Modelling and solving spare parts supply chain network design problems

Spare parts are key operational assets in order to minimise unexpected equipment downtimes that may significantly impact a company’s results. The spare parts supply chain network supports the entire spare parts operations management and it is essential to achieve the planned goals. However, most of the traditional literature on spare parts management has not focused on the underlying supply chain network. Thus, this paper studies the integration of supply chain network design and control with traditional spare parts management. In particular, a generic network optimisation modelling structure is proposed, with simultaneous optimisation of warehouse locations and inventory control decisions, allowing minimising the total costs associated with the spare parts supply chain network. The generic model is specified based on three inventory control policies widely employed in the industry, which are suitable for managing a great variety of spare parts, i.e. (s, Q), (R, s, S) and (S-1, S). Furthermore, a solution approach is proposed based on Generalised Benders Decomposition. Finally, numerical results from a real-world application case in the process industry are shown and discussed.     

Bullwhip and inventory variance in a closed loop supply chain

A simple dynamic model of a hybrid manufacturing/remanufacturing system is investigated. In particular we study an infinite horizon, continuous time, APIOBPCS (Automatic Pipeline Inventory and Order Based Production Control System) model. We use Åström’s method to quantify variance ratios in the closed loop supply chain. Specifically we highlight the effect of a combined “in-use” and remanufacturing lead-time and the return rate on the inventory variance and bullwhip produced by the ordering policy. Our results clearly show that a larger return rate leads to less bullwhip and less inventory variance in the plant producing new components. Thus returns can be used to absorb demand fluctuations to some extent. Longer remanufacturing and “in-use” lead-times have less impact at reducing inventory variance and bullwhip than shorter lead-times. We find that, within our specified system, that inventory variance and bullwhip is always less in supply chains with returns than supply chains without returns. We conclude by separating out the remanufacturing lead-time from the “in-use” lead-time and investigating its impact on our findings. We find that short remanufacturing lead-times do not qualitatively change our results.     

Nervousness in inventory control: Analytical results

Using a rolling horizon planning framework in inventory control leads to nervousness in the planning system caused by instability of order release decisions in successive planning cycles. For a single-stage inventory system with stochastic demand it is shown analytically, how planning stability is affected by policy parameters if (s, n Q) and (s, S) control rules are applied. It turns out that the reorder points does not influence stability whereas the lot sizeQ and minimum reorder quantityS-s can have a considerable impact. Under the aspect of nervousness the (s, n Q) policy can be assessed to be less risky than the (s, S) rule.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

A prototype knowledge-based system (KBS) for selection of inventory control policies

In a previous paper Parlar presents an expert system for advising on the selection of production/inventory models. A deficiency of this system is that the user must review the reference literature to locate the corresponding inventory control policy. This paper presents a prototype expert system where the knowledge base contains the control policy equations for reorder level (L), reorder quantity (Q) and total system cost (TC). Moreover, after identifying the inventory control policy equations, the expert system then shells to an external computer program to numerically solve the model that the rules select. It is believed that the output of more precise information to the user will lead to more accurate usage of inventory models.     

Optimization and optimality of a joint pricing and inventory control policy in periodic-review systems with lost sales

This paper studies a periodic review dynamic pricing and inventory control problem with fixed ordering cost included. Demand is uncertain and price-sensitive in a general form. At the end of each period, all unmet demand is lost. We focus on the optimization and optimality of an (s, S, p)-type policy, which operates as follows: whenever the inventory level is less than or equal to s, an order is placed to order-up-to level S; when the inventory level is larger than s, no order is issued; the price p is specified by the inventory level. We further numerically investigate the optimal solutions and their sensitivity to cost parameters and demand uncertainty.     

Optimal inventory control of lumpy demand items using (s,S) policies with a maximum issue quantity restriction and opportunistic replenishments

This paper presents a modified (s, S) inventory model which describes the characteristics of an inventory system with lumpy demand items. A maximum issue quantity restriction of w units and a critical inventory position of A units are incorporated into the inventory control policy. Customer orders with demand sizes larger than the maximum issue quantity will be filtered out from the inventory system and satisfied by using special replenishment orders in order to avoid disruption to the inventory system. The option of opportunistic replenishments is introduced to further minimize the total replenishment cost. An opportunistic replenishment is initiated if the level of the current inventory position is equal to or below the critical level when a customer demand with a size exceeding the maximum issue quantity arrives, which does not only initiate a direct shipment to the customer, but also raises the inventory position to S. Two effective algorithms are developed to determine the optimal values of w, A, s and S simultaneously. The first algorithm is based on the branch-and-bound tree search technique, and the second one is based on the concept of genetic algorithms. Numerical examples are used to illustrate the effectiveness of the algorithms developed. The effects of changes in the cost and system parameters on the optimal inventory control policy are also studied by using sensitivity analysis.     

