Yale T. Herer

Transshipments: An emerging inventory recourse to achieve supply chain leagility

Abstract Supply chain designs are constrained by the cost-service trade-off. Cost minimization typically leads to physically efficient or lean supply chains at the expense of customer responsiveness or agility. Recently, the concept of leagility has been introduced. Research on leagility, defined as the capability of concurrently deploying the lean and agile paradigms, hinges heavily on the identification of the decoupling point, which, in turn, is enabled by postponement. Postponement strategies, however, present a cross-functional challenge for implementation. As a tactical solution to achieve leagility without postponement, we introduce transshipments, which represent a common practice in multi-location inventory systems involving monitored movement of stock between locations at the same echelon level of the supply chain. Through a series of models, we establish how transshipments can be used to enhance both agility and leanness.

Heuristics for a One-Warehouse Multiretailer Distribution Problem with Performance Bounds

We investigate the one warehouse multiretailer distribution problem with traveling salesman tour vehicle routing costs. We model the system in the framework of the more general production/distribution system with arbitrary non-negative monotone joint order costs. We develop polynomial time heuristics whose policy costs are provably close to the cost of an optimal policy. In particular, we show that given a submodular function which is close to the true order cost then we can find a power-of-two policy whose cost is only moderately greater than the cost of an optimal policy. Since such submodular approximations exist for traveling salesman tour vehicle routing costs we present a detailed description of heuristics for the one warehouse multiretailer distribution problem. We formulate a nonpolynomial dynamic program that computes optimal power-of-two policies for the one warehouse multiretailer system assuming only that the order costs are non-negative monotone. Finally, we perform computational tests which compare our heuristics to optimal power of two policies for problems of up to sixteen retailers. We also perform computational tests on larger problems; these tests give us insight into what policies one should employ.

The metered inventory routing problem, an integrative heuristic algorithm

Abstract The Metered Inventory Routing Problem (MIRP) involves a central warehouse, a fleet of trucks with a finite capacity, and a set of customers, for each of whom there is an estimated consumption rate, and a known storage capacity. The objective is to the determine when to service each customer, as well as the route to be performed by each truck, in order to minimize the total discounted costs. The problem is solved on a rolling horizon basis, taking into consideration holding, transportation, fixed ordering, and stockout costs. The algorithm we develop uses the concept of ‘temporal distances’; in short, the temporal distance between two customers is the cost of moving these customers to a common period. A simulation study is performed to demonstrate the effectiveness of our procedure.

Optimal and heuristic algorithms for the multi-location dynamic transshipment problem with fixed transshipment costs

We consider centrally controlled multi-location systems, which coordinate their replenishment strategies through the use of transshipments. In a dynamic deterministic demand environment the problem is characterized by several locations, each of which has known demand for a single product for each period in a given finite horizon. We consider replenishment, transshipment and inventory holding costs at each location, where the first two have location-dependent fixed, as well as linear components, and the third is linear and identical to all locations. We prove that the resulting dynamic transshipment problem is NP-hard, identify a special structure which is satisfied by an optimal solution and develop, based on this structure, an exponential time algorithm to solve the problem optimally. In addition, we develop a heuristic algorithm, based on partitioning the time horizon, which is capable of solving larger instances than the optimal solution. Our computational tests demonstrate that the heuristic performs extremely well.

Multi-location transshipment problem with capacitated production

We consider coordination among stocking locations through replenishment strategies that explicitly take into account lateral transshipments, i.e., transfer of a product among locations at the same echelon level. Our basic contribution is the incorporation of supply capacity into the traditional transshipment model. Our goal is to analyze the impact on system behavior and on stocking locations’ performance of the fact that the supplier may fail to fulfill all the replenishment orders. We therefore formulate the capacitated supply scenario as a network flow problem embedded in a stochastic optimization problem, which is solved through a sample average approximation method. We find that, depending on the production capacity, system behavior can vary drastically. Moreover, in a production-inventory system, we find evidence that either capacity flexibility (i.e., extra production) or transshipment flexibility (i.e., pooling) is required to maintain a desired level of service.

