Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with aremanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulativecapacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds.lot-sizing;equivalent models

A Polyhedral Study of the Static Probabilistic Lot-Sizing Problem

We study the polyhedral structure of the static probabilistic lot-sizing problem and propose valid inequalities that integrate information from the chance constraint and the binary setup variables. We prove that the proposed inequalities subsume existing inequalities for this problem, and they are facet-defining under certain conditions. In addition, we show that they give the convex hull description of a related stochastic lot-sizing problem. We propose a new formulation that exploits the simple recourse structure, which significantly reduces the number of variables and constraints of the deterministic equivalent program. This reformulation can be applied to general chance-constrained programs with simple recourse. The computational results show that the proposed inequalities and the new formulation are effective for the the static probabilistic lot-sizing problems

Lot-sizing with stock upper bounds and fixed charges

Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the stock variables. We show that the convex hull of solutions of the discrete lot-sizing problem is obtained as the intersection of two simpler sets, one involving just 0-1 variables and the second a mixing set with a variable upper bound constraint. For these two sets we derive both inequality descriptions and polynomial-size extended formulations of their respective convex hulls. Finally we carry out some limited computational tests on single-item constant capacity lot-sizing problems with upper bounds and fixed charges on the stock variables in which we use the extended formulations derived above to strengthen the initial mixed integer programming formulations.mixed integer programming, discrete lot-sizing, stock fixed costs, mixing sets

A Polynomial Time Algorithm for a Deterministic Joint Pricing and Inventory Model

In this paper we consider the uncapacitated economic lot-size model, where demand is adeterministic function of price. In the model a single price need to be set for all periods. Theobjective is to find an optimal price and ordering decisions simultaneously. In 1973 Kunreuther and Schrage proposed an heuristic algorithm to solve this problem. The contribution of our paper is twofold. First, we derive an exact algorithm to determine the optimal price and lot-sizing decisions. Moreover, we show that our algorithm boils down to solving a number of lot-sizing problems that is quadratic in the number of periods, i.e., the problem can be solved in polynomial time.pricing;inventory;production;lot-sizing

Four equivalent lot-sizing models

We study the following lot-sizing models that recently appeared in the literature: a lot-sizing model with a remanufacturing option, a lot-sizing model with production time windows, and a lot-sizing model with cumulative capacities. We show the equivalence of these models with a classical model: the lot-sizing model with inventory bounds

Economic lot-sizing games

In this paper we introduce a new class of OR games: economic lot-sizing (ELS) games.There are a number of retailers that have a known demand for a fixed number of periods.To satisfy demand the retailers order products at the same manufacturer. By placing jointorders instead of individual orders, costs can be reduced and a cooperative game arises. In this paper we show that ELS games are balanced. Furthermore, we show that two specialclasses of ELS games are concave.Game Theory;Lot-sizing;Inventory;Production

Perencanaan dan Pengendalian Bahan Baku Polyester Fleece Fabrics dengan Pola Data Statik (Studi Kasus : PT. Asia Pasific Fibers, Tbk-karawang)

PT. Asia Pacific Fibers adalah Perusahaan yang memproduksi bahan Polyester Fleece Fabrics yang memiliki masalah dalam hal pengendalian inventory. Perusahaan ini selalu mengalami over-inventory setelah melakukan proses produksi. Perencanaan kebutuhan ataupun pengendalian bahan baku diperlukan agar Perusahaan dapat mengalokasikan bahan baku tepat dan sesuai dengan apa yang dibutuhkan tanpa adanya waste. Pengolahan data yang digunakan dalam penelitian ini adalah menggunakan peramalan dengan menggunakan 12 Months Simple Moving Average, kemudian menentukan karakteristik data permintaan sepanjang tahun 2015 dengan menggunakan metode Peterson-Silver Rule, dan kemudian menentukan perbandingan estimasi total biaya dengan menggunakan teknik lot sizing Lot for Lot dan teknik lot sizing Economic Order Quantity. Karakteristik data yang didapat dari hasil penelitian dengan menggunakan metode Peterson-Silver Rule merupakan data statik. Estimasi total biaya yang didapat dengan menggunakan teknik lot sizing Lot for Lot adalah Rp. 1.784.294.627, dan estimasi total biaya yang didapat dengan menggunakan metode Economic Order Quantity adalah Rp. 625.367.083. Berdasarkan hasil perhitungan dan analisa, maka lebih baik Perusahaan mengganti strategi teknik lot sizing Lot for Lot dengan teknik lot sizing Economic Order Quantity dalam proses order bahan baku, karena hasil analisa estimasi total biaya pemesanan bahan baku yang didapat dengan menggunakan teknik lot sizing Economic Order Quantity jauh lebih murah

Demand uncertainty and lot sizing in manufacturing systems: the effects of forecasting errors and mis-specification

This paper proposes a methodology for examining the effect of demand uncertainty and forecast error on lot sizing methods, unit costs and customer service levels in MRP type manufacturing systems. A number of cost structures were considered which depend on the expected time between orders. A simple two-level MRP system where the product is manufactured for stock was then simulated. Stochastic demand for the final product was generated by two commonly occurring processes and with different variances. Various lot sizing rules were then used to determine the amount of product made and the amount of materials bought in. The results confirm earlier research that the behaviour of lot sizing rules is quite different when there is uncertainty in demand compared to the situation of perfect foresight of demand. The best lot sizing rules for the deterministic situation are the worst whenever there is uncertainty in demand. In addition the choice of lot sizing rule between ‘good’ rules such as the EOQ turns out to be relatively less important in reducing unit cost compared to improving forecasting accuracy whatever the cost structure. The effect of demand uncertainty on unit cost for a given service level increases exponentially as the uncertainty in the demand data increases. The paper also shows how the value of improved forecasting can be analysed by examining the effects of different sizes of forecast error in addition to demand uncertainty. In those manufacturing problems with high forecast error variance, improved forecast accuracy should lead to substantial percentage improvements in unit costs