Evaluation of Procurement Scenarios in One-Dimensional Cutting Stock Problem with a Random Demand Mix

The one-dimensional cutting stock problem describes the problem of cutting standard length stock material into various specified sizes while minimizing the material wasted (the remnant or drop as manufacturing terms). This computationally complex optimization problem has many manufacturing applications. One-dimensional cutting stock problems arise in many domains such as metal, paper, textile, and wood. To solve it, the problem is formulated as an integer linear model first, and then solved using a common optimizer software. This paper revisits the stochastic version of the problem and proposes a priority-based goal programming approach. Monte Carlo simulation is used to simulate several likely inventory order policies to minimize the total number of shortages, overages, and the number of stocks carried in inventory

Maximizing space utilization in unit-load warehouses.

In a unit-load warehouse, products are stored and retrieved in pallet quantities. Examples include retail distribution centers (DC), third-party DCs, and transshipment hubs in freight transportation. Expenses related to space are a significant component of the operational cost of unit-load warehouses; therefore, maximizing space utilization is important. Moreover, the continuing revolution of retail e-commerce is changing the role and design of modern distribution centers (Boysen et al., 2018). An important trend with serious implications for design is the desire of many distributors to locate DCs in or near metropolitan areas in order to support same-day service or better (Thuermer, 2018). Land in these areas is very expensive, so there is a need to make the best use of existing space. The ability to store more products in the same space increases inventory availability and therefore service, and the ability to store the same inventory in a smaller footprint reduces costs. In this dissertation, we propose two strategies to improve space utilization in unit-load warehouses. We aim to minimize what we called loss of vertical space within slots (LVS)—the mismatch between the height of the pallet and the height of the slot where it is stored. LVS is a significant problem because it is standard practice to design storage racks in unit-load warehouses with all slots of equal height (maximum pallet height) such that every pallet can fit in every slot; however, pallet heights vary greatly. We propose the use of storage racks with multiple slot heights so that slot heights can better match the distribution of pallet heights. We analyzed historic (forecasted) inventory levels and the pallet heights to determine a robust design that guarantees a desired storage service level. Our method addresses the new warehouse design decisions that arise when having multiple slot heights: How to arrange the different slot heights in the rack-bays? How to organize the layout? How to avoid storage shortages? How do different slot heights affect travel times? We found that using multiple slot heights in unit-load warehouses has significant benefits in terms of footprint, expected travel time, and racking cost. For a typical warehouse, we expect space savings of 25–35 percent, depending on the number of slot types, and savings of 15–25 percent in annual operating cost. Although using multiple slot heights significantly decreases the loss of vertical space within slots, it does not completely eliminate it, and in warehouses where inventory levels are highly variable or product mixes change rapidly, this wasted space can still be significant. Examples of this situation in practice include warehouses with correlated order profiles, demands with seasonal peaks, new product launches, and distribution network consolidations. For such business environments, we propose pallet racks with dynamic heights as a way to maximize space utilization. Contrary to traditional pallet racks, the uprights and beams of pallet racks with dynamic heights are equipped with a mechanism to adjust slot heights easily. We found that pallet racks with dynamic heights have expected space savings of 16–30 percent when compared to traditional pallet racks

The stochastic trim-loss problem

The cutting stock problem (CSP) is one of the most fascinating problems in operations research. The problem aims at determining the optimal plan to cut a number of parts of various length from an inventory of standard-size material so to satisfy the customers demands. The deterministic CSP ignores the uncertain nature of the demands thus typically providing recommendations that may result in overproduction or in profit loss. This paper proposes a stochastic version of the CSP which explicitly takes into account uncertainty. Using a scenario-based approach, we develop a two-stage stochastic programming formulation. The highly non-convex nature of the model together with its huge size prevent the application of standard software. We use a solution approach designed to exploit the specific problem structure. Encouraging preliminary computational results are provided.Stochastic programming Trim-loss problem Branch and bound