The segmented bidirectional single-loop topology for material flow systems

This paper introduces the segmented bidirectional single-loop (SBSL) flow topology for carrier-based material handling systems. This configuration is based on a single-loop flow-path structure that is divided into non-overlapping segments, each containing a single carrier operating in a bidirectional mode. The design procedure comprises a 0 – 1 mixed-integer formulation to determine the single-loop including the pickup and delivery station location. The second stage is a segmentation procedure to determine the non-overlapping segments in the loop. Finally the performance of the SBSL is evaluated by means of simulation.

Economic optimization of off-line inspection in a process that also produces non-conforming units when in control and conforming units when out of control

A finite batch of units is produced by a process subject to random failures. The process starts from the in-control state and may shift, while producing a unit, to the out of control state. We consider the case that inspection is conducted after all the units of the batch have been produced, when the production order of the units is preserved. Most research has assumed that while in the in-control state, the process produces only conforming units and in the out of control state, it produces only non-conforming ones. In our research we relax this assumption, i.e. we consider that in the in-control state the process may also produce non-conforming units and in the out of control state, it may also produce conforming ones. Using dynamic programming, we develop an optimal inspection/disposition policy that finds which units to inspect and how to dispose of uninspected units in order to minimize the expected cost, which includes inspection and penalty costs due to classification errors. In addition to the optimal policy, we develop several heuristic policies since the computational complexity of the dynamic programming calculations is O(3N). We then perform computational studies to check the behavior of the optimal and heuristic policies and also to compare the latter policies.

Economic optimization of off-line inspection in a process subject to failure and recovery

In certain types of processes, verification of the quality of the output units is possible only after the entire batch has been processed. We develop a model that prescribes which units should be inspected and how the units that were not inspected should be disposed of, in order to minimize the expected sum of inspection costs and disposition error costs, for processes that are subject to random failure and recovery. The model is based on a dynamic programming algorithm that has a low computational complexity. The study also includes a sensitivity analysis under a variety of cost and probability scenarios, supplemented by an analysis of the smallest batch that requires inspection, the expected number of inspections, and the performance of an easy to implement heuristic.

Off-line inspections under inspection errors

The problem of off-line inspection is of both practical and theoretical interest. It has been the subject of research in somewhat simplistic scenarios. In this paper, the theoretical coverage of this problem is extended to include inspection errors. In particular, a process which is subject to random failures that sequentially produces a batch of units is investigated. After the batch is complete, off-line inspections are performed. In the proposed model it is these inspections that are subject to errors. The optimal inspection policy, i.e., which units should be inspected and the inspection order so as to minimize the expected number of inspections, is determined. The considered objective function is to find the point at which the machine fails with a given confidence level. The optimal policy is found by a dynamic programming algorithm and four different heuristic policies are investigated. An extensive computational study that examines the behavior of both the optimal and heuristic policies is presented. In particular, the effect of the model parameters on the behavior of the optimal policy is analyzed. The heuristic policies are computationally studied with the goal of comparing their quality to the optimal solution, and also to compare the heuristics themselves.

Self-correcting inspection procedure under inspection errors

Abstract In this paper we present a novel treatment of the inspection-system design problem when inspection is unreliable and subject to classification errors. Our approach, based on the theory of Error-Correcting Codes (ECC), leads to the development of a Self-Correcting Inspection (SCI) decision rule that does not require complete knowledge of inspection error probabilities. We show that the proposed rule assures correct classification, if the number of inspection errors is less than a certain number. We analyze the performance of the SCI decision rule under different inspection situations, including some situations that are uncommon in the field of error-correcting codes. Then, we show how the underlying mathematical structure can be applied to determine the number of inspections and the level of inspection reliability in order to minimize the sum of inspection-related costs. The practical contribution of this work lies in that it expands the ability of the designer of inspection systems to deal with cases where there is very little or no information regarding the reliability of the inspection operations.