Development and analysis of mathematical and simulation models of decision-making tools for remanufacturing

This article presents decision-making tools for remanufacturing. The first decision-making tool was used to address inventory lot-sizing problems in a hybrid remanufacturing–manufacturing system with varying remanufacturing fraction. In this article, the new inventory lot-sizing model with variable remanufacturing lot sizes has been shown to exhibit better performance than the benchmark model with fixed remanufacturing lot sizes. The new inventory lot-sizing model is anticipated to become a valuable decision-making tool in companies that are planning to adopt remanufacturing. The second decision-making tool was applied to address a production and inventory planning problem in a remanufacturing system considering different remanufacturing policies for a given remanufacturing strategy. For a remanufacture-to-stock system with two quality remanufacturables groups four alternative policies were examined, a policy which specifies simultaneous processing utilising dedicated resources was shown to be the best policy to achieve a shorter remanufacturing cycle time. For a remanufacture-to-order system with two quality remanufacturables groups, the three relevant policies of the four alternative policies were examined, a policy which specifies sequential processing and switching between various quality remanufacturables groups was shown to be the best policy to achieve a shorter remanufacturing cycle time. The production and inventory planning simulation models in a remanufacturing system are expected to become significant decision-making tools in remanufacturing operations.     

Optimizing multi-stage production with constant lot size and varying number of unequal sized batches

This paper describes a model for a multi-stage production/inventory system in which a uniform lot size is produced through all stages with a single setup and without interruption at each stage. Partial lots, called batches, may be transported to the next stage upon completion. The number of the unequal sized batches may differ across stages. Considering setup costs, inventory holding costs, and transportation costs, an optimization method is developed to determine the economic lot size and the optimal batch sizes for each stage. The method is illustrated by a computational example and further numerical simulations.     

Resource-constrained materials requirements planning- MRP rc

Computerized MRP systems used in industrial practice have been criticized by researchers as well as industrial users with respect to their limited ability to generate feasible production schedules. In this paper the lot size planning stage of a typical MRP system is considered. Several modelling alternatives for multi-level lot sizing are discussed with the help of a small example. A resourceconstrained approach to lot sizing- called MRP rc- is presented that cooperates with standard production planning and control systems. In this approach the item-by-item lot size planning is substituted by the heuristic solution of a multi-level multi-item dynamic capacitated lot sizing problem with setup times for general product structures.     

Discrete time-varying demand lot-sizing models with learning and forgetting effects

This paper deals with the problem of incorporating both learning and forgetting effects into discrete timevarying demand lot-sizing models to determine lot sizes. Forgetting is retrogression in learning which causes a loss of labour productivity due to breaks between intermittent production runs. Formulae are derived for calculating the production cost required to produce the first unit of each successive lot over a finite planning horizon. An optimal lotsizing model and three heuristic models are developed by extending the existing models without learning and forgetting considerations. Numerical examples and computational experience indicate that larger lot sizes are needed when the phenomenon of learning and forgetting exists. Several important conclusions are drawn from a comparison of the three heuristic solutions with the optimal solution, and suggestions for future research and for lot-size users to choose an appropriate lot-sizing technique are made.     

Job route selection model for workload balancing between workstations in flexible flow line

A flexible flow line (FFL) consists of several groups of identical machines. All work-orders flow along the same path through successive machine groups. Thus, the balancing of workloads between machine groups in order to maximize total productivity is emphasized. On the other hand, many different types of work-orders, in varying batch or lot sizes, are produced simultaneously. The mix of work-orders, their lot sizes, and the sequence in which they are produced affect the workload. However, the work-orders and their lot sizes are pre-fixed and cannot be changed. Because of these reasons, an optimal route selection model has been developed using heuristic search and a min-max algorithm for balancing the workload between machine groups in the FFL.     

