We consider the multi-item inventory lot-sizing problem with supplier selection. The problem consists of determining an optimal purchasing plan in order to satisfy dynamic deterministic demands for multiple items over a finite planning horizon, considering that multiple suppliers are available to purchase from. As the complexity of the problem was an open question, we show that it is NP-hard. We propose a facility location extended formulation for the problem which can be preprocessed based on the cost structure and describe new valid inequalities in the original space of variables. Furthermore, we study the projection of the extended formulation into the original space and show the connection between the inequalities generated by this projection and the newly proposed inequalities. Additionally, we present a simple and easy to implement yet very effective MIP (mixed integer programming) heuristic using the extended formulation. Besides, we introduce two new benchmark sets of instances to assess the performance of the approaches under different cost structures. Computational results show that the preprocessing approach can significantly reduce the size of the formulation to be solved, allowing both an increase in the number of instances solved to optimality within the time limit and a reduction on the average time to solve them. Moreover, the described inequalities can improve the performance of a standard formulation for nearly all instance groups. They can also be used to provide strong lower bounds for certain large instances for which the preprocessed facility location formulation fails even to provide a linear relaxation bound due to memory limitations. Furthermore, the proposed MIP heuristic outperforms the heuristics available in the literature as it obtains solution values which at least match those reported for all instance groups, strictly improving most of them.
We consider a multi-stage stochastic lot-sizing problem with service level constraints and supplier-driven product substitution. A firm has multiple products and it has the option to meet demand from substitutable products at a cost. Considering the uncertainty in future demands, the firm wishes to make ordering decisions in every period such that the probability that all demands can be met in the next period meets or exceeds a minimum service level. We propose a rolling-horizon policy in which a two-stage joint chance-constrained stochastic program is solved to make decisions in each time per…
This paper addresses the two-stocking locations single item non-stationary stochastic lot-sizing problem. The inventory level at each location is reviewed periodically. Items can be reordered and received from a common central warehouse and can also be transshipped laterally from the other location. Lateral transshipment is assumed to be proactive to re-distribute the stock between two stocking locations. Therefore, the order of action in each period is: transshipping (if necessary), reordering (if necessary) and satisfying the demand at each location and each installation. The costs are impos…
Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper addresses the complexity of uncapacitated multi-plant lot-sizing problems. We consider a multi-item uncapacitated multi-plant lot-sizing problem with fixed transfer costs and show that two of its very restricted special cases are already NP-hard. Namely, we show that the single-item uncapacitated multi-plant lot-sizing problem with a single period and the multi-item uncapacitated …
Control of Dual-Sourcing Inventory Systems using Recurrent Neural Networks
Frankfurt School of Finance and Management（法兰克福金融管理学院）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Zurich（苏黎世大学）；Erasmus University Rotterdam（鹿特丹伊拉斯姆斯大学）
This paper proposes a mathematical model for the design of a two-echelon supply chain where a set of suppliers serve a set of terminal facilities that receive uncertain customer demands. This model integrates a number of system decisions in both the planning and operational stages, including facility location, multi-level service assignments, multi-modal transportation configuration, and inventory management. In particular, we consider probabilistic supplier disruptions that may halt product supply from certain suppliers from time to time. To mitigate the impact from supplier disruptions, a te…
This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing triangular fuzzy numbers. It is assumed that the imperfect items identified by screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred…
Recent developments in urbanization and e-commerce have pushed businesses to deploy efficient systems to decrease their supply chain cost. Vendor Managed Inventory (VMI) is one of the most widely used strategies to effectively manage supply chains with multiple parties. VMI implementation asks for solving the Inventory Routing Problem (IRP). This study considers a multi-product multi-period inventory routing problem, including a supplier, set of customers, and a fleet of heterogeneous vehicles. Due to the complex nature of the IRP, we developed a Modified Adaptive Genetic Algorithm (MAGA) to s…
The two-echelon inventory-routing problem (2E-IRP) addresses the coordination of inventory management and freight transportation throughout a two-echelon supply network. The latter consists of geographically widespread customers whose demand over a discrete planning horizon can be met from either their local inventory or intermediate facilities' inventory. Intermediate facilities are located in the city outskirt and are supplied from distant suppliers. The 2E-IRP aims to minimize transportation costs and inventory costs while meeting customers' demand. A route-based formulation is proposed and…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The cost structure includes time-varying holding costs, unitary production costs and setup costs. We establish a new lower bound for this problem by using a subtle time decomposition. We formulate this NP-hard problem as a global constraint and show that bound consistency can be achieved in pseudo-polynomial time and when not including the costs, in polynomial time…
This paper introduces an integrated lot sizing and scheduling problem inspired from a real-world application in off-the-road tire industry. This problem considers the assignment of different items on parallel machines with complex eligibility constraints within a finite planning horizon. It also considers a large panel of specific constraints such as: backordering, a limited number of setups, upstream resources saturation and customers prioritization. A novel mixed integer formulation is proposed with the objective of optimizing different normalized criteria related to the inventory and servic…
This paper investigates a stochastic inventory management problem in which a cash-constrained small retailer periodically purchases a product from suppliers and sells it to a market while facing non-stationary demands. In each period, the retailer's available cash restricts the maximum quantity that can be ordered. There exists a fixed ordering cost for the retailer when purchasing. We partially characterize the optimal ordering policy by showing it has an $\bf s-C$ structure: for each period, when initial inventory is above the $\bf$s threshold, no product should be ordered no matter how much…
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…
In this paper, we propose an inventory model where items are inspected through multiple screening processes before delivery to customers. Each screening process has independent screening rate and defective percentage. Defective items screened out are stored and then returned to supplier. Shortage backordering are also allowed in the model. Two approaches are used to obtain the closed-form optimal order size and the maximum backordering quantity. Numerical examples are also provided to demonstrate the use of the model.
In this paper, we formulate an optimal ordering policy as a stochastic control problem where each firm decides the amount of input goods to order from their upstream suppliers based on the current inventory level of its output good. For this purpose, we provide a closed-form solution for the optimal request of the raw materials for given a fixed production policy. We implement the proposed policy on a 15-firm acyclic network based on a real product supply chain. We first simulate ideal demand situations, and then we implement demand-side shocks (i.e., demand levels outside of those considered …
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 …
Dual-sourcing inventory systems, in which one supplier is faster (i.e. express) and more costly, while the other is slower (i.e. regular) and cheaper, arise naturally in many real-world supply chains. These systems are notoriously difficult to optimize due to the complex structure of the optimal solution and the curse of dimensionality, having resisted solution for over 40 years. Recently, so-called Tailored Base-Surge (TBS) policies have been proposed as a heuristic for the dual-sourcing problem. Under such a policy, a constant order is placed at the regular source in each period, while the o…
