An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned backorders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely backordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer

An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned back orders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely back ordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer

PELABELAN TOTAL (a,d)-H-ANTI AJAIB PADA GRAF RODA

Abstrak: Suatu graf sederhana G=(V(G), E(G)) memuat selimut-H jika setiap sisi dalamberada dalam satu subgraf G yang isomorfik dengan H. Pelabelan total selimut-H-(a,d) anti ajaib pada graf G adalah sebuah fungsi bijektif x:V(G)ÈE(G)®{1,2,...,|V(G)+E(G)|} sehingga semua subgraf pada H’ isomorfik dengan Hyang memiliki bobot w(H’)= åvÎV(H’)x(v)+ åeÎE(H’)x(e) yang merupakan barisan aritmatika a, a+d, a_2d,...,a+(t-1)d dengan a dan d adalah bilangan bulat positif dan t adalah jumlah subgraf dari G yang isomorfik dengan H. Pelabelan x disebut sebuah pelabelan total (a,d)-H-super anti ajaib, jika x(V(G))={1,2,...,|V(G)|}.Hasil penelitian ini adalah pada graf roda Wn  terdapat pelabelan total (a,d)-H-anti ajaib dengan  n³3 dan d=[1,3] dan H adalah graf kipas Fn.Kata Kuncilol : pelabelan total anti ajaib-(a,d)-H, graf roda, graf kipa

Fuzzy EOQ Model with Trapezoidal and Triangular Functions Using Partial Backorder

EOQ fuzzy model is EOQ model that can estimate the cost from existing information. Using trapezoid fuzzy functions can estimate the costs of existing and trapezoid membership functions has some points that have a value of membership . TR ̃C value results of trapezoid fuzzy will be higher than usual TRC value results of EOQ model . This paper aims to determine the optimal amount of inventory in the company, namely optimal Q and optimal V, using the model of partial backorder will be known optimal Q and V for the optimal number of units each time a message . EOQ model effect on inventory very closely by using EOQ fuzzy model with triangular and trapezoid membership functions with partial backorder. Optimal Q and optimal V values for the optimal fuzzy models will have an increase due to the use of trapezoid and triangular membership functions that have a different value depending on the requirements of each membership function value. Therefore, by using a fuzzy model can solve the company's problems in estimating the costs for the next term