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Closed loop repairable parts inventory system: a literature review.

Abstract

The paper reviews published literature related to multi--echelon inventory models for repairable items. Our objective is to understand the existing analytical models and their application in the context of the management of spare parts where repair facilities are resource--constrained. The focus of the review is restricted to the models which are suitable for practical application. A variety of models applicable to multi echelon inventory system are reviewed and the Multi--Echelon Technique for Recoverable Item Control (METRIC) model and its variations, Level of Repair Analysis (LORA) are described. Taxonomy, showing the current position in the context of the existing research is also presented.

Keywords: Repairable Parts Inventory System; Multi--Echelon Technique for Recoverable Item Control; queuing models; Level-of-Repair Analysis (LORA)

JEL codes: MO11; N60; G31

INTRODUCTION

Repairable part inventories are particularly expensive parts of the machines which are normally repaired and replaced for the smooth working of the machines. Here failed inventory of items may go through a transformation, termed in general as repairs but the inventory is neither lost nor produced. Failure events drive the demand and dynamics in repairable item multi--echelon models. The inventory position of repairable part inventory is governed by the repair capacity which is normally assumed to be constant, repair time and number of back orders of the parts as against the finished product inventories or work in process whose stock levels are governed by production capacities and demand uncertainty and increased or decreased accordingly. Further, in addition to a small local repair activities, the members of these supply chain pools the repair activities and the spare parts to a single location for mutual benefits.

The variations in the inventory policies motivated the authors to further understand the modeling efforts done in this area and present the related unaddressed issues. There are few studies that summarise this work namely Pierskalla and Voelker [1976]; Nahmias [1981]; Guide Jr. and Srivastava [1997] and Kennedy et al. [2002]. The most recent was in 2002, hence, there is a need to update these discussions and present the gaps in the present literature.

We first categorized the literature into three categories, providing an overview of the related literature till 2002 in the first phase. In the second phase, an attempt is made to classify the related literature published till date. Parameters like solution methodology (exact or approximate), inventory policy, underlined model (deterministic or stochastic) and variations/ modifications are used for the classification purpose.

The objectives of the study are to present the published literature in above categories and provide the Taxonomy. More specifically the study will try to answer the following question related to Repairable Parts Inventory System:

(a) How has the present literature related to multi--echelon repairable parts inventory systems classified?

(b) What are the features, applications and limitations of each of these categories?

(c) Which solution methods are used in each of these categories? What types of models are used for repairable parts inventory?

(d) What are the applications of the models pertaining to repairable parts inventory systems?

This review will be a ready reference to the researcher and decision makers working in industries with heavy utilization of equipments like Chemical processing industries, Petrochemical industries, Defense systems, Mass transit systems such as airlines, Road transport etc. It will be helpful in finding the better inventory policy parameters and options/alternatives thereof, in assisting the managerial decision making for purchase of repairable items and in determining the capacity requirements at the base and depots.

The basic model studied in the literature consists of one central reconditioning unit (the Depot) and several bases. Each base requires a set of working parts and maintains an inventory of spare items. All failed items are repaired at the central reconditioning unit (although in some cases repair at the base is also possible) which also maintains an inventory of spare items. A one--for--one replenishment policy is usually adopted, which implies that an item is ordered always, i.e., the items are not batched for repair or re--supply request. Whenever an item fails at any base, there are three events that occur simultaneously: (a) Replacement of the failed item with a spare item from the inventory, if available in base inventory; otherwise, back--ordered at the base till a replacement arrives from the repair depot, (b) sending of failed item for repair to the reconditioning unit, and (c) shipment of the replacement item by central depot if available in inventory; otherwise back--ordered by the depot with the replacement request till the item is repaired and available.

There is wide literature related to multi--echelon repairable parts inventory systems published in past and can be broadly classified into three categories according to the approaches used to address them. They are:

* Multi--Echelon Technique for Recoverable Item Control (METRIC).

* Queuing based models

* Level-of-Repair Analysis (LORA)

The next part of the paper has been organized through different sections dealing with the topic. The section 2 reviews the literature related to METRIC. The section 3 presents the Queuing based models. The section 4 reviews the LORA. The section 5 presents classification of current literature on the predefined parameters and last section provides the Taxonomy and shows the future direction for the research in the area.