The Value of Quality Grading in Remanufacturing

In this paper we consider a tactical production‐planning problem for remanufacturing when returns have different quality levels. Remanufacturing cost increases as the quality level decreases, and any unused returns may be salvaged at a value that increases with their quality level. Decision variables include the amount to remanufacture each period for each return quality level and the amount of inventory to carry over for future periods for both returns (unremanufactured), and finished remanufactured products. Our model is grounded with data collected at Pitney‐Bowes from their mailing systems remanufacturing operations. We derive some analytic properties for the optimal solution in the general case, and provide a simple greedy heuristic to computing the optimal solution in the case of deterministic returns and demand. Under mild assumptions, we find that the firm always remanufactures the exact demand in each period. We also study the value of a nominal quality‐grading system in planning production. Based on common industry parameters, we analyze, via a numerical study, the increase in profits observed by the firm if it maintains separate inventories for each quality grade. The results show that a grading system increases profit by an average of 4% over a wide range of parameter values commonly found in the remanufacturing industry; this number increases as the returns volume increases. We also numerically explore the case where there are capacity constraints and find the average improvement of a grading system remains around 4%.     

Setups and effective capacity: the impact of lot sizing techniques in an MRP environment

This study investigates how lot sizing techniques influence the profit performance, inventory level, and order lardiness of an assembly job shop controlled by MRP. Four single-level lot sizing techniques are compared by simulation analysis under two levels of master schedule instability and two levels of end item demand. A second analysis investigates the influence of a multilevel lot sizing technique, the generalized constrained-K (GCK) cost modification, on the four single-level techniques at low demand and low nervousness. The analyses reveal a previously unreported phenomenon. Given the same inventory costs, the single-level lot sizing techniques generate substantially different average batch sizes. The lot sizing techniques maintain the following order of increasing average batch size (and decreasing total setup time):

economic order quantity (EOQ)

period order quantity (POQ)

least total cost (LTC)

Silver-Meal heuristic (SML)

The causes for different average batch sizes among the lot sizing techniques are analysed and explained. Demand lumpiness, inherent in multilevel manufacturing systems controlled by MRP, is found to be a major factor. The number of setups each lot sizing technique generates is the primary determinant of profit performance, inventory level, and order tardiness. EOQ, a fixed order quantity technique, is less sensitive to nervousness than the discrete lot sizing techniques. EOQ_, however, generates the smallest average batch size, and, therefore, the most setups. Since setups consume capacity, EOQ, is more sensitive to higher demand. SML generates the largest average batch sizes, and is, therefore, less sensitive to increased demand. At low demand, the other lot sizing techniques perform better on all criteria. They generate smaller batches and, therefore, shorter actual lead times. The GCK cost modification increases the average batch size generated by each lot sizing technique. GCK improves the profit and customer service level of EOQ the lot sizing technique with the smallest batches. GCK causes the other lot sizing techniques to generate excessively large batches and, therefore, excessively long actual lead times.     

Production planning and control for remanufacturing: exploring characteristics and difficulties with case studies

Production planning and control for remanufacturing is a major managerial challenge in the operations management. Researches demonstrate the need for decision-making methods in this context, which has generated theoretical and quantitative studies. However, this area still lacks empirical studies dealing with the practical, day-to-day difficulties of remanufacturers. The purpose of this paper is to link the literature and practice in a systematic in such a way that it is possible to show the similarities and differences between theoretically listed needs and real cases, thereby extending the results of previous research. For this purpose, four case studies are considered. The cases involve original equipment manufacturers (OEM) of automotive parts that have remanufacturing operations. The results indicate that these companies have difficulties that have not been addressed to date in the literature related to the uncertainties inherent in remanufacturing. In addition, we find that these companies use simplified decision-making approaches.     

