Managing transshipments in a multi-retailer system with approximate policies

Using the right transshipment policy is important when transshipments are exercised under demand uncertainty. Optimal transshipment policy can be quite complex in a multi-firm system as optimal actions depend on all system variables. Moreover, both how to select requested retailer and how to respond to requests are in question. We introduce simple, close-to-optimal heuristic transshipment policies for multiple retailers. We first show that heuristic policies may perform even better than self-optimal policy, which is explained by Braess’s paradox. Then we test the performances of various heuristics with respect to centrally optimal policy. When retailers can observe others’ inventory levels, more effective transshipments can be made. Otherwise, a random selection performs quite well. We also observe that although always-accept respond policy is quite close to centrally optimal in small systems, the performance of pairwise-optimal holdback levels to respond requests is more clear and consistent for larger systems.     

A Semi-Markov decision problem for proactive and reactive transshipments between multiple warehouses

Lateral transshipments are an effective strategy to pool inventories. We present a Semi-Markov decision problem formulation for proactive and reactive transshipments in a multi-location continuous review distribution inventory system with Poisson demand and one-for-one replenishment policy. For a two-location model we state the monotonicity of an optimal policy. In a numerical study, we compare the benefits of proactive and different reactive transshipment rules. The benefits of proactive transshipments are the largest for networks with intermediate opportunities of demand pooling and the difference between alternative reactive transshipment rules is negligible.     

An index heuristic for transshipment decisions in multi-location inventory systems based on a pairwise decomposition

In multi-location inventory systems, transshipments are often used to improve customer service and reduce cost. Determining optimal transshipment policies for such systems involves a complex optimisation problem that is only tractable for systems with few locations. Consequently simple heuristic transshipment policies are often applied in practice. This paper develops an approximate solution method which applies decomposition to reduce a Markov decision process model of a multi-location inventory system into a number of models involving only two locations. The value functions from the subproblems are used to estimate the fair charge for the inventory provided in a transshipment. This estimate of the fair charge is used as the decision criterion in a heuristic transshipment policy for the multi-location system. A numerical study shows that the proposed heuristic can deliver considerable cost savings compared to the simple heuristics often used in practice.     

An inventory model with unidirectional lateral transshipments

This paper deals with a continuous review inventory system with Poisson demand, in which lateral transshipments are allowed. In case of a shortage at a location, another location acts as a supplier, if it is possible. A common assumption in earlier papers is that transshipments are allowed between all locations. This network configuration may, however, not be the best choice for many reasons. One such reason is that it may be difficult to establish contracts between locations regarding the design of the transshipment policy. Another reason is that a system with many transshipment links is much more complex than a system with few transshipment links. In this paper, we study a system where transshipments are allowed only in one direction. This may be a reasonable policy if the locations have very different backorder/lost sales costs. Our approach is relatively simple and fast, and works well in most cases.     

Optimal lateral transshipment policies for a two location inventory problem with multiple demand classes

We consider an inventory model for spare parts with two stockpoints, providing repairable parts for a critical component of advanced technical systems. As downtime costs for these systems are expensive, ready–for–use spare parts are kept in stock to be able to quickly respond to a breakdown of a system. We allow for lateral transshipments of parts between the stockpoints upon a demand arrival. Each stockpoint faces demands from multiple demand classes. We are interested in the optimal lateral transshipment policy. There are three ways in which a demand can by satisfied: from own stock, via a lateral transshipment, or via an emergency procedure. Using stochastic dynamic programming, we characterize and prove the structure of the optimal policy, that is, the policy for satisfying the demands which minimizes the average operating costs of the system. This optimal policy is a threshold type policy, with state-dependent thresholds at each stockpoint for every demand class. We show a partial ordering in these thresholds in the demand classes. In addition, we derive conditions under which the so-called hold back and complete pooling policies are optimal, two policies that are often assumed in the literature. Furthermore, we study several model extensions which fit in the same modeling framework.     