2. MULTI--ECHELON TECHNIQUE FOR RECOVERABLE ITEM CONTROL (METRIC)

We begin this section by reviewing the mathematical models developed under the common framework of METRIC. The basic assumptions of the METRIC model are as follows:

(a) One for one (S--1, S) replenishment

(b) No condemnation of items (failed items are fully recoverable)

(c) Poisson failure process

(d) Large working--part population at the bases

(e) Adequate capacity at the repair facility, i.e. the repair time is independent of the present part in repairs and there is no waiting or batching of items before repair begins.

(f) Base demands for depot stock are served on an FCFS basis.

(g) No lateral supply between the bases

Sherbrooke [1968] developed the basic METRIC model. The item failure rate is assumed to be a compound Poisson process where the batches of demand (failures) follow the Poisson process and the number of demands per batch has logarithmic distribution. The number of failed items in transition from any base to the reconditioning unit as well as the number of failed items under repair at the reconditioning unit is assumed to be in the M/G/" queuing system. Due to the ample repair capacity assumption, successive replenishment lead times are assumed to be statistically independent.

In the METRIC model, the expected back--order level is used to evaluate performance. The process of estimating expected back--orders is repeated for generating table showing possible combinations of depot and base stock levels.

Then an expected back--orders vs. investment trade--off curves is plotted using marginal analysis, which helps managers in making strategic stock--related decisions.

2.1. Limitations of METRIC Based Models

There are several limitations/restrictive assumption of METRIC--based models. They are following:

* These models have a complex and rigorous analytical structure, which is sometime difficult for practicing community to understand and operate. Moreover, these models may not be applicable in specific real--life situations.

* There is always a need to define the distribution for the failure process as a Poisson failure process for analytical tractability. This is due to the special properties of the Poisson process. Similarly, the service times at the repair facility are often assumed to be exponentially distributed, again for analytical tractability.

* In the METRIC models, the distribution of replenishment lead times is captured using PALM's theorem. If there is finite capacity at the repair facility, the replenishment lead time will be a complex function of Work--in --Process (WIP) and the input flow rate of failed items to the repair facility.

* A one--for--one replenishment policy is always assumed, i.e., as and when an item fails, it is immediately sent to the repair facility and a simultaneous replenishment order is made. The other replenishment policies like continuous--review--batched replenishment (only one paper by [Moinzadeh and Lee 1986]) and periodic--review policies are not well--studied in the literature.

* FCFS priority is always assumed for the re--supply network in the literature.

3. QUEUING BASED MODELS

This section provides a brief overview of the queuing network models as they form the theoretical basis of application for the queuing approach to the multi--echelon repairable parts inventory system. After this overview, we discuss the queuing models which are developed specifically for the repairable item inventory problem.

Based on the literature, we can divide the queuing networks into three classes, i.e., open, closed and mixed queuing networks [Jackson 1963; Gordon and Newell 1967]. In an open network, the item that arrives in the system eventually departs from it. There are several arrival processes (from other nodes and outside) and departure processes (to other nodes and outside) pertaining to each node of the queuing network. In a closed network, the number of items in the system remains fixed, i.e., either there is no attrition of items from the system or if an item is removed from the system, it is replaced by a new item. Many of the METRIC--related systems resemble this type of network, where the parts are completely recoverable.

3.1. Queuing Models Applied to Repairable Item Inventory Problem

The standard machine repair problem in queuing is one of the basic applications in the field. In this model there is a finite repair capacity and a finite source of population from which failures occur. The failure rate is dependent on the state of the system i.e., the number of failed items in the system.

Advances and modifications of basic queuing models for machine repair problems are summarized in Table 3 below:

3.2. Limitations of Existing Queuing Network Models

The existing queuing network models have several limitations, some of which are listed below:

* As we see, the main purpose of the queuing--based methods is to analyze the current status of a given system in terms of the steady--state probability distribution of a number of repairable items at different stages. Substantial work may be necessary to use these results to formulate an objective function and optimize it.

