Shortening cycle times in multi-product,capacitated production environments through quality level improvements and setup reduction

This paper addresses the issue of investing in reduced setup times and defect rates for a manufacturer of several products operating in a JIT environment. Production cycle times can be shortened by investing in setup time and defect rate reductions, respectively. The objective is to determine optimal levels of setup time and defect rate reductions along with the corresponding optimal levels of investments respectively, and the optimal production cycle time for each product. The problem is constrained by demand requirements, process improvement budget limitations, and manufacturing and warehousing capacity constraints. We consider the cases of product-specific quality improvements and joint-product quality improvements. A general nonlinear optimization models of these problems are formulated. A convex geometric programming approximation of these models is developed respectively, in order to solve them. The approximation can be made to any desired degree of accuracy. Our empirical findings provide insights into a number of managerial issues surrounding investment decisions in product-specific quality improvements and setup reductions due to a product redesign as well as in joint-product improvements due to a process redesign.     

An EPQ model with setup cost and process quality as functions of capital expenditure

This paper considers an economic production quantity (EPQ) model with imperfect production processes, in which the setup cost and process quality are functions of capital expenditure. The mathematical model is derived to investigate the effects of an imperfect production process on the optimal production cycle time when capital investment strategies in setup reduction and process quality improvement are adopted. An efficient procedure is developed to find the optimal production run length, setup cost and process quality. Finally, a numerical example is provided to illustrate the theoretical results. Some managerial implications are also included.     

Dynamic setup reduction in production lot sizing with nonconstant deterministic demand

We examine three production policies under nonconstant, deterministic demand and dynamic setup cost reduction, where a decision to invest in setup reduction is made at the beginning of each period of a planning horizon. The three production policies are the reorder point, order quantity (s, Q) policy; the fixed production cycle, variable order quantity (t, Q_i) policy; and the variable production cycle, variable order quantity (t_i, Q_i). We study the behavior of the total relevant cost and develop a lot sizing and an investment solution procedure. Numerical examples are provided and dynamic setup cost reduction is compared with static setup cost reduction, where the decision to invest in setup reduction is made only at the initial setup.     

A note on “quality improvement and setup reduction in the joint economic lot size model”

In a recent paper, Affisco et al. [J.F. Affisco, M.J. Paknejad, F. Nasri, Quality improvement and setup reduction in the joint economic lot size model, European Journal of Operations Research 142 (2002) 497–508] propose a quality-adjusted joint economic lot size model that considers investments in quality improvement and setup cost reduction. In particular, they consider a single-vendor, single-buyer, deterministic demand economic lot-sizing problem, and they investigate the potential impact of economic investments in the vendor’s quality improvement and setup cost reduction efforts on the system-wide costs. However, the particular form of the investment function that they use to represent the cost of investments in quality improvement does not represent actual practice in many industries. Hence, in this note, we develop modified models for quality improvement and simultaneous quality improvement and setup cost reduction using a modified form of the investment function. Our fundamental results and conclusions are substantially different than those in Affisco et al. (2002).     

Optimal production plans and shipment schedules in a supply-chain system with multiple suppliers and multiple buyers

This research addresses an optimal policy for production and procurement in a supply-chain system with multiple non-competing suppliers, a manufacturer and multiple non-identical buyers. The manufacturer procures raw materials from suppliers, converts them to finished products and ships the products to each buyer at a fixed-interval of time over a finite planning horizon. The demand of finished product is given by buyers and the shipment size to each buyer is fixed. The problem is to determine the production start time, the initial and ending inventory, the cycle beginning and ending time, the number of orders of raw materials in each cycle, and the number of cycles for a finite planning horizon so as to minimize the system cost. A surrogate network representation of the problem developed to obtain an efficient, optimal solution to determine the production cycle and cycle costs with predetermined shipment schedules in the planning horizon. This research prescribes optimal policies for a multi-stage production and procurements for all shipments scheduled over the planning horizon. Numerical examples are also provided to illustrate the system.     

