Multiple in-cycle transshipments with positive delivery times

We study a centralized inventory sharing system of two retailers that are replenished periodically. Between two replenishments, a unit can be transshipped to a stocked-out retailer from the other. It arrives a transshipment time later, during which the stocked-out retailer incurs backorder cost. Without transshipment, backorder cost is incurred until the next replenishment. Since the transshipment time is shorter than the time between two replenishments, transshipments can reduce the backorder cost at the stocked-out retailer and the holding costs at the other retailer. The system is directed by a centralized inventory manager, who minimizes the long-run average cost consisting of replenishment, holding, backorder, and transshipment costs. The transshipment policy is characterized by hold-back inventory levels, which are nonincreasing in the remaining time until the next replenishment. The transshipment policy differs from those in the literature because we allow for multiple transshipments between replenishments, positive transshipment times, and backorder costs. We also discuss the challenges associated with positive replenishment time and develop upper and lower bounds of average cost in this case. Bounds are numerically shown to have an average gap of 1.1%. A heuristic solution is based on the upper bound and differs from the optimal cost by at most this gap. © 2011 Production and Operations Management Society

Optimal transshipments and reassignments under periodic orcyclic holding cost accounting

Cataloged from PDF version of article.In a centrally managed system, inventory at a retailer can be transshipped to a stocked-out retailer to meet demand. As the inventory at the former retailer may be demanded by future customers of that retailer and transshipment time/cost is non-negligible, it can be more profitable to not transship in some situations. When unsatisfied demand is backordered, reassignment of inventory to a previously backordered demand can perhaps become profitable as demand uncertainty resolves over time. Despite this intuition, we prove that no reassignments are necessary for cost optimality under periodic holding cost accounting in a two-retailer system. This remains valid for multi-retailer systems according to numerical analyses. When holding costs are accounted for only at the end of each replenishment cycle, reassignments are necessary for optimality but insignificant in reducing the total cost. In most instances tested, the decrease in total cost from reassignments is below 2% for end of cycle holding cost accounting. These results simplify transshipment policies and facilitate finding good policies in both implementation and future studies, as reassignments can be omitted from consideration in optimization models under periodic holding cost accounting and in approximation models under cyclical cost accounting

In-Season Transshipments Among Competitive Retailers

Cataloged from PDF version of article.A decentralized system of competing retailers that order and sell the same product in a sales season is studied. When a customer demand occurs at a stocked-out retailer, that retailer requests a unit to be transshipped from another retailer who charges a transshipment price. If this request is rejected, the unsatisfied customer may go to another retailer with a customer overflow probability. Each retailer decides on the initial order quantity from a manufacturer and on the acceptance/rejection of each transshipment request. For two retailers, we show that retailers' optimal transshipment policies are dynamic and characterized by chronologically nonincreasing inventory holdback levels. We analytically study the sensitivity of holdback levels to explain interesting findings, such as smaller retailers and geographically distant retailers benefit more from transshipments. Numerical experiments show that retailers substantially benefit from using optimal transshipment policies compared to no sharing. The expected sales increase in all but a handful of over 3,000 problem instances. Building on the two-retailer optimal policies, we suggest an effective heuristic transshipment policy for a multiretailer system

Planning and scheduling approaches to operate a particular FMS

This paper contains a detailed description of a thirteen machine COMAU FMS for a company in Torino, Italy. The monthly and daily problems that need to be addressed and the approaches that are suggested to operate this system efficiently are detailed. The trickier problems and constraints are those of tool management, especially tool loading. Detailed tooling data and their analysis are also presented. The complete spectrum of operational problems addressed range from aggregate planning to detailed scheduling, including fixture and inventory management. Breakdown situations are also addressed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29836/1/0000183.pd

A hierarchical approach to solving machine grouping and loading problems of flexible manufacturing systems