* These models are limited to FCFS, Poisson failure and exponential service times, similar to METRIC--based models.

* Markov chain--based models have an additional disadvantage in terms of large state space in general settings. Hence, these queuing models for the repairable item inventory system are rarely implemented in practice.

4. LEVEL-OF-REPAIR ANALYSIS

Level-of-Repair Analysis (LORA) a phrase commonly used in military jargon [Barros 1998]. It is defined as tool used to decide "not only the repair or discard location for the items that make up a system or equipment, but the extent of maintenance permitted and the resources needed to support the maintenance process." [Crabtree and Sandel 1989]. It is mostly used for complex system like Aircrafts whose non availability results in loses to the user and also needs a large number of support equipments and skilled people for maintenance [Saranga and Kumar 2006]. LORA can be used for deciding about [Basten et al. 2012].

(a) Components to be repaired or replaced upon failure

(b) Location where the repair and discard of failed component happens

(c) Location where the resources can be deployed for repairing, discarding or movement of the failed components

LORA is used to finds best combination of repair/reject decision and also helps to decide a level of maintenance so that total support cost for the system can be minimize [Saranga and Kumar 2006]. Table 4 below summarizes the various LORA based model models

5. RECENT DEVELOPMENT IN REPAIRABLE PARTS INVENTORY SYSTEM

The literature related to Repairable Parts Inventory System in recent past is more towards the applications of base model using either METRIC or queuing based models in the different industry settings. The objective in these studies is to develop methods which will optimize the stocks so as to reduce overall cost and improve the service delivery (in terms of repair time reduction). Researcher used simulation modeling and also developed appropriate heuristics for achieving these objectives. The impact of various contract types, cooperative strategies, inventory ordering policies like batch ordering is evaluated in these studies.

Table 5 below presents the classification of the recent papers.

6. TAXONOMY OF THE MULTI--ECHELON CLOSED--LOOP INVENTORY SYSTEM

As we can see, not much attention has been given to periodic review replenishment in comparison to continuous review reorder point replenishment for which there are some exact results in the literature. To the best of our knowledge, there is no available analytical model or research paper addressing the periodic review policy in the context of the closed loop multi--echelon repairable inventory items.

As far as general settings are concerned, Hadley and Whitin [1963] have used the periodic review (R, T) policy in their book. Graves [1996] examines a multi echelon system with a general system topology. In this work, an assumption regarding schedule of preset replenishment, is made at each location. It is further argued that such scheduled shipments are general practice, in order to utilize the transportation resources efficiently.

The lack of an analytical model with the periodic review inventory policy in the context of repairable items motivates us to look for other solution methodologies. Choice of the discrete--event--simulation due to its wider applicability and its flexibility in customizing the approach to a specific problem context without restrictive assumptions is promising one.

Acknowledgement

The authors thank the anonymous referees, and the editor for their valuable feedback, which significantly improved the positioning and presentation of this paper.

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ROHIT KAPOOR * AND SUDHIR AMBEKAR

* Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, E-mail: rohitk@iimidr.ac.in, f10sudhiru@iimidr.ac.in

Table 1 below gives the overview of the work done in METRIC.

Table 1 Various METRIC Models and Their Extensions

Source           METRIC Modifications /      Description
                 Improvements

Simon [1971]     Inclusion of non            The model follows a
                 -recoverable failures       one--for--one
                                             replenishment policy
                                             between the bases and
                                             the depot, wherein depot
                                             uses a continuous review
                                             policy for studying the
                                             stationary properties of
                                             a two--echelon
                                             repairable item system

Muckstadt        Multi--indenture            Developed the multi--
[1973]                                       indenture problem (MOD--
                                             METRIC) where each item
                                             is assumed to be of the
                                             first indenture or Line
                                             Repairable Units and
                                             composed of
                                             subcomponents or Shop
                                             Replaceable Units

Sherbrooke       Two--parameter              Assumes that aggregate
[1986]           approximation for the       outstanding orders of
Graves [1985]    distribution of             all the bases at any
                 outstanding orders at       time equates to the
                 the bases                   addition of the number
                                             of back--orders in the
                                             depot for a specified
                                             target stock at the
                                             beginning of the time
                                             period and aggregate
                                             failure at all bases
                                             over the time interval
                                             equivalent to the
                                             delivery time from the
                                             repair depot to the
                                             base.

