CORS / Optimization Days
HEC Montréal, May 2931, 2023
CORSJOPT2023
HEC Montreal, 29 — 31 May 2023
IS Inventory Systems
May 30, 2023 03:30 PM – 05:10 PM
Location: Saine Marketing (green)
Chaired by Michel Gendreau
4 Presentations

03:30 PM  03:55 PM
Periodic review stochastic inventory control system with both fixed order cost and nonUniform random yield
We study a periodic review stochastic inventory control system for a single product at a single location with both fixed order cost and random yield. The structure of the optimal inventory control policy in any period has been an open problem over three decades. A Negative Dominance (ND) property has been identified for the expected total cost function in any period. With the help of this ND property, the search of the optimal order quantity is simple. We have shown that there exists a critical initial inventory level at the beginning of any period such that the expected total cost function has the ND property at an initial inventory level below this critical initial inventory level. Furthermore, we have identified a lower and an upper bounds for the initial inventory levels in any period such that it is optimal to order a positive quantity at any initial inventory level below this lower bound but it is optimal to order nothing at any initial inventory level above this upper bound in any period.

03:55 PM  04:20 PM
Perishable Inventory Routing Problem with Uncertain Demand
In the Perishable Inventory Routing Problem (PIRP) with uncertain demand, a decisionmaker decides the number of units delivered to each retailer and determines delivery routes, considering inventory, transportation, and wastage costs. Inventory decisions are highly affected by the remaining shelflife of the products available. Due to the complex nature of PIRP, optimal solutions can be obtained only for small networks, and approximate dynamic programming methods fail to handle it effectively.
In this work, we decompose the PIRP into a Perishable Inventory Problem (PIP) and a Vehicle Routing Problem (VRP) and address them sequentially in two distinct phases. By successfully determining the replenishment quantities first, we then solve the VRP using stateoftheart algorithms. To achieve this, we create a direct lookahead policy that enables us to identify replenishment quantities in PIP efficiently. We propose an approximated twostage stochastic programming with a fixed cost representing the routing costs of the second phase.
We conduct an extensive numerical analysis based on the delivery of platelets to a set of hospitals and show that the proposed policy requires a few sample paths of uncertain demand to provide promising outcomes. We also observe that the proposed framework significantly outperforms the known algorithms in the literature. 
04:20 PM  04:45 PM
The integrated capacitated lotsizing and storage problem with multiple storage locations and fixed storage costs
In this study, the integration between the lotsizing and the storage assignment problem is addressed. Traditional lotsizing problems have been studied for decades. However, only recent studies have further considered decisions related to the assignment of items to inventory locations after production. In our problem, the storage space is divided into several separate locations, and the inventory is assigned to the storage locations according to specific conditions. Relocation of inventory is also possible, if required. In addition to the traditional cost elements from the lotsizing problem, we consider others relevant inventoryrelated costs, such as the storage fixed cost, handling cost, and relocation cost. A general mathematical model, as well as a transportation reformulation, is proposed. To solve the integrated problem, we have designed several heuristics that consists of splitting the problem into smaller subproblems, which are then solved sequentially. Computational experiments are carried out to evaluate the behavior of the integration between the lotsizing and the storage assignment decisions and the different solution approaches. Additional analyses assess the impact of some key input parameters of the problem on the solution.

04:45 PM  05:10 PM
Online order batching and picker routing in pickertoparts warehouses
In ecommerce, the demand for sameday and instant deliveries is continually growing and comes along with great challenges for the providers. In contradiction to the increased customer expectations, where short delivery times and reactiveness are major competitive arguments, most existing research on operational planning for ecommerce warehousing is concentrated on solving offline planning problems, where all information on customer orders is supposed to be given a priori. In this work, we examine batching and picker routing problems in pickertoparts warehouses from the online perspective, where the incoming orders arrive dynamically over time. We use competitive analysis and extensive computational experiments to derive wellperforming online policies. Based on this analysis, we derive recommendations for highstake investment decisions in the context of pickertoparts warehouses, such as the acquisition of the pickassist mobile robots and the installation of the put walls.
Keywords: ecommerce; pickertoparts warehouses; online optimization; batching problems; picker routing problems