Lot‐sizing Decisions Under Limited‐time Price Reduction*

We consider the optimal lot‐sizing policy for an inventoried item when the vendor offers a limited‐time price reduction. We use the discounted cash flow (DCF) approach in our analysis, thereby eliminating the sources of approximation found in most of the earlier studies that use an average annual cost approach. We first characterize the optimal lot‐sizing policies and their properties, then develop an algorithm for determining the optimal lot sizes. We analytically demonstrate that the lot sizes derived using an average annual cost approach for the different variants of the problem are, in general, larger than the DCF optimum. While DCF analysis is more rigorous and yields precise lot sizes, we recognize that the associated mathematical models and the solution procedure are rather complex. Since simple and easy‐to‐understand policies have a strong practical appeal to decision makers, we propose a DCF version of a simple and easy‐to‐implement heuristic called the “Early Purchase” (EP) strategy and discuss its performance. We supplement our analytical developments with a detailed computational analysis and discuss the implications of our findings for decision making.     

Managing a Remanufacturing System with Random Yield: Properties,Observations, and Heuristics

We study a remanufacturing system that involves the ordering of a serviceable product and the remanufacturing of multiple types of returned products (cores) into the serviceable product. In addition to random demand for the serviceable product and random returned quantities of different types of cores in each time period, the remanufacturing yield of each type of core is also uncertain. By analyzing a multi‐period stochastic dynamic program, we derive several properties of the optimal ordering/remanufacturing policy. In addition to some insights, these properties can be used to reduce the search effort of the optimal policy. We also demonstrate that some existing results derived from related models no longer hold in remanufacturing systems with random yield. Recognizing the optimal ordering/remanufacturing policy is highly complex, we examine three simple heuristics that can be efficiently solved and implemented in practice. Among these three heuristics, our numerical analysis suggests that the heuristic that captures most of the yield uncertainty and future system evolvement as well as some of the properties of the optimal ordering/remanufacturing policy outperforms the other two heuristics.     

Lot sizing in workload control systems

An important basis for workload control (WLC) is the existence of functional relationships between the mean level of work-in-process (WIP) and the values of important goal variables, like average flow time, capacity utilization, etc. These functional relationships are largely influenced by the lot sizes. This means that the usual objective of lot sizing must be supplemented by considering the impact of lot sizes on the relationships between WIP and the other goal variables. Here it is shown that this insight leads to flow time oriented lot sizing models. This type of lot sizing models is analysed. It is argued that the derivation of simple rules for lot sizing is an important research topic, and a model for deriving such rules is presented. Some rules are derived from the model, assuming that the batches are processed by an M/G/1 server, and it is shown that these rules support insights based on simulation in the 1980s. Topics for future research are outlined as well.     

An Advanced Heuristic for Multiple‐Option Spare Parts Procurement after End‐of‐Production

After‐sales service is a major source of profit for many original equipment manufacturers in industries with durable products. Successful engagement in after‐sales service improves customer loyalty and allows for competitive differentiation through superior service like an extended service period during which customers are guaranteed to be provided with service parts. Inventory management during this period is challenging due to the substantial uncertainty concerning demand over a long time horizon. The traditional mechanism of spare parts acquisition is to place a large final order at the end of regular production of the parent product, causing major holding costs and a high level of obsolescence risk. With an increasing length of the service period, more flexibility is needed and can be provided by adding options like extra production and remanufacturing. However, coordinating all three options yields a complicated stochastic dynamic decision problem. For that problem type, we show that a quite simple decision rule with order‐up‐to levels for extra production and remanufacturing is very effective. We propose a heuristic procedure for parameter determination which accounts for the main stochastic and dynamic interactions in decision making, but still consists of relatively simple calculations that can be applied to practical problem sizes. A numerical study reveals that the heuristic performs extremely well under a wide range of conditions, and therefore can be strongly recommended as a decision support tool for the multi‐option spare parts procurement problem. A comparison with decision rules adapted from practice demonstrates that our approach offers an opportunity for major cost reductions.     