Moinzadeh        Continuous review (r, Q)    In this policy the base
and Lee [1986]   policy both at the base     sends items to the
                 as well as the depot        depots for repair after
                                             there are Q numbers of
                                             failed items and base
                                             also places an order of
                                             same size to the depots
                                             simultaneously to
                                             replenish the stock.
                                             Upon receiving the
                                             failed items from each
                                             base, the depot sends
                                             the items to the base in
                                             batches of Q quantity if
                                             it has sufficient
                                             inventory on hand,
                                             otherwise, a back--
                                             order is made at the
                                             depot

Lee [1987];      Lateral transshipment       Pooling groups are
                 between bases               formed by grouping
                                             identical bases. It
                                             assumes that each pool
                                             has identical bases. In
                                             case of non fulfillment
                                             of the demand from the
                                             stock on hand at a base,
                                             an emergency lateral
                                             transshipment is done
                                             from the stock--on--
                                             hand at another base in
                                             the same pooling group
                                             to fill this demand,
                                             otherwise the demand is
                                             back--ordered.

Axsater [1990]

Jung [1993]      Non--homogeneous failure    The mean failure rate of
                 process at the base         items is assumed to vary
                                             with time and is based
                                             on the concept of
                                             reliability improvement.
                                             Increased usage and
                                             failures will lead to
                                             design or repair
                                             improvement and the mean
                                             time between failures of
                                             items is an increasing
                                             function of the total
                                             operational time. Spare
                                             stock levels at the
                                             bases and at the repair
                                             facility are estimated
                                             using the approach of
                                             Graves [1985],

Kim et al.       Algorithm for stock         The stock level which
[1996]           level at the base           minimizes the total
                                             expected holding and
                                             shortage--cost function
                                             is found by the
                                             bisection method.
                                             Another stock level
                                             which satisfies the
                                             fill--rate criterion is
                                             also obtained. The
                                             maximum of these is
                                             chosen to be the optimal
                                             stock level.

Diaz and         Capacity constraint and     Three cases of limited
Fu [1997]        different priority          repair capacity are
                 classes for repair          considered, viz., M/M/c,
                                             M/G/c single class
                                             and M/G/c--multi -class
                                             priority. It has been
                                             shown that the
                                             performance levels of
                                             spare items at bases
                                             significantly differ
                                             under the assumption of
                                             finite repair capacity.

Wang et al.      Base--dependent             The steady--state
[2000]           distribution of transit     probability distribution
                 times from the base to      function of transit
                 the depot                   times for each base is
                                             derived and from this
                                             the distribution of
                                             outstanding orders is
                                             estimated. Through the
                                             analytical results, it
                                             has been shown that
                                             there is a significant
                                             difference in the
                                             service levels at the
                                             bases when they differ
                                             in their transit times
                                             to the depots.

Rustenberg       Application of VARI-        The study observes
et al. [2001]    METRIC on a complex--       through an extensive
                 technology organization     literature review that
                                             the VARI--METRIC method
                                             requires some
                                             modifications with
                                             respect to the
                                             capacitated systems and
                                             the hybrid product
                                             structures with both,
                                             repairable and non--
                                             repairable parts.

Wang et al.      Priority class of           Exact steady--state
[2002]           service differing in        probability
                 replenishment lead times    distributions of random
                                             base delays are derived
                                             for both the services.
                                             There is a significant
                                             reduction in inventory
                                             when the service is
                                             changed from emergency
                                             to non -emergency type.

Table 2
General Queuing Network Models

Source            Queuing Environment         Description

Jackson [1963]    Poisson arrival,            Under the product--form
                  exponential service         structure, the system is
                  times, multi--stages,       solved by analyzing each
                  FCFS, open queuing          node separately and then
                  network, exact analysis     the results are
                                              combined. In this case,
                                              the joint probability
                                              distribution of queue
                                              lengths at each node in
                                              the system is equal to
                                              the product of the
                                              probability distribution
                                              of queue lengths at each
                                              node

Gordon and        Exponential service         Suggested approximate
Newell [1967]     time, multi--stages,        expressions for the
                  closed queuing networks,    marginal probability
                  exact and approximate       distribution of items in
                  analysis.                   the system. An
                                              asymptotic analysis for
                                              closed systems with very
                                              large number of stages
                                              is also carried out.

