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

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

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

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

DYNAMIC LOT-SIZING PROBLEMS: A Review on Model and Efficient Algorithm

Due to their importance in industry, dynamic demand lot-sizing problems are frequently studied.This study consider dynamic lot-sizing problems with recent advances in problem and modelformulation, and algorithms that enable large-scale problems to be effectively solved.Comprehensive review is given on model formulation of dynamic lot-sizing problems, especiallyon capacitated lot-sizing (CLS) problem and the coordinated lot-sizing problem. Bothapproaches have their intercorrelated, where CLS can be employed for single or multilevel/stage, item, and some restrictions. When a need for joint setup replenishment exists, thenthe coordinated lot-sizing is the choice. Furthermore, both algorithmics and heuristics solutionin the research of dynamic lot sizing are considered, followed by an illustration to provide anefficient algorithm

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

Lot Sizing Material Requirement Planning Pada Produk Tipe Wall Mounting Di Industri Box Panel

Objek studi adalah pabrik di industri panel listrik. Permasalahaan yang sering terjadi dalam pelaksanaan proses produksi adalah persediaan bahan baku. Terjadi keterlambatan bahan baku dan komponen standar yang seharusnya sudah ada dalam ± 5 hari kerja menjadi 20 hari kerja atau lebih. Keterlambatan ini dapat memberikan dampak dalam pengiriman produk kepada konsumen. Material requiretment planing yang digunakan sebagai metode untuk menentukan apa, kapan dan berapa jumlah komponen dan material yang dibutuhkan untuk memenuhi kebutuhan dari suatu perencanaan produksi. Studi diawali dengan perhitungan jumlah kebutuhan dan barang yang dibutuhkan menggunakan peramalan didukung sofware WINQSB. Selanjutnya dihitung total biaya persediaan bahan baku dengan menggunakan teknik Lotsizing Lot For Lot (LFL), Fix Ordet Quantity (FOQ), Economy Order Quantity (EOQ), dan Period Order Quantity (POQ). Berdasarkan hasil dan analisa, teknik lot sizing menunjukkan total biaya persediaan terendah sebesar Rp 562.787.335, tetapi pada penerapan sering terjadi lead time yang berlebih karna lamanya pengiriman. Dengan kondisi tersebut dipilih metode Fix Order Quantity yang memiliki biaya terendah kedua setelah Lot For Lot yaitu sebesar Rp 577.194.547, dan stock pengaman yang tidak terlalu besar

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

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