Forecasting Product Returns for Remanufacturing Operations

Driven by legislative pressures, an increasing number of manufacturing companies have been implementing comprehensive recycling and remanufacturing programs. The accurate forecasting of product returns is important for procurement decisions, production planning, and inventory and disposal management in such remanufacturing operations. In this study, we consider a manufacturer that also acts as a remanufacturer, and develop a generalized forecasting approach to determine the distribution of the returns of used products, as well as integrate it with an inventory model to enable production planning and control. We compare our forecasting approach to previous models and show that our approach is more consistent with continuous time, provides accurate estimates when the return lags are exponential in nature, and results in fewer units being held in inventory on average. The analysis revealed that these gains in accuracy resulted in the most cost savings when demand volumes for remanufactured products were high compared to the volume of returned products. Such situations require the frequent acquisition of cores to meet demand. The results show that significant cost savings can be achieved by using the proposed approach for sourcing product returns.     

A TECHNIQUE TO MINIMIZE OVERTIME IN THE CAPACITATED MRP PROBLEM

Since the development of early versions of material requirements planning (mrp) systems, it has been known that a weak link in this technique is the failure to consider the available capacity at the time the lot sizes for individual items are calculated. Ignoring the available capacity may result in infeasible production plans, i.e., those that can only be accomplished with the use of overtime. We present a technique to search for feasible production plans by means of minimizing the total overtime. The technique is based on modifying periodic-order-quantity (poq) lot sizes within a tabu search framework. Computational experiments with the largest problem structure reported in the literature show that the procedure is effective in determining lot sizes for individual items that either minimize or eliminate overtime. Additional experiments reveal that, with appropriate calibration of search parameters, the procedure is also able to deal with more general cost functions (e.g., those that include holding and setup costs).     

Planning and Control in Multi-Cell Manufacturing

This research compares Material Requirements Planning (MRP), Kanban, and Period Batch Control (PBC) as alternative approaches to the planning and control of multi-cell manufacturing involving flow cells and assembly. Since previous research on performance of these systems in cellular manufacturing has been primarily conceptual, the experiments reported here provide new insights into their comparative performance. The results show that the production environment is a major factor in system choice. Three operating factors—Master Production Schedule (MPS) volume variation, MPS mix variation, and setup time/lot size—clearly affect system choice. All systems performed well under Justin-Time (JIT) conditions; there was no advantage to Kanban. Under the mixed conditions of high MPS variation, but small setup time/lot sizes, PBC produced superior performance compared to Kanban and MRP. Under non-JIT conditions, MRP was seen as clearly more effective. Finally, the results indicate that when conditions permit very small lot sizes relative to requirements, Kanban may perform best, even when MPS variation is high.     

Solving the Economic Lot-Scheduling Problem Using the Method of Prime Subperiods

In recent years the reported successes of Japanese production systems, particularly the just-in-time approach to inventory control, has caused managers to focus more of their attention on efficient decision-making procedures for determining production schedules that minimize inventory costs. One such potential area of attention is the economic lot-scheduling problem (ELSP), which occurs in a variety of manufacturing environments where machining operations are prevalent. The economic lot-scheduling problem addresses the determination of lot sizes for N products with constant demand (and cycled through one machine with a given production rate) to minimize setup and inventory costs. The most successful solution approaches to the ELSP have been based on the concept of a basic period that is of sufficient length for the production of all items, even though each item might not be produced during each repetition of the basic period. This paper proposes a heuristic approach to the solution of the ELSP (referred to as the method of prime subperiods), which is an extension of the basic period approaches. The procedure is described and demonstrated via an example and then tested using a set of six example problems previously employed in the literature related to the ELSP. The results indicate as good or superior performance by the proposed method of prime subperiods.     