Baskett           Service time with           Joint probability
et al. [1975]     rational Laplace            distribution (steady-
                  transformation; open,       state) of queue lengths
                  closed and mixed            is derived for multi--
                  network.                    node, multi--class
                                              items. Four cases--
                                              those of queue
                                              discipline, first--
                                              come--first--served
                                              (FCFS), processor
                                              sharing, no queuing, and
                                              last--come--first--
                                              served (LCFS)--are
                                              analyzed.

Reiser and        Closed networks, mean       Through--put time (when
Lavenberg         value analysis              an item is processed at
[1980]                                        a node), throughput
                                              rates and queue lengths
                                              are updated sequentially
                                              according to Little's
                                              Law. The convergence of
                                              queue lengths at several
                                              nodes is used as a
                                              stopping criterion.

Whitt [1983];     General arrival, general    Uses the decomposition
Bitran and        service time, multi--       approach for analyzing
Tirupati [1988]   stages, Open networks,      the complex open queuing
                  approximate analysis        networks. In the
                  using decomposition         decomposition approach,
                  approach.                   the interaction between
                                              the various nodes is
                                              analyzed first. Then the
                                              network is decomposed
                                              into sub--systems of
                                              individual stations and
                                              analyzed. The results
                                              are then recomposed to
                                              obtain the network
                                              performance

Table 3
Queuing Models Applied to Repairable Item Inventory Problem

Source          Problem Characteristics/    Description
                Solution Methodology

Gross et al.    Multi-echelon, Poisson      The model consists of a
[1983]          failure, Exponential        system which has a single
                service time, FCFS,         base with a base repair
                Implicit enumeration        facility and a depot
                                            repair facility. The
                                            system here is viewed as
                                            a network with three
                                            nodes, one for operating
                                            and spare machines at the
                                            base, one for machines in
                                            base repair, and one for
                                            machines in depot repair.
                                            An optimization problem
                                            is also solved where the
                                            decision variables are
                                            the base and depot repair
                                            capacities along with the
                                            spare items. The cost is
                                            minimized subject to the
                                            constraint of operational
                                            availability

Gross et al.    Multi-echelon, Poisson      The number of items owed
[1987];         failure, Exponential        by the depot to the bases
Gupta and       service time, FCFS,         (back--orders) is fixed
Albright        Decomposition approach      so that the problem can
[1992]                                      be decomposed. After
                                            decomposing, problem at
                                            each base is solved using
                                            one--dimensional birth--
                                            and--death process. The
                                            problem at depot is
                                            solved using an n--
                                            dimensional birth--and--
                                            death model

Gross et al.    Multi--echelon, Poisson     The model simplifies the
[1993]          failure, Exponential        inversion and a solution
                service time, FCFS,         is obtained by
                Iterative procedure         iterations. Methods for
                                            carrying out iterations
                                            include the Jacobi
                                            iteration, Gauss--Seidel
                                            and the bi-conjugate
                                            gradient.

Daryanani and   Multi--echelon, Poisson     The model gives
Miller [2002]   failure, Exponential        computational formula for
                service time, Dynamic       the steady--state
                backorder filling           probabilities.
                policy, iterative
                procedure involving the
                taboo structure of state
                space.

Table 4
LORA Models

Authors         Tools used to model LORA     Description

Alfredsson      Mathematical framework       A mathematical framework
[1997]          using both LORA and          for solving the problems
                METRIC                       related to decision about
                                             the optimizing the amount
                                             of spare part to be
                                             stocked, level of test
                                             equipment, tools and
                                             repair man power to be
                                             installed and the
                                             locations of these
                                             installations and spares
                                             using C programming.

