Easy Capacitated Facility Location Problems, with Connections to Lot-Sizing

Constant Approximation Algorithm for Non-Uniform Capacitated Multi-Item Lot-Sizing via Strong Covering Inequalities

We study the non-uniform capacitated multi-item lot-sizing (\lotsizing) problem. In this problem, there is a set of demands over a planning horizon of $T$ time periods and all demands must be satisfied on time. We can place an order at the beginning of each period $s$, incurring an ordering cost $K_s$. The total quantity of all products ordered at time $s$ can not exceed a given capacity $C_s$. On the other hand, carrying inventory from time to time incurs inventory holding cost. The goal of the problem is to find a feasible solution that minimizes the sum of ordering and holding costs. Levi e…

The lateral transhipment problem with a-priori routes, and a lot sizing application

We propose exact solution approaches for a lateral transhipment problem which, given a pre-specified sequence of customers, seeks an optimal inventory redistribution plan considering travel costs and profits dependent on inventory levels. Trip-duration and vehicle-capacity constraints are also imposed. The same problem arises in some lot sizing applications, in the presence of setup costs and equipment re-qualifications. We introduce a pure dynamic programming approach and a branch-and-bound framework that combines dynamic programming with Lagrangian relaxation. Computational experiments are c…

一种求解具有分段线性生产成本的经济批量问题的新型精确算法

A Novel exact algorithm for economic lot-sizing with piecewise linear production costs

本文针对具有分段线性生产成本的经济批量问题，提出了一种时间复杂度为O(T^{m+2})的新型精确算法，改进了Ou此前的最先进算法，并引入了若干具有独立价值的新颖算法技术。

Two-level lot-sizing with inventory bounds

We study a two-level uncapacitated lot-sizing problem with inventory bounds that occurs in a supply chain composed of a supplier and a retailer. The first level with the demands is the retailer level and the second one is the supplier level. The aim is to minimize the cost of the supply chain so as to satisfy the demands when the quantity of item that can be held in inventory at each period is limited. The inventory bounds can be imposed at the retailer level, at the supplier level or at both levels. We propose a polynomial dynamic programming algorithm to solve this problem when the inventory…

一个具有单件订货量折扣和非递增价格的O(n log n)算法

An $O(n\log n)$ Algorithm for Single-Item Lot Sizing with a One-Breakpoint All-Units Discount and Non-Increasing Prices

本文提出一个O(n log n)算法，解决具有单件订货量折扣和非递增价格的单件订货问题，改进了传统算法的时间复杂度。

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 …