On the computational complexity of uncapacitated multi-plant lot-sizing problems

Valid inequalities, preprocessing, and an effective heuristic for the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure

We consider the uncapacitated three-level lot-sizing and replenishment problem with a distribution structure. In this NP-hard problem, a single production plant sends the produced items to replenish warehouses from where they are dispatched to the retailers in order to satisfy their demands over a finite planning horizon. The goal of the problem is to determine an integrated production and distribution plan minimizing the total costs, which comprehends fixed production and transportation setup as well as variable inventory holding costs. We describe new valid inequalities both in the space of …

A Mixed Integer Programming Model Formulation for Solving the Lot-Sizing Problem

This paper addresses a mixed integer programming (MIP) formulation for the multi-item uncapacitated lot-sizing problem that is inspired from the trailer manufacturer. The proposed MIP model has been utilized to find out the optimum order quantity, optimum order time, and the minimum total cost of purchasing, ordering, and holding over the predefined planning horizon. This problem is known as NP-hard problem. The model was presented in an optimal software form using LINGO 13.0.

A hybrid heuristic for capacitated three-level lot-sizing and replenishment problems with a distribution structure

We consider the capacitated three-level lot-sizing and replenishment problem with a distribution structure (3LSPD-C), recently proposed in the literature. In 3LSPD-C, a single production plant delivers items to the warehouses from where they are distributed to their corresponding retailers. There is a capacity on the total amount the plant can produce in each period, whereas there are no capacities on transportation. The goal of the problem consists in determining an integrated three-echelon production and distribution plan minimizing the total cost, which is composed of fixed costs for produc…

Probabilistic forecasting for sizing in the capacity firming framework

This paper proposes a strategy to size a grid-connected photovoltaic plant coupled with a battery energy storage device within the \textit{capacity firming} specifications of the French Energy Regulatory Commission. In this context, the sizing problem is challenging due to the two-phase engagement control with a day-ahead nomination and an intraday control to minimize deviations from the planning. The two-phase engagement control is modeled with deterministic and stochastic approaches. The optimization problems are formulated as mixed-integer quadratic problems, using a Gaussian copula methodo…

Dynamic lot size MIPs for multiple products and ELSPs with shortages, capacity and changeover limits

Scheduling multiple products with limited resources and varying demands remain a critical challenge for many industries. This work presents mixed integer programs (MIPs) that solve the Economic Lot Sizing Problem (ELSP) and other Dynamic Lot-Sizing (DLS) models with multiple items. DLS systems are classified, extended and formulated as MIPs. Especially, logical constraints are a key ingredient in succeeding in this endeavour. They were used to formulate the setup/changeover of items in the production line. Minimising the holding, shortage and setup costs is the primary objective for ELSPs. Thi…

面向净零能耗住宅的线性规划用于光伏板与电池的容量配置问题

Net-Zero Energy House-oriented Linear Programming for the Sizing Problem of Photovoltaic Panels and Batteries

本文针对净零能耗住宅中光伏板与电池容量配置问题，将含非凸约束的优化模型转化为可计算的线性规划，并结合共享经济投资策略，在日本社区案例中验证其长期实现净零能耗、降低电费且减小电网影响的效果。