Joint optimisation of production rate and preventive maintenance in machining systems

This paper studies an integrated control strategy of production and maintenance for a machining system which produces a single type of product to meet the constant demand. Different from previous research, we assume in this study that during the production, the production rate not only influences the life of cutting tool, but also the reliability of the machine. Both the replacement of cutting tool and the preventive maintenance (PM) of machine are considered in this paper. The machine is preventively maintained at the Nth tool replacement or correctively repaired at the machine failure, whichever occurs first. PM and corrective repair may cause shortage which can be reduced by controlling inventory. There are two decision variables p and N, where p denotes the production rate and N denotes the number of cutting tool replacement before the PM is performed. An integrated model is developed to simultaneously determine the optimal production rate and PM policy that minimise the total expected cost per unit item produced. Finally, an illustrative example and sensitivity analysis are given to demonstrate the proposed model.     

Performance evaluation for tandem multi-factory supply chains: an approximate solution

Predicting the performance of multistage manufacturing systems is usually viewed as challenging because of unexpected machine breakdowns, random processing times, uncertain inter-factory transportation times, etc. In this paper, the authors formulate an approximate model for the tandem manufacturing systems, where the inventory in each buffer is monitored based on the (s, Q) discipline. This model divides a multistage system into a series of primitive line segments, each of which is characterised by a continuous time discrete state Markov process. The model may be applied in two types of systems: (1) tandem flow lines with batch processing and (2) multi-factory manufacturing supply chain, where inter-factory material transportation is required. Based on the model, a number of commonly used performance measures, including throughput, inventory, transportation frequency, etc., can be estimated. These estimates may enable manufacturers to evaluate the performance of the systems, and hence improve the management of production and inventory.     

Approximation of the probability distribution of the customer waiting time under an (r,s, q) inventory policy in discrete time

We study a single-item periodic review (r, s, q) inventory policy. Customer demands arrive on a discrete (e.g. daily) time axis. The replenishment lead times are discrete random variables. This is the time model underlying the majority of the Advanced Planning Software systems used for supply chain management in industrial practice. We present an approximation of the probability distribution of the customer waiting time, which is a customer-oriented performance criterion that captures supplier–customer relationships of adjacent nodes in supply chains. The quality of the approximation is demonstrated with the help of a simulation experiment.     

The trans-shipment problem in a two-echelon,multi-location inventory system with lost sales

In this paper, we address a two-echelon, multi-location pooling inventory system that consists of an outside supplier, a warehouse and two retailers. To control their inventories, both warehouse and retailers use (R,?s,?S) policy. The retailers face stochastic customer demands for a single product and the warehouse receives only the replenishment orders of retailers. In case of stock-out at retailers, emergency trans-shipments are used to satisfy the unmet demand at one retailer with the surplus from the other retailer. When the stock is insufficient at the warehouse, we propose two rationing policies to allocate on-hand stock between retailers. The demand that cannot be satisfied neither by stock on-hand nor by trans-shipment from retailers is considered lost. Our work has two objectives. First, we propose an inventory model based on three components: the optimisation inventory model, the trans-shipment policy and the rationing policies for determining the best values of (s,?S) at each location that minimise total system cost. Second, we validate this model via an empirical simulation study that allows us to identify the influential parameters on trans-shipment benefits.     

Impact of quality regulation policy on performance of a remanufacturing supply chain with non-waste returns

Quality issues in a remanufacturing supply chain with non-waste returns have been reported many times. To address these issues, the government proposes different quality regulation policies. This paper develops a multi-agent simulation model to study how the quality regulation policy affects the performance of a remanufacturing supply chain with non-waste returns. Here, the main performance includes profit and hazard ratio of products. Our results indicate that self-regulation of the market cannot realize a desirable outcome (low hazard ratio and high manufacturer’s profit). Adjusting quality regulation probability is more efficient than adjusting the penalty for inferior products. From the view of increasing manufacturer’s average profit, or improving the government’s efficiency, the best policy is the solely adjusting supervision probability policy. From the view of reducing hazard ratio, the best policy is adjusting supervision probability- penalty policy. The appropriate penalty for inferior products can realize the desirable outcome. With an increasing supervision probability, the hazard ratio decreases, and the manufacturer’s average profit increases because the remanufacturing cost and penalty for inferior products decrease.     

A joint replenishment policy with individual control and constant size orders

We consider inventory systems with multiple items under stochastic demand and jointly incurred order setup costs. The problem is to determine the replenishment policy that minimises the total expected ordering, inventory holding, and backordering costs–the so-called stochastic joint replenishment problem. In particular, we study the settings in which order setup costs reflect the transportation costs and have a step-wise cost structure, each step corresponding to an additional transportation vehicle. For this setting, we propose a new policy that we call the (s, 𝒬) policy, under which a replenishment order of constant size 𝒬 is triggered whenever the inventory position of one of the items drops to its reorder point s. The replenishment order is allocated to multiple items so that the inventory positions are equalised as much as possible. The policy is designed for settings in which backorder and setup costs are high, as it allows the items to independently trigger replenishment orders and fully exploits the economies of scale by consistently ordering the same quantity. A numerical study is conducted to show that the proposed (s, 𝒬) policy outperforms the well-known (𝒬, S) policy when backorder costs are high and lead times are small.     

