities that control the movement of materials from suppliers to the manufacture.

In this research, an optimization methodology, based on Mixed Integer Nonlinear Programming MINLP approach is developed and solved with branch and bound algorithm.

The result of this research, which obtained the total cost of optimal inbound logistics include material cost, transportation cost, and administration cost. This model can also be used as a tool for the company in making decisions about the type and the number of container also with the total of the optimal material load in each container, therefore the optimal container space utilization value can be obtained."

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Per tahun 2022, industri mi instan menjadi kontributor terbesar sektor industri makanan dan minuman. Penelitian ini membahas permasalahan pada proses penyediaan bahan baku di industri makanan dan minuman dengan objek penelitian mi instan. Pada permasalahan tersebut terjadi peningkatan total biaya penyediaan bahan baku dengan beberapa faktor penyebab berupa peningkatan harga bahan baku, kenaikan biaya pemesanan, dan ketidakoptimalan dalam membuat perkiraan jumlah produksi. Oleh karena itu, dibutuhkan manajemen persediaan yang baik dengan menentukan jumlah dan waktu pemesanan yang sesuai dengan jumlah permintaan. Penelitian ini menggunakan dua metode. Metode pertama adalah metode peramalan Winter’s Method untuk mendapatkan perkiraan jumlah permintaan pada periode mendatang. Untuk mengembangkan model matematika, digunakan metode Mixed Integer Linear Programming (MILP) untuk mendapatkan total biaya persediaan yang minimal. Pengolahan data dilakukan pada tujuh bahan baku pembuatan mi instan. Implementasi pengembangan model menghasilkan jumlah pemesanan sebesar Rp218.736.638 dan waktu pemesanan dilakukan mingguan sebanyak 35 kali secara keseluruhan.

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As of 2022, the instant noodle industry has emerged as the foremost contributor to the food and beverage sector. This study delves into the predicaments encountered during the procurement process of raw materials within the food and beverage industry, with a specific focus on the context of instant noodles. The identified issue encompasses an escalating total cost of raw material procurement, attributed to several causal factors such as mounting raw material prices, increased ordering costs, and unoptimized production quantity estimations. Consequently, it necessitates the implementation of effective inventory management strategies by determining the optimal order quantities and ordering time in alignment with the demand volume. This research uses two methodologies. The initial approach employs the Winter’s Method forecasting technique to derive an approximation of the forthcoming demand volume. Subsequently, the development of a mathematical model incorporates the application of the Mixed Integer Linear Programming (MILP) method, aimed at minimizing the overall inventory costs. The data processing phase of this study is carried out on seven raw materials. The implementation of the model results in a total inventory cost of Rp218.736.638 and ordering time that is set in weekly interval amounting to 35 in total.

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"separation theorems are then derived based on these theorems. This is followed by a chapter on convex functions that includes theorems of the alternative for such functions. These results are used in obtaining the saddlepoint optimality conditions of nonlinear programming without differentiability assumptions. Properties of differentiable convex functions are derived and then used in two key chapters of the book, one on optimality conditions for differentiable nonlinear programs and one on duality in nonlinear programming. Generalizations of convex functions to pseudoconvex and quasiconvex functions are given and then used to obtain generalized optimality conditions and duality results in the presence of nonlinear equality constraints. The book has four useful self-contained appendices on vectors and matrices, topological properties of n-dimensional real space, continuity and minimization, and differentiable functions."