Production-inventory control policy under warm/cold state-dependent fixed costs and stochastic demand: partial characterization and heuristics

The motivation for our study comes from some production and inventory systems in which ordering/producing quantities that exceed certain thresholds in a given period might eliminate some setup activities in the next period. Many examples of such systems have been discussed in prior research but the analysis has been limited to production settings under deterministic demand. In this paper, we consider a periodic-review production-inventory model under stochastic demand and incorporate the following fixed-cost structure into our analysis. When the order quantity in a given period exceeds a specified threshold value, the system is assumed to be in a “warm” state and no fixed cost is incurred in the next period regardless of the order quantity; otherwise the system state is considered “cold” and a positive fixed cost is required to place an order. Assuming that the unsatisfied demand is lost, we develop a dynamic programming formulation of the problem and utilize the concepts of quasi-K-convexity and non-K-decreasing to show some structural results on the optimal cost-to-go functions. This analysis enables us to derive a partial characterization of the optimal policy under the assumption that the demands follow a Pólya or uniform distribution. The optimal policy is defined over multiple decision regions for each system state. We develop heuristic policies that are aimed to address the partially characterized decisions, simplify the ordering policy, and save computational efforts in implementation. The numerical experiments conducted on a large set of test instances including uniform, normal and Poisson demand distributions show that a heuristic policy that is inspired by the optimal policy is able to find the optimal solution in almost all instances, and that a so-called generalized base-stock policy provides quite satisfactory results under reasonable computational efforts. We use our numerical examples to generate insights on the impact of problem parameters. Finally, we extend our analysis into the infinite horizon setting and show that the structure of the optimal policy remains similar.     

Joint management of capacity and inventory in make-to-stock production systems with multi-class demand

We evaluate the benefits of coordinating capacity and inventory decisions in a make-to-stock production environment. We consider a firm that faces multi-class demand and has additional capacity options that are temporary and randomly available. We formulate the model as a Markov decision process (MDP) and prove that a solution to the optimal joint control problem exists. For several special cases we characterize the structure of the optimal policy. For the general case, however, we show that the optimal policy is state-dependent, and in many instances non-monotone and difficult to implement. Therefore, we consider three pragmatic heuristic policies and assess their performance. We show that the majority of the savings originate from the ability to dynamically adjust capacity, and that a simple heuristic that can adjust production capacity (based on workload fluctuation) but uses a static production/rationing policy can result in significant savings.     

The time-dependent capacitated profitable tour problem with time windows and precedence constraints

We introduce the time-dependent capacitated profitable tour problem with time windows and precedence constraints. This problem concerns determining a tour and its departure time at the depot that maximizes the collected profit minus the total travel cost (measured by total travel time). To deal with road congestion, travel times are considered to be time-dependent. We develop a tailored labeling algorithm to find the optimal tour. Furthermore, we introduce dominance criteria to discard unpromising labels. Our computational results demonstrate that the algorithm is capable of solving instances with up to 150 locations (75 pickup and delivery requests) to optimality. Additionally, we present a restricted dynamic programing heuristic to improve the computation time. This heuristic does not guarantee optimality, but is able to find the optimal solution for 32 instances out of the 34 instances.     

A hybrid multistart heuristic for the uncapacitated facility location problem

We present a multistart heuristic for the uncapacitated facility location problem, based on a very successful method we originally developed for the p-median problem. We show extensive empirical evidence to the effectiveness of our algorithm in practice. For most benchmarks instances in the literature, we obtain solutions that are either optimal or a fraction of a percentage point away from it. Even for pathological instances (created with the sole purpose of being hard to tackle), our algorithm can get very close to optimality if given enough time. It consistently outperforms other heuristics in the literature.     

Efficient solution of large scale,single-source,capacitated plant location problems

The single-source, capacitated plant location problem is considered. This problem differs from the capacitated plant location problem by the additional requirement that each customer must be supplied with all its demand from a single plant. An efficient heuristic solution, capable of solving large problem instances, is presented. The heuristic combines Lagrangian relaxation with restricted neighbourhood search. Computational experiments on two sets of problem instances are presented.     