A flexible manufacturing system (FMS) is an integrated system of computer numerically controlled (CNC) machine tools, each having an automatic tool interchange capability, and all connected by an automated material handling system. One or more computers control most real-time functions.Flexible manufacturing is realized to be an efficient alternative to conventional manufacturing that allows simultaneous machining of small to medium batches of a variety of part types. Parts can flow through the system in unit batch sizes. These systems typically machine five to forty different part types.In managing these systems, technological requirements indicate that several decisions must be made prior to system start-up. With these requirements in mind, previous research has defined a set of production planning problems, providing a conceptual framework to aid an FMS manager in setting up his/her system to enable efficient production. Several approaches have been taken to solve several of these problems and we describe those here. The main focus in this paper is on only two of these planning problems, the machine grouping and loading problems. In brief, the FMS machine grouping problem is to partition the mi machine tools of type i into gi groups to maximize expected production, subject to FMS technological and capacity constraints. Machines in a group are identically tooled and hence can perform the same operations during production. The FMS loading problem is to allocate operations and associated tooling of a selected set of part types among the machine groups, according to some appropriate (system dependent) loading objective, also subject to technological and capacity constraints.This paper ties some previous results together by suggesting a hierarchical approach to solve actual grouping and loading problems. Both problems are first defined at an aggregated level of detail and in the context of a queyeing network model. At this level, much information is suppressed. However, the robustness of the model allows the application of the obtained theoretical results to a lower level in the hierarchy that considers all details of these problems. In addition, results obtained using the aggregate model can be used as input to the detailed models. Here, the grouping and loading problems are formulated in all detail as nonlinear integer programs, using all available and required information. The use of these models to solve realistic machine grouping and loading problems is then described. Finally, future research needs are suggested.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/26252/1/0000333.pd

On the nonconcavity of throughput in certain closed queueing networks

Analytic queueing network models are being used to analyze various optimization problems such as server allocation, design and capacity issues, optimal routing, and workload allocation. The mathematical properties of the relevant performance measures, such as throughput, are important for optimization purposes and for insight into system performance.We show that for closed queueing networks of m arbitrarily connected single server queues with n customers, throughput, as a function of a scaled, constrained workload, is not concave. In fact, the function appears to be strictly quasiconcave. There is a constraint on the total workload that must be allocated among the servers in the network. However, for closed networks of two single server queues, we prove that our scaled throughput is concave when there are two customers in the network and strictly quasi-concave when there are more than two customers. The mathematical properties of both the scaled throughput and reciprocal throughput are demonstrated graphically for closed networks of two and three single server queues.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25952/1/0000018.pd

Algorithms for efficient planning and operation of a particular FMS

This article is a detailed case study of a particular FMS that will be operational in 1989. It describes the daily planning and operating problems that will need to be addressed. The algorithms that will operate this system are presented. Given the daily changing production requirements, the algorithms begin with an aggregate planning feasibility check. Then planning, scheduling, inventory management, and breakdowns are addressed.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45447/1/10696_2004_Article_BF00183873.pd

A study of FMS part type selection approaches for short-term production planning

This research compares seven approaches from the literature to the selection of part types for simultaneous production over the next time horizon. A flexible approach to the selection of part types and the simultaneous determination of their mix ratios so as to balance aggregate machine workloads is presented. Constraints on tool magazine capacity are considered. Simulation studies are conducted on realistic, detailed models of flexible flow systems (FFSs) configured as pooled machines of equal sizes. The simulated settings are constructed to evaluate the impact of such factors as blocking, transportation, buffer utilizations, and fixture requirements and limitations of various types.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45438/1/10696_2004_Article_BF00713157.pd

The optimality of balancing workloads in certain types of flexible manufacturing systems

Symmetric mathematical programming is used to analyze the optimality of balancing workloads to maximize the expected production in a single-server closed queuing network model of a flexible manufacturing system (FMS). In particular, using generalized concavity we prove that, even though the production function is not concave, balancing workloads maximizes the expected production in certain types of m-machine FMS's with n parts in the system. Our results are compared and contrasted with previous models of production systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/25713/1/0000270.pd