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

Abstract

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.

Introduction

Customers, in today’s global competitive environment, demand products that are highly differentiated, low-cost, and high-quality. In addition, the product development and life cycles are growing ever shorter. Hence, in order to compete effectively, manufacturers must be able to manufacture a wide variety of products in a cost-effective manner, and to respond quickly to changes in the product designs and volumes. In other words, competitive priorities have shifted from an economies-of-scales focus to one that is built around quality and flexibility (see among others Sethi and Sethi, 1990, Etienne-Hamilton, 1994). The way to meet this challenge has been to implement advanced manufacturing technologies such as Flexible Manufacturing Systems (Buzacott and Yao, 1986) and Just-In-Time (JIT) manufacturing principles (Schonberger, 1982, Monden, 1983). However, it is well-known that a fundamental prerequisite to the successful use of these technologies is to have short setup/changeover times (Shingo, 1985, Shingo, 1990). With short setup times, short production cycles – with small lots and inventories – become economical. Small lots and inventories in turn, expose inefficiencies and quality problems so that action can be taken to remedy them. Hence, it is no surprise that setup reduction and quality improvement programs have become so prevalent in industry over the past two decades (e.g., Johansen and McGuire, 1986, Byrne, 1995).

Mathematical models to address the issue of investing in reduced setups began to appear in the mid-1980s. In his seminal work, Porteus (1985) introduced the first known of such model, which dealt with the problem of selecting the appropriate level of investment in setup cost reductions. Considering a single-product, this paper analytically demonstrated the relationships that exist in the EOQ model between setup cost reductions, inventory costs, and demand. Various authors have proposed variations or extensions of this model, considering either a single product (e.g., Diaby, 1995, Li et al., 1997, Nye et al., 2001) or multiple products (e.g., Spence and Porteus, 1987, Kim et al., 1995, Banerjee et al., 1996, Leschke and Weiss, 1997, Diaby, 2000, Gupta and Magnusson, 2005). For single product models, Diaby (1995) developed a model for setup reductions in the context of the dynamic lot-sizing problem, which included explicitly setup times and setup costs. An efficient dynamic programming procedure was proposed to solve it. Assuming instead a stochastic demand, Li et al. (1997) proposed a model in which, in addition to setup costs, lead time and variance of annual demand forecast errors were reduced through investments. This model did not explicitly consider setup times, but included stock-out costs. Nye et al. (2001) proposed a queuing theory-based approach to explicitly model the costs of work-in-progress inventories, in addition to the investments in setup time reductions. Apart from Diaby (1995)’s model which incorporated a set of constraints on production capacity, single-product models have been unconstrained in general. With regards to multiple products models, Spence and Porteus (1987) examined a capacitated EOQ model, under production capacity constraints and showed how investing in setup time reductions contributes to increasing the effective production capacity. Similarly, Kim et al. (1995) showed, but under budget and capacity constraints, how a setup time reduction program can be an attractive alternative to overtime or outsourcing, given that it results on the increase of the capacity, in addition to savings in inventory costs. Both invariant and variant setup times between products were assumed in that paper. Therefore, the case of one investment to reduce the common setup times was considered as well as the case of different investments to reduce the setup times for the different products. The latter was also assumed in Banerjee et al. (1996), where a model was proposed to evaluate, under budget and capacity constraints, the impacts that various levels of investments in setup time reduction for different products have on the lot-sizes and the total relevant costs of setup, inventory, and amortization investment in setup time reductions. A non-linear optimization model was developed and an heuristic procedure solution was proposed to solve it. Since these models were developed in the case of static demands, Diaby (2000) developed an extended model assuming a dynamic manufacturing environment, multiple manufacturing resources, multiple setup reduction resources, and a general, non-increasing, piecewise-linear setup time reduction investment function. A dynamic manufacturing setting was also considered in Leschke and Weiss (1997), but the paper’s objective was to investigate how various rules of assigning setup time reduction investment opportunities to various products affect the benefits that can be achieved, under budget and capacity constraints.

In terms of quality improvement, many authors have explored the relationship between investment in a production process to reduce it’s variance and improve quality levels (Chen and Tsou, 2003, Kulkarni and Prybutok, 2004, Yang and Pan, 2004, Kulkarni, 2008, Kulkarni, 2008, Abdul-Kader et al., 2010, Annadurai and Uthayakumar, 2010). Kulkarni and Prybutok (2004) study the application of a modified form of the Reflected Normal loss function for optimal process investment/variance reduction decisions. Yang and Pan (2004) present an integrated inventory model to minimize the sum of the ordering/setup cost, holding cost, quality improvement investment and crashing cost by simultaneously optimizing the order quantity, lead time, process quality and number of deliveries while the probability distribution of the lead time demand is normal. Kulkarni (2008) examine a joint lot-sizing and process investment problem with random yield and backorders and develop stochastic models which provide the optimal inspection and lot-sizing policy as well as the optimal process investment for variance reduction. Kulkarni (2008) consider a multi-product environment where optimal production lot-sizing and investing for quality improvement in several production processes are calculated across products in the presence of a budget constraint. Abdul-Kader et al. (2010) consider investment in quality improvement to adjust the mean and variance of the process. The direct cost of poor quality is represented by a symmetrical truncated loss function. Annadurai and Uthayakumar (2010) discuss a mixture inventory model with back orders and lost sales in which the order quantity, reorder point, lead time and setup cost are decision variables. They assumed that an arrival order lot may contain some defective items and the number of defective items is a random variable. Chen and Tsou (2003), However, deal with the optimal design problem for process improvement by balancing the sunk investment cost and revenue increments due to the process improvement. They develop an optimal model based on Taguchi cost functions.