Enhanced lateral transshipments in a multi-location inventory system

In managing an inventory network, two approaches to the pooling of stock have been proposed. Reactive transshipments respond to shortages at a location by moving inventory from elsewhere within the network, while proactive stock redistribution seeks to minimize the chance of future stockouts. This paper is the first to propose an enhanced reactive approach in which individual transshipments are viewed as an opportunity for proactive stock redistribution. We adopt a quasi-myopic approach to the development of a strongly performing enhanced reactive transshipment policy. In comparison to a purely reactive approach to transshipment, service levels are improved while a reduction in safety stock levels is achieved. The aggregate costs incurred in managing the system are significantly reduced, especially so for large networks. Moreover, an optimal policy is determined for small networks and it is shown that the enhanced reactive policy substantially closes the gap to optimality.     

Single vehicle routing with predefined client sequence and multiple warehouse returns: the case of two warehouses

We examine three interesting cases of the single vehicle routing problem with a predefined client sequence and two load replenishment warehouses. Given the location and demand of the clients, we seek the minimal cost route, which includes optimal load replenishment visits to the warehouses in order to fully satisfy the client demand. The cases studied vary with respect to inventory availability at each warehouse and are of increasing complexity. We have developed solution algorithms that address this complexity, ranging from a standard dynamic programming algorithm for the simplest case, to labeling algorithms and a new partitioning heuristic. The efficiency of these algorithms has been studied by solving a wide range of problem instances, and by comparing the results with those obtained from a state-of-the-art MILP solver.     

Optimal patient and personnel scheduling policies for care-at-home service facilities

In this paper we study the problem of personnel planning in care-at-home facilities. We model the system as a Markov decision process, which leads to a high-dimensional control problem. We study monotonicity properties of the system and derive structural results for the optimal policy. Based on these insights, we propose a trunk reservation heuristic to control the system. We provide numerical evidence that the heuristic yields close to optimal performance, and scales well for large problem instances.     

Multi-item spare parts systems with lateral transshipments and waiting time constraints

This paper deals with the analysis of a multi-item, continuous review model of two-location inventory systems for repairable spare parts, used for expensive technical systems with high target availability levels. Lateral and emergency shipments occur in response to stockouts. A continuous review basestock policy is assumed for the inventory control of the spare parts. The objective is to minimize the total costs for inventory holding, lateral transshipments and emergency shipments subject to a target level for the average waiting time per demanded part at each of the two locations. A solution procedure based on Lagrangian relaxation is developed to obtain both a lower bound and an upper bound on the optimal total cost. The upper bound follows from a heuristic solution. An extensive numerical experiment shows an average gap of only 0.31% between the lower and upper bounds. The experiment also gives insights into the relative improvement achieved by applying lateral transshipments and or the system approach. We also apply the proposed model to actual data from an air carrier company.     

Service differentiation through selective lateral transshipments

We consider a multi-item spare parts problem with multiple warehouses and two customer classes, where lateral transshipments are used as a differentiation tool. Specifically, premium requests that cannot be met from stock at their preferred warehouse may be satisfied from stock at other warehouses (so-called lateral transshipments). We first derive approximations for the mean waiting time per class in a single-item model with selective lateral transshipments. Next, we embed our method in a multi-item model minimizing the holding costs and costs of lateral and emergency shipments from upstream locations in the network. Compared to the option of using only selective emergency shipments for differentiation, the addition of selective lateral transshipments can lead to significant further cost savings (14% on average).     