Barros [1998]   Integer programming          This model is used for
                                             maintenance planning as a
                                             tool for deciding among
                                             the options available for
                                             level of repair. The
                                             model divides the time
                                             dependent life-cycle
                                             maintenance cost in two
                                             fixed and variable costs
                                             for getting the optimum
                                             solution.

Saranga and     Genetic Algorithm            Optimization model for
Kumar [2006]                                 maintenance of aircraft
                                             engine. This algorithm
                                             can be effectively used
                                             for deciding about
                                             allocation of
                                             repair/reject option
                                             among different echelons.
                                             This allocation will help
                                             in minimizing total
                                             maintenance cost where in
                                             total life cycle cost
                                             (LCC) will also be
                                             minimum at the design
                                             stage.

Basten et al.   Integer programming by       Specific problem solved
[2009]          removing the integrality     in this study is a NP
                constraints                  hard problem. The
                                             integrality constraints
                                             on most of the variables
                                             are removed. The problem
                                             is a linear programming
                                             problem after removal of
                                             the integrality
                                             constraints and can be
                                             solved in polynomial
                                             time. The computational
                                             time is dependent on
                                             number of components in
                                             the system, indenture and
                                             echelon levels and number
                                             of fixed cost sets of the
                                             components.

Brick and       Mixed integer programming    The model considered
Uchoa [2009]                                 discrete location of
                                             facilities and
                                             installation of
                                             capacitated resources and
                                             applied to 15 real world
                                             problem which has
                                             distinct maintenance
                                             polices. This technique
                                             is considered as more
                                             comprehensive as compared
                                             to other methods and can
                                             be solved in reasonable
                                             time using any commercial
                                             solvers.

Basten et al.   Minimum cost flow problem    The modeling consist of
[2011]          with side constraints        four nodes-source node,
                                             decision node,
                                             transformation node and
                                             sink node and the use of
                                             resources act as side
                                             constraints. An
                                             occurrence of failures of
                                             a certain subsystem at a
                                             certain system location
                                             as a source node is
                                             modeled. From these
                                             source nodes it is moved
                                             to Decision nodes which
                                             consists of three
                                             decisions namely, move
                                             the component to next
                                             level, repair the
                                             component or reject the
                                             component. If the repair
                                             option is chosen at
                                             decision node then parts
                                             are moved to the
                                             transformation node which
                                             represents the repair of
                                             a parent component. If
                                             the decision process end
                                             with any of the decision
                                             then parts are moved to a
                                             sink node.

Basten et al.   Integrated Algorithm for     The model solves the
[2012 A]        jointly solving of LORA      problem of maintenance of
                and spare parts stocking     capital goods like MRI-
                problems                     scanner at hospital or
                                             baggage handling system
                                             at airport. It has shown
                                             significant amount of
                                             cost reduction. It
                                             developed an integrated
                                             algorithm which jointly
                                             solved LORA and spare
                                             parts stocking problems
                                             based on Alfredsson,
                                             [1997] mathematical
                                             model. The spare part
                                             stocking problem was
                                             solved by using a METRIC
                                             method. This integrated
                                             algorithm was effective
                                             for solving two-echelon
                                             (or single-echelon),
                                             single-indenture problems

Table 5
below presents the classification of the recent papers.

Source            METRIC Modifications /      Problem
                  Improvements                Characteristics

Jung [2003]       algorithm to find the       Multi-echelon repairable
                  spare inventory level at    inventory system with
                  each base so as to          emergency lateral
                  minimize total expected     transshipments
                  cost

Caglar et al.     minimize the system-        two-echelon, multi-item
[2004]            wide inventory cost         spare parts inventory
                  subject to a response       system; Poisson process
                  time constraint ateach      for part failure; highly
                  field depot                 reliable and very
                                              expensive parts

Kilpi and         balanced inventory          Standard statistical
Veps.al.ainen     pooling arrangements        model of component
[2004]            among various airlines      availability showing
                                              relations between the
                                              four factors of
                                              availability
                                              (reliability, turnaround
                                              time, service level and
                                              the number of units
                                              supported)

Kim et al.        An algorithm to find        general repair time
[2007]            spare inventory level to    distribution; M/G/c
                  minimize the total          queuing system for both
                  expected cost and           base and depots repair
                  simultaneously to
                  satisfy a specified
                  minimum service rate