Joint determination of production quantity,inspection schedule,and quality control for an imperfect process with deteriorating products

In this paper, we study the simultaneous effects of both deteriorating product items and deteriorating production processes on economic production quantity, inspection schedules, and the economic design of control charts. Deterioration times for both product and process are assumed to follow arbitrary probability distributions. The product quality characteristic, however, is assumed to be normally distributed. Applications of the proposed model are demonstrated through illustrative examples.     

Quality improvement and setup reduction in the joint economic lot size model

The co-maker concept has become accepted practice in many successful global business organizations. This fact has resulted in a class of inventory models known as joint economic lot size (JELS) models. Heretofore such models assumed perfect quality production on the part of the vendor. This paper relaxes this assumption and proposes a quality-adjusted JELS model. In addition, classical optimization methods are used to derive models for the cases of setup cost reduction, quality improvement, and simultaneous setup cost reduction and quality improvement for the quality-adjusted JELS. Numerical results are presented for each of these models. Comparisons are made to the basic quality-adjusted model. Results indicate that all three policies exhibit significantly reduced total cost. However, the simultaneous model results in the lowest cost overall and the smallest lot size. This suggests a synergistic impact of continuous improvement programs that focus on both setup and quality improvement of the vendor's production process. Sensitivity analysis indicates that the simultaneous model is robust and representative of practice.     

Integrated production-inventory models with imperfect production processes and a limited capacity for raw materials

This paper deals with inventory models that unify the decisions for raw materials and the finished product for a single product manufacturing system. The product is manufactured in batches and raw materials are jointly replenished from outside suppliers. The system is assumed to deteriorate during the production process. As a result, some proportion of nonconforming items is produced. The objective is to minimize the total variable cost for the system. A solution procedure is developed to find a near optimal solution for the basic model. The analysis for the basic model is extended to cases where the proportion of defective items is not constant or the defective rate is a function of production setup cost.     

A production scheduling heuristic for an electronics manufacturer with sequence-dependent setup costs

In this paper, we develop a three-step heuristic to address a production scheduling problem at a high volume assemble-to-order electronics manufacturer. The heuristic provides a solution for scheduling multiple product families on parallel, identical production lines so as to minimize setup costs. The heuristic involves assignment, sequencing, and time scheduling steps, with an optimization approach developed for each step. For the most complex step, the sequencing step, we develop a greedy randomized adaptive search procedure (GRASP). We compare the setup costs resulting from the use of our scheduling heuristic against a heuristic previously developed and implemented at the electronics manufacturer that assumes approximately equal, sequence-independent, setup costs. By explicitly considering the sequence-dependent setup costs and applying GRASP, our empirical results show a reduction in setups costs for an entire factory of 14–21% with a range of single production line reductions from 0% to 49%.     

Cooperation in assembly systems: The role of knowledge sharing networks

Process improvement plays a significant role in reducing production costs over the life cycle of a product. We consider the role of process improvement in a decentralized assembly system in which a buyer purchases components from several first-tier suppliers. These components are assembled into a finished product, which is sold to the downstream market. The assembler faces a deterministic demand/production rate and the suppliers incur variable inventory costs and fixed setup production costs. In the first stage of the game, which is modeled as a non-cooperative game among suppliers, suppliers make investments in process improvement activities to reduce the fixed production costs. Upon establishing a relationship with the suppliers, the assembler establishes a knowledge sharing network – this network is implemented as a series of meetings among suppliers and also mutual visits to their factories. These meetings facilitate the exchange of best practices among suppliers with the expectation that suppliers will achieve reductions in their production costs from the experiences learned through knowledge sharing. We model this knowledge exchange as a cooperative game among suppliers in which, as a result of cooperation, all suppliers achieve reductions in their fixed costs. In the non-cooperative game, the suppliers anticipate the cost allocation that results from the cooperative game in the second stage by incorporating the effect of knowledge sharing in their cost functions. Based on this model, we investigate the benefits and challenges associated with establishing a knowledge sharing network. We identify and compare various cost allocation mechanisms that are feasible in the cooperative game and show that the system optimal investment levels can be achieved only when the most efficient supplier receives the incremental benefits of the cost reduction achieved by other suppliers due to the knowledge transfer.     