Modeling formulation and a new heuristic for the railroad blocking problem

The railroad blocking problem is an important issue at the tactical level of railroad freight transportation. This problem consists of determining paths between the origins and destinations of each shipment to minimize the operating and user costs while satisfying the railroad supply and demand restrictions. A mixed-integer program (MIP) is developed to find the optimal paths, and a new heuristic is developed to solve the proposed model. This heuristic decomposes the model into two sub-problems of manageable size and then provides feasible solutions. We discuss the performance of the proposed heuristic for a set of instances with up to 90 stations. A comparison with the CPLEX MIP solver shows that the heuristic gives the exact solution for 10 out of 15 instances. For the remaining instances, the heuristic obtained solutions within a tolerance of 0.03–0.84%. Furthermore, compared with the CPLEX MIP solver, the heuristic reduced the run time by an average of 85% for all 15 instances. Finally, we present the computational results of the heuristic applied to Iranian railroads.     

Solving the routing and wavelength assignment problem with a multilevel distributed memetic algorithm

The Routing and Wavelength Assignment problem is a graph optimization problem which deals with optical networks, where communication requests in a network have to be fulfilled. In this paper, we present a multilevel distributed memetic algorithm (ML-DMA) for the static RWA which finds provable optimal solutions for most benchmark instances with known lower bounds and is capable of handling large instances. Components of our ML-DMA include iterated local search, recombination, multilevel scaling, and a gossip-based distribution algorithm. Results demonstrated that our ML-DMA is among the most sophisticated heuristic RWA algorithms published so far.     

Multi-location transshipment problem with capacitated transportation

We consider coordination among stocking locations through replenishment strategies that take explicitly into consideration transshipments, transfer of a product among locations at the same echelon level. We incorporate transportation capacity such that transshipment quantities between stocking locations are bounded due to transportation media or the location’s transshipment policy. We model different cases of transshipment capacity as a capacitated network flow problem embedded in a stochastic optimization problem. Under the assumption of instantaneous transshipments, we develop a solution procedure based on infinitesimal perturbation analysis to solve the stochastic optimization problem, where the objective is to find the policy that minimizes the expected total cost of inventory, shortage, and transshipments. Such a numerical approach provides the flexibility to solve complex problems. Investigating two problem settings, we show the impact of transshipment capacity between stocking locations on system behavior. We observe that transportation capacity constraints not only increase total cost, they also modify the inventory distribution throughout the network.     

Capacity allocation for demand of different customer-product-combinations with cancellations, no-shows, and overbooking when there is a sequential delivery of service

We consider a problem where different classes of customers can book different types of services in advance and the service company has to respond immediately to the booking request confirming or rejecting it. Due to the possibility of cancellations before the day of service, or no-shows at the day of service, overbooking the given capacity is a viable decision. The objective of the service company is to maximize profit made of class-type specific revenues, refunds for cancellations or no-shows as well as the cost of overtime. For the calculation of the latter, information of the underlying appointment schedule is required. Throughout the paper we will relate the problem to capacity allocation in radiology services. Drawing upon ideas from revenue management, overbooking, and appointment scheduling we model the problem as a Markov decision process in discrete time which due to proper aggregation can be optimally solved with an iterative stochastic dynamic programming approach. In an experimental study we successfully apply the approach to a real world problem with data from the radiology department of a hospital. Furthermore, we compare the optimal policy to four heuristic policies, of whom one is currently in use. We can show that the optimal policy significantly improves the currently used policy and that a nested booking limit type policy closely approximates the optimal policy and is thus recommended for use in practice.     

一类多商品设施选址问题的基于线性松弛解的启发式方法

多商品设施选址问题是众多设施选址问题中一类重要而困难的问题.在这一问题中,顾客的需求可能包含不止一种商品.对于大规模问题,成熟的商业求解器往往不能在满意的时间内找到高质量的可行解.研究了无容量限制的单货源多商品设施选址问题的一般形式,并给出了应用于此类问题的两个启发式方法.这两个方法基于原选址问题的线性规划松弛问题的最优解,分别通过求解紧问题和邻域搜索的方式给出了原问题的一个可行上界.理论分析指出所提方法可以实施于任意可行问题的实例.数值结果表明所提方法可以显著地提高求解器求解此类设施选址问题的求解效率.