Kim et al.        Performance based           Poisson process for part
[2007 A]          contract using multitask    failure; repair facility
                  principal-agent model       with infinite capacity
                                              modeled as an M/G/"
                                              queue; each supplier is
                                              compensated based on his
                                              total realized cost and
                                              realized backorder level

Wong et al.       cost allocation problem     Game theoretic models;
[2007]            in the context of           two games-1) games with
                  repairable spare parts      full cooperation; 2)
                  pooling                     games with competition

Kutanoglu and     An algorithm to find        Two-echelon distribution
Mahajan [2009]    inventory level at local    system with one central
                  warehouses that meet all    warehouse (depot) and
                  the time-based service      large number of local
                  level constraints at        warehouses (bases);
                  minimal costs with          infinite capacity at
                  emergency lateral           depots; Poisson demands;
                  transshipments              warehouses share their
                                              inventory;

Kilpi et al.      Impact of various type      Four types of
[2009]            of co-operative             co-operative strategies
                  strategies on inventory     considered namely solo,
                  levels and overall cost     ad-hoc cooperation,
                  using a game theoretical    co-operative pooling and
                  setting                     commercial pooling

Mirzahosseinian   inventory model for a       Poisson process for part
and Piplani       repairable parts system     failure; exponential
[2011]            operating under             distribution for repair
                  Performance based           time; M/M/m queue
                  contract                    inventory system;

Jin and           Trade-offs between          Renewal equation and
Tian [2012]       reliability design and      Poisson process for
                  inventory level             estimating the aggregate
                                              fleet failures

Basten et al.     iterative algorithm to      Poisson process for part
[2012 A]          solve the joint problem     failure; repair lead
                  of LORA and spare parts     time are IID
                  stocking

Tracht et al.     cost-optimal inventory      Poisson process for part
[2013]            levels subject to budget    failure; repair time is
                  and inventory level         assumed to be constant;
                  limitations                 ample repair capacity

Ruan et al.       Configuration and           Four stage process-1)
[2014]            optimization method of      forecast spares demand
                  partial repairable          rate; 2) optimize spare
                  spares                      stock based on spares
                                              model and algorithm; 3)
                                              determine the support
                                              constraint targets; 4)
                                              calculate spares reorder
                                              point and order quantity

Tracht et al.     impact of varying repair    Single item system; no
[2014]            capacity on a system for    item condemnations; the
                  repairable items            repair shop uses first-
                                              come-first-serve (FCFS)
                                              prioritization; Poisson
                                              process for part
                                              failure; exponential
                                              distribution for repair
                                              time

Source            Solution      Models       Inventory Policy
                  Method

Jung [2003]       Approximate   Stochastic   Continuous review

Caglar et al.     Heuristic                  Continuous review, base
[2004]                                       stock policy

Kilpi and         Simulation
Veps.al.ainen     model
[2004]

Kim et al.        Approximate   Stochastic   Continuous review
[2007]

Kim et al.        Exact                      One-for-one base stock
[2007 A]                                     policy

Wong et al.       Exact         Stochastic   One-for-one base stock
[2007]

Kutanoglu and     Implicit      Integer      One-for-one base stock
Mahajan [2009]    enumeration   nonlinear    policy
                                program

Kilpi et al.      Simulation
[2009]            model

Mirzahosseinian   Exact         Stochastic   One-for-one base stock
and Piplani
[2011]

Jin and           Heuristic                  Multi-phase adaptive
Tian [2012]                                  inventory control policy

Basten et al.     Heuristic                  One-for-one base stock
[2012 A]

Tracht et al.     simulation                 One-for-one base stock
[2013]            model

Ruan et al.       Exact                      Combination of (s-1, s)
[2014]                                       and (R, Q) inventory
                                             policy

Tracht et al.     Simulation    Stochastic   Continuous review
[2014]            model
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Author:Kapoor, Rohit; Ambekar, Sudhir
Publication:Indian Journal of Economics and Business
Article Type:Report
Geographic Code:1USA
Date:Apr 1, 2015
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