Evaluation of three production planning procedures for the use of recipe flexibility

Process industries often obtain their raw materials from mining or agricultural industries. These raw materials usually have variations in quality, which often lead to variations in the recipes used for manufacturing a product. Another reason for varying the recipe is to minimize production costs by using the cheapest materials that still lead to a satisfactory quality in the product. A third reason for using recipe flexibility is that it may occur that at the time of production not all materials for the standard recipe are available. In earlier research we showed under what conditions the use of this type of recipe flexibility should be preferred to the use of high materials stock to avoid materials shortages. We also showed that the use of recipe flexibility to account for material shortages can be justified if the material replenishment leadtime is long, the demand uncertainty is high and the required service level is high. In this paper we assume that these conditions are satisfied and we investigate three different production planning procedures that make use of recipe flexibility to cope with the uncertainty in demand and supply. We assume that the customer order leadtime is much smaller than the material replenishment leadtime, and therefore demand uncertainty is high. The optimal procedure optimizes material use over a planning horizon equal to the material replenishment leadtime, taking into account the customers orders and knowledge of the distribution function of future demand. The deterministic procedure also optimizes the material use over the material replenishment leadtime, but it assumes a deterministic demand level for unknown orders. The simplest, myopic procedure optimizes material use over only the accepted customer orders. These three procedures are investigated via an experimental design of computer simulations of an elementary small scale model of the production planning situation. The results show that the optimal procedure outperforms the other two procedures. Furthermore, for a realistic cost structure in feed industry under certain circumstances the use of the optimal procedure may lead to a 4% increase in profit. However, this improvement must be weighted against the cost incurred by the operational use of this complex procedure. Based on these considerations and the numerical results in this paper, we may expect that for some situations in practice the use of the simplest myopic procedure, optimizing material use only over the available customer orders, will be justified from an overall cost point of view.     

The effect of supply uncertainty in price-setting newsvendor models

We consider a price-setting newsvendor model in which a firm needs to make joint inventory and pricing decisions before the selling season. The supply process is uncertain such that the received quantity is the product of the order quantity and a random yield rate. Two cost structures are investigated, the in-house production case in which the firm pays for the input quantity and the procurement case in which the firm pays for the quantity received only. Our objective is to investigate the effect of yield randomness on optimal decisions and expected profit. By using the theory of stochastic comparisons, we find that under both cost structures, a less variable yield rate leads to a lower optimal price and a higher expected profit. Moreover, we show that in the in-house production case, a stochastically larger yield rate also results in a lower optimal price and a higher profit, but this is not true in the procurement case. Examples show that the effect of supply uncertainty on optimal order quantity is not universal.     

Process mean determination under constant raw material supply

Setting the mean (target value) for a production process is an important decision for a producer when material cost is a significant portion of production cost. Because the process mean determines the process conforming rate, it affects other production decisions, including, in particular, production setup and raw material procurement policies. In this paper, we consider the situation in which the product of interest is assumed to have a lower specification limit, and the items that do not conform to the specification limit are scrapped with no salvage value. The production cost of an item is a linear function of the amount of the raw material used in producing the item, and the supply rate of the raw material is finite and constant. Furthermore, it is assumed that quantity discounts are available in the raw material cost and that the discounts are determined by the supply rate. Two types of discounts are considered in this paper: incremental quantity discounts and all-unit quantity discounts. A two-echelon model is formulated for a single-product production process to incorporate the issues associated with production setup and raw material procurement into the classical process mean problem. Efficient solution algorithms are developed for finding the optimal solutions of the model.     

Admission policies for the customized stochastic lot scheduling problem with strict due-dates

This papers considers admission control and scheduling of customer orders in a production system that produces different items on a single machine. Customer orders drive the production and belong to product families, and have family dependent due-date, size, and reward. When production changes from one family to another a setup time is incurred. Moreover, if an order cannot be accepted, it is considered lost upon arrival. The problem is to find a policy that accepts/rejects and schedules orders such that long run profit is maximized. This problem finds its motivation in batch industries in which suppliers have to realize high machine utilization while delivery times should be short and reliable and the production environment is subject to long setup times.We model the joint admission control/scheduling problem as a Markov decision process (MDP) to gain insight into the optimal control of the production system and use the MDP to benchmark the performance of a simple heuristic acceptance/scheduling policy. Numerical results show that the heuristic performs very well compared with the optimal policy for a wide range of parameter settings, including product family asymmetries in arrival rate, order size, and order reward.     