Vendor-managed inventory and the effect of channel power

We analyze decentralized supply chains that follow general continuous review (Q, R) inventory policies subject to vendor-managed inventory agreements where the supplier chooses the order quantity Q, and the retailer chooses the reorder point R. Within the VMI scenario, we explore the effect of divisions of channel power on supply chain and individual agent performance by examining different game theoretic models. Optimal policies and analytical results, including existence and uniqueness proofs for equilibrium solutions under VMI, are derived. Numerical results are provided to compare the effectiveness of VMI and to analyze different channel power relationships under a variety of environmental conditions. We find that VMI can result in considerable supply chain savings over traditional relationships and that the relative division of channel power can significantly effect the performance of VMI. Interestingly, we find that the greatest system benefits from VMI arise in asymmetric channel power relationships, but that individual agents lack the incentive to assume a leadership role.     

Inventory management in a lateral collaborative manufacturing supply chain: a simulation study

Due to global competition, firms are seeking more effective supply chain (SC) collaboration in order to provide quality products with less cost, at the right time and in the right quantity. The present study examines manufacturing SC collaboration on the basis of holding cost, backorder cost and ordering cost. The types of collaboration examined are vertical, horizontal and lateral collaboration. This research emphasises lateral collaboration by determining the impact of inventory policies ((s, S) and (s, Q) inventory policies) on SC performance. For better understanding, a conceptual model is provided that is supported by a numerical example. As the study of SCs is complex in nature, a simulation approach has been employed to show the impact of lateral collaboration on performance measures such as the total cost, which is the sum of several cost components: inventory holding cost, backorder cost and ordering cost. The research is based on two manufacturing SCs where the manufacturer is taken as the collaborative node. To allow more clarity, a separate study on each cost component has been conducted. The laterally collaborative SC was simulated on ARENA 9.0, a simulation package. The results show that the efficacy of lateral collaboration outperforms horizontal collaboration due to having the individual SC members at more liberty to make decisions.     

Planning stability under (s,S) inventory control rules

The problem of planning instability caused by new and actualized data in material coordination systems with periodic review and replanning activities has been discussed from several viewpoints in literature and it is of great practical importance. The application of a rolling horizon planning framework in forecast-dependent inventory control leads to nervousness in the planning system caused by different order release decisions in successive planning cycles. In this paper a setup-oriented planning stability concerning deviations of planned orders in all periods of a given stability horizon in a single-stage inventory system with arbitrary stochastic demand is analyzed. The influence of an (s, S) control rule on planning stability is derived analytically. It is shown that the reorder points does not affect stability whereas the minimum reorder quantityS-s has a considerable impact. Especially, it is analyzed how planning stability depends on the length of the stability horizon, on period-specific weights, and on the accuracy of demand forecasts.     

Continuous review (s,S) policies for inventory systems incorporating a cutoff transaction size

In this paper, a mathematical model is developed for the analysis of optimal replenishment policies for items which experience lumpy demands. In order to avoid disrupting the inventory system, a cutoff transaction size of w units is specified such that customer demands with sizes exceeding w units will be filtered out of the inventory system and treated as special orders to be satisfied by special deliveries. Customer demands with sizes > units will be met From stock. The control discipline is the (s, S) inventory policy with continuous review and the nature of the demands is approximated by a stuttering Poisson distribution. Recursive formulae are developed for the determination of the probabilities of the lead time demand and the available inventory position. The optimal values of the control parameters, s and S, are determined. The theoretical results obtained are illustrated with a numerical example.     

Dynamic product acquisition in closed loop supply chains

We consider a closed-loop supply chain where demand can either be satisfied by manufacturing new products or by buying back used products from customers and upgrading their functionality by remanufacturing. A joint buy-back pricing and manufacturing–remanufacturing decision model at the operations–marketing interface is presented that allows for dynamic parameters, e.g. product life cycles and seasonal aspects. The model allows the identification of beneficial opportunities for buying back and storing used products for immediate and future recovery. We present a new deterministic, dynamic, continuous-time optimisation model, derive necessary and sufficient optimality conditions, and develop a solution algorithm to find the cost-minimising manufacturing and remanufacturing policies as well as buy-back strategies for used products based on Pontryagin's Maximum Principle. It is shown that, in general, an optimal policy will include time intervals where returns are acquired so as to synchronise demand and remanufacturing, where returns are acquired and stored for future remanufacturing, and intervals where demand is satisfied by a mix of manufactured and remanufactured products. Furthermore, we discuss several reactive and proactive acquisition and remanufacturing heuristics and show under which conditions they are optimal. The findings are illustrated by numerical examples.     

An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not ‘as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

Joint decisions for R/M integrated supply chain using system dynamics methodology

In the remanufacturing/manufacturing (R/M) integrated supply chain, the decisions of the manufacturer, the wholesaler, the retailer, the parts producer, the raw materials supplier, the collector, and the disassembly centre are interactional. In this paper, a system dynamics model is proposed to examine the long-term behaviour of the R/M integrated supply chain with reuse, remanufacturing, and recycling. The optimal decision sets of the remanufacturing ratio and the setup period of remanufacturing (r) are given, the joint decisions of all members of R/M integrated supply chain under optimal r are presented by the simulation results, and the impacts of optimal r on the joint decisions are analysed.