Birger Raa

Modeling inventory routing problems in supply chains of high consumption products

Given a distribution center and a set of sales-points with their demand rates, the objective of the inventory routing problem (IRP) is to determine a distribution plan that minimizes fleet operating and average total distribution and inventory holding costs without causing a stock-out at any of the sales-points during a given planning horizon. We propose a new model for the long-term IRP when demand rates are stable and economic order quantity-like policies are used to manage inventories of the sales-points. The proposed model extends the concept of vehicle routes (tours) to vehicle multi-tours. To solve the nonlinear mixed integer formulation of this problem, a column generation based approximation method is suggested. The resulting sub-problems are solved using a savings-based approximation method. The approach is tested on randomly generated problems with different settings of some critical factors to compare our model using multi-tours as basic constructs to the model using simple tours as basic constructs.

Generating the group of reversible logic gates

Reversible logic plays a fundamental role both in ultra-low power electronics and in quantum computing. It is therefore important to have an insight into the structure of the group formed by the reversible logic gates and their cascading into reversible circuits. Such insight is gained from constructing chains of maximal subgroups. The subgroup of control gates plays a prominent role, as it is a Sylow 2-subgroup.

An enriched model for the integrated berth allocation and quay crane assignment problem

Given the increasing pressure to improve the efficiency of container terminals, a lot of research efforts have been devoted to optimizing container terminal operations. Most papers deal with either the Berth Allocation Problem (BAP) or the (Quay) Crane Assignment Problem (CAP). In the literature, handling times are often simplified to be berth dependent or proportional to vessel size to ignore the CAP when scheduling vessels. This is unsatisfactory for real-life applications because the handling time primarily depends on the number of containers to be handled and the number of cranes deployed. Only a limited number of papers deal with the combination of berth allocation and crane assignment. In these papers however, authors often have resorted to algorithmic simplifications that limit the practical use of the models. This paper presents an integrated BAP-CAP model taking into account vessel priorities, preferred berthing locations and handling time considerations. The proposed MILP model is validated on real-life data illustrating the potential to support operational and tactical decision-making.

A robust dynamic planning strategy for lot-sizing problems with stochastic demands

We consider the question of generating robust plans for production planning problems under uncertainty. In particular, we present an alternative approach to generate robust solutions for lot-sizing problems with stochastic demand. The proposed approach is dynamic and includes a decision rule that guides the planner. The decision rule parameters are determined so that the number of expected planning adaptations and their magnitudes are under control. The robust approach and its related models are presented together with some computational results to show how it performs compared to other approaches.

Analysis of the single-vehicle cyclic inventory routing problem

The single-vehicle cyclic inventory routing problem (SV-CIRP) consists of a repetitive distribution of a product from a single depot to a selected subset of customers. For each customer, selected for replenishments, the supplier collects a corresponding fixed reward. The objective is to determine the subset of customers to replenish, the quantity of the product to be delivered to each and to design the vehicle route so that the resulting profit (difference between the total reward and the total logistical cost) is maximised while preventing stockouts at each of the selected customers. This problem appears often as a sub-problem in many logistical problems. In this article, the SV-CIRP is formulated as a mixed-integer program with a nonlinear objective function. After a thorough analysis of the structure of the problem and its features, an exact algorithm for its solution is proposed. This exact algorithm requires only solutions of linear mixed-integer programs. Values of a savings-based heuristic for this problem are compared to the optimal values obtained for a set of some test problems. In general, the gap may get as large as 25%, which justifies the effort to continue exploring and developing exact and approximation algorithms for the SV-CIRP.

A hybrid approach to designing inbound-resupply strategies

We model the behavior of the demand distribution and lead-time distribution separately and determine the value of demand during lead time by discrete-event simulation. A new methodology determines the optimal inbound-resupply strategy when suppliers ship goods to receivers. An evolutionary metaheuristic uses discrete-event simulation to calculate safety stock levels and minimize total logistics costs.

Cyclic scheduling of multiple tours with multiple frequencies for a single vehicle

This paper discusses a cyclic scheduling problem arising in cyclic inventory routing, in which a single vehicle has to make multiple tours with different frequencies. The objective is to find a minimal makespan schedule in which the vehicle never travels more than 8 hours per day [and] all tours are repeated with constant intervals. A mathematical model and a best-fit insertion heuristic are presented for this problem. Computational experiments show that the heuristic finds the optimal solution for 79 out of 100 randomly generated test instances.

Revisiting Service-level Measurement for an Inventory System with Different Transport Modes

Abstract In a stochastic supply link between a supplier and a receiver the receiver will call upon the supplier who can replenish his inventory at the lowest total cost. This total cost typically contains the order costs, transportation costs and inventory costs. A crucial component of the total inventory costs are the costs of safety stock, which is held by the receiver to protect against stockouts. The optimal amount of safety stock can either be derived from the cost of a stockout or from an imposed service level. Since the cost of a stockout cannot always be determined easily, the service‐level approach is a common point of departure for practitioners and academics. Several ways are discussed in the literature to specify the service level, and the definition used can have an important impact on the derived level of safety stock. In this paper the literature on the inventory‐theoretic framework for transport selection is surveyed, with particular emphasis on the criterion that is used to establish safety stock levels. A case study based on real‐life data is then presented to illustrate the impact of two different service‐level definitions on the total logistics costs.

The Berth Allocation and Quay Crane Assignment Problem Using a CP Approach

This paper considers the combination of berth and crane allocation problems in container terminals. We propose a novel approach based on constraint programming which is able to model many realistic operational constraints. The costs for berth allocation, crane allocation, time windows, breaks and transition times during gang movements are optimized simultaneously. The model is based on a resource view where gangs are consumed by vessel activities. Side constraints are added independently around this core model. The model is richer than the state of the art in the operations research community. Experiments show that the model produces solutions with a cost gap of 1/10 (7,8%) to 1/5 (18,8%) compared to an ideal operational setting where operational constraints are ignored.

Cardinality reasoning for bin-packing constraint: application to a tank allocation problem

Flow reasoning has been successfully used in CP for more than a decade. It was originally introduced by Regin in the well-known Alldifferent and Global Cardinality Constraint (GCC) available in most of the CP solvers. The BinPacking constraint was introduced by Shaw and mainly uses an independent knapsack reasoning in each bin to filter the possible bins for each item. This paper considers the use of a cardinality/flow reasoning for improving the filtering of a bin-packing constraint. The idea is to use a GCC as a redundant constraint to the BinPacking that will count the number of items placed in each bin. The cardinality variables of the GCC are then dynamically updated during the propagation. The cardinality reasoning of the redundant GCC makes deductions that the bin-packing constraint cannot see since the placement of all items into every bin is considered at once rather than for each bin individually. This is particularly well suited when a minimum loading in each bin is specified in advance. We apply this idea on a Tank Allocation Problem (TAP). We detail our CP model and give experimental results on a real-life instance demonstrating the added value of the cardinality reasoning for the bin-packing constraint.