Optimal production run time for two-stage production system with imperfect processes and allowable shortages

This paper considers a two-stage production system with imperfect processes. Shortages are allowed, and the unsatisfied demand is completely backlogged. In addition, the capital investment in process quality improvement is adopted. Under these assumptions, we first formulate the proposed problem as a cost minimization model where the production run time and process quality are decision variables. Then we develop the criterion for judging whether the optimal solution not only exists but also is unique. If the criterion is not satisfied, the production system should not be opened. An algorithm for the computations of the optimal solutions is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.     

Optimal production run time for a deteriorating production system under an extended inspection policy

A deteriorating production system is subjected to random deterioration from an in-control state to an out-of-control state with a general shift distribution. In order to reduce the defective items, part inspection policy, under which production inspections are performed only at the end of the production run, and full inspection policy are both considered in the literature. Moreover, the former dominates the latter. Since the product produced towards the end of a production cycle are more likely to be defective, it can further economize the inspection costs that they are directly reworked without inspection. In this paper, we propose an extended product inspection policy for a deteriorating production system. Product inspections are performed in the middle of a production cycle, and after the inspection, all products produced until the end of the production run are fully reworked. Based on the model, we show that there exists a production run time and a corresponding unique inspection policy such that the expected total cost per item per cycle is minimized. Finally, numerical examples are provided to illustrate our extended inspection policy, and indicate that such product inspection model will reduce the quality-related cost than part inspection does.     

Inventory and investment in setup and quality operations under Return On Investment maximization

In this paper, we construct and analyze a Return On Investment (ROI) maximization model for inventory and capital investment in setup and quality operations under an investment budget constraint. Specifically, we show how such an ROI maximization model can be formulated and derive analytical results such as the conditions under which the inventory is reduced and for the determination of the unique global optimal solution. In addition, by applying the Reformulation-Linearization Technique (RLT), we show via numerical examples how this nonconvex optimization model can be solved effectively and how RLT may produce superior results to those from the conventional Cut Across the Board Rule (CABR). Various managerial insights are provided throughout the paper. For example, as the investment budget increases (or decreases), a fundamental shift of investment strategies (setup cost reduction vs. quality improvement) may be necessary so as to maximize ROI.     

A multiperiod model for production planning and design in a multiproduct batch environment

A general multiperiod model to optimize simultaneously production planning and design decisions applied to multiproduct batch plants is proposed. This model includes deterministic seasonal variations of costs, prices, demands and supplies. The overall problem is formulated as a mixed-integer linear programming model by applying appropriate linearizations of non-linear terms. The performance criterion is to maximize the net present value of the profit, which comprises sales, investment, inventories, waste disposal and resources costs, and a penalty term accounting for late deliveries. A noteworthy feature of this approach is the selection of unit dimensions from the available discrete sizes, following the usual procurement policy in this area. The model simultaneously calculates the plant structure (parallel units in every stage, and allocation of intermediate storage tanks), and unit sizes, as well as the production planning decisions in each period (stocks of both product and raw materials, production plans, policies of sales and procurement, etc.).     

An economic production lot size model in an imperfect production system

The paper investigates an EPL (Economic Production Lotsize) model in an imperfect production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘in-control’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective (imperfect), in ‘out-of-control’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.     

Optimization of two-step investment in a production process

We consider the problem of optimizing the control of a production process. The control parameters are the capacity utilization and the investment in the growth of the production capacity. We assume that the investments are divided into two parts: initial investment aimed at creating production facilities, and investment aimed at increasing the capacity during the production process. The initial and increased capacities and the moment of changing the capacity are variable parameters to be specified. The price of the product is assumed to be a random process. The problem is to optimize the production process and to construct a control strategy that maximizes the average discounted profit. We propose an approach to the construction of an optimal adaptive strategy for controlling the production. The approach is based on the dynamic programming method.