Production planning and control for remanufacturing: literature review and analysis

This article reviews the literature on production planning and control (PPC) for remanufacturing. The objectives are threefold: to determine whether the gaps identified by Guide (Guide Jr, V.D.R., 2000. Production planning and control for remanufacturing: industry practice and research needs. Journal of Operations Management, 18, 467–483) on the subject with respect to the main complicating characteristics of remanufacturing have been fulfilled; to classify the literature based on an appropriate structure to obtain a better understanding of the subject identifying sources of future research and to provide a useful source for scholars and practitioners. Seventy-six papers were examined and classified. It was found that none of the studies deals simultaneously with all of the complicating characteristics, and that more practical research is needed. In addition it was found that we lack studies regarding forecasting and aggregate planning considering disassembly of returned products, material matching restrictions or stochastic routings, master production scheduling considering material matching restrictions or stochastic routings, ordering system and capacity planning considering material matching restrictions and inventory control and management considering stochastic routings.     

Order Dispatching and Labor Assignment in Cellular Manufacturing Systems

Although order and labor dispatching in the job shop manufacturing setting have been investigated extensively over the last three decades, its representation of actual processes found in practice today is limited due to the move to cellular manufacturing (CM). Manufacturing cells have become an important approach to batch manufacturing in the last two decades, and their layout structure provides a dominant flow structure for the part routings. The flow shop nature of manufacturing cells adds a simplifying structure to the problem of planning worker assignments and order releases, which makes it more amenable to the use of optimization techniques. In this paper we exploit this characteristic and present two mathematical modeling approaches for making order dispatching and labor assignment/reassignment decisions in two different CM settings. The two formulations are evaluated in a dynamic simulation setting and compared to a heuristic procedure using tardiness as the primary performance measure. The formulations are superior to the heuristic approach and can be incorporated into detail scheduling systems that are being implemented by corporations employing enterprise resource planning (ERP) systems today.     

O(m2) ALGORITHMS FOR THE TWO AND THREE SUBLOT LOT STREAMING PROBLEM

Lot streaming is the process of splitting a job or lot into sublots to reduce its makespan on a sequence of machines. The goal in the lot streaming problem is to find the optimal size of each sublot that will minimize the makespan. The makespan is defined as the time the last sublot completes its processing on the last machine. If the sizes of these sublots are restricted to remain the same on all machines, the solution is called a consistent sublot solution. However, if the sizes of the sublots are allowed to vary, the solution is referred to as a nonconsistent or variable sublot solution. Also, if the machines must be in operation continuously from the first to the last sublot, the solution is a no idling solution. When setups are explicitly considered in the problem, there will be two cases. If setups on each machine require some portion of the first sublot be present by the machine, the problem is referred to as the attached setup time problem. If setups can be performed ahead of time before the first sublot reaches the particular machine, the corresponding problem is referred to as the detached setup problem. Finally, if the machines are allowed to be idle between the processing of sublots, the resultant solution is an intermittent idling solution. In this paper, the consistent sublot lot streaming problem with intermittent idling and no setups is discussed. The models developed also assume that the number of sublots are fixed and known. The m machine two sublot lot streaming problem is reviewed. An algorithm for the three sublot, m machine problem is derived using a network representation of the problem. The complexity of the algorithm is O (m²). Finally, using the insights from three sublot problem, a heuristic algorithm is provided for the m machine, n sublot problems. The results on the proposed heuristic are very encouraging; average percent deviation from optimal makespan is approximately at 0.76% on 155 randomly generated problems with different m and n values.     

Marginal analysis production planning

A forward looking with backward recourse production planning heuristic is developed using marginal analysis. In the search for a minimum cost solution, a set of rules derived by Kunreuther and Morton for determining planning horizons is employed. It is shown that the logic of the heuristic is similar to several dynamic lot-sizing models. The marginal analysis production planning (MAPP) heuristic is computationally more efficient than optimizing approaches and gives results that are generally less than 5% more expensive than the optimal solution. In addition, through the notion of level periods, the heuristic permits the user to easily investigate strategies where the work force size and daily production rate remain constant for a specified number of periods.