The focus of all models discussed above has been on the benefits associated with setup time reductions or quality improvement. The benefits from joint quality improvements and setup reduction have been generally ignored. Porteus (1986) addressed this gap by proposing a model, in the context of EOQ model, to simultaneously deal with joint investment decisions in process quality improvements and setup cost reductions, assuming that a process can move out of control with a given probability, while producing a lot. Hong and Hayya (1993) examined these joint decisions, in the context of dynamic, discrete lot-sizing problem, under investment budget constraints. An efficient solution based on lagrangian analysis was proposed. Similarly, Hong and Hayya (1995) defined the conditions where the entire budget is invested in quality improvements or in setup time reductions. The assumptions of no interruptions of the production process and a single period where considered in these works. Assuming that the machine inspection occurs instead at the end of each period, Gong et al. (1997) proposed a discounted, multi-period Markovian decision model was with the objective of developing an optimal decision rule to minimize the expected total operating cost of the machine. Vörös (1999) considered a model in which it is assumed that the production process is interrupted once quality issues are detected. Freimer et al. (2006) assumed instead that the process deteriorates over time, with defective units being repaired instantaneously at a known unit cost. In particular their study established how the marginal value of setup cost reduction (or process improvement) is related to the optimal run length. Affisco et al. (2002) investigated, in a context of supplier–customer relationship, how joint investment decisions in process quality improvements and setup cost reductions result in total system savings, due to a larger decrease in supplier replacement costs, supplier setup costs, and customer inspection costs than the increase of investment costs in quality improvements and setup reductions. However, as pointed out by Liu and C¸entikaya (2007), the logarithmic function that was used in Affisco et al.’s (2002) paper to represent the cost of investments in quality improvement does not represent actual practices in many industries. A modified form was introduced and findings showed that although these joint investment decisions are worthwhile, a careful analysis is required rather than solely relying on the benefits of reducing inventory related costs. Leung (2007) measured the quality as the expected fraction of a lot that is acceptable, instead of the process going out of control with the production of the next unit. Unlike other works, that paper explicitly included the costs of interest charges and depreciation resulting from the investment in setup time reductions or quality improvements, and formulated the inventory decision model using geometric programming, under process reliability constraints. Finally, while all the models discussed so far have focused on cost minimization objective functions, Li et al. (2008) developed a model that seeks, in the general context of economic ordering quantity problem and under budget constraints, the maximization of the return on investment (ROI), as measured by the ratio of profit per unit time over the investment per unit time. Their study showed how changes in budget availability affect investment strategies (setup reduction vs. quality improvement) so as to maximize the return on investment.

In general, work that deals with joint investment decisions of setup time reductions and quality improvement assume that a single product is produced and cannot readily be extended to multiple products (Ouyang et al., 2002). In addition, operational constraints are generally ignored in these models. The exception to this are Hong and Hayya, 1993, Hong and Hayya, 1995, Li et al., 2008, where budget constraints were explicitly taken into account. On the other hand, the few models that consider multiple products have limited scope. For instance, adopting the common cycle approach, Hwang et al. (1993) developed a geometric programming based model, under manufacturing capacity constraints, assuming the same improvement ratios in setup reductions as well as yield for all products. However, as pointed out by Moon (1994), that model may not result in meaningful solutions, given that it ignores a number of technical constraints. Although an updated model including the missing constraints was developed as well as a solution procedure based on Lagrangian analysis, it cannot be generalized in an obvious way to handle (a) constraints other than manufacturing capacity; (b) a cost function other than the one used (i.e., the power-form function) to represent total investment cost of setup reductions and quality improvements; and (c) different improvement ratios in setup reductions as well as yield for all products.

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. Demand for each product occurs at a constant rate. Production cycle times can be shortened by investing in setup time and defect rate reductions, respectively. The problem is to determine optimal levels of setup time reductions, defect rate reductions, and production cycle time for each product, subject to demand, process improvement budget, and manufacturing and warehousing capacity constraints, respectively. Therefore, we extend previous work by handling different types of constraints and cost functions of total investment cost of setup reductions and quality improvements which are representative of many manufacturing settings. Unlike previous works, we deal both with product improvements (due to, for example, product redesign) and process improvements (due to, for example, process redesign). General nonlinear optimization models of this problem are formulated. A convex geometric programming approximation of these models is developed 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.

The plan of the paper is as follows. The product-specific improvement model and the geometric programming approximation are developed in Section 2. The joint-product improvements model is presented in Section 3. Numerical implementation is discussed in Section 4. Empirical studies and managerial insights are presented in Section 5. Finally, conclusions are discussed in Section 6.