UC Berkeley

It is well accepted that uncertainties in supply, production processes, and demand have a major impact on the manufacturers' production and inventory decisions. Manufacturers in capital-intensive industries such as automotive, chemical and food processing face special challenges because they need to maintain high levels of utilization, leaving little flexibility to respond to fluctuations in demands and production yields. Furthermore, many such firms produce multiple products within the same factory, requiring time-consuming or costly changeovers between products, and unanticipated changeovers due to various sources of uncertainty can lead to a reduction in usable capacity and/or an increase in changeover-related costs.

The goal of the dissertation is to develop multi-product production and inventory strategies for manufacturers who use stable production plans due to economies of scale in production and tight capacity, and face various sources of uncertainty. This dissertation consists of two studies. In the first study (Chapters 2 and 3), we investigate a supply chain problem in which a manufacturer needs to maintain a stable production plan while attempting to be responsive to unpredictable orders from distributors. The distributors would like to order in full truckloads as much as possible to spread the high per-truckload cost of transportation across a larger quantity of items. As a consequence, their preferred ordering policy tends to exhibit variability in the time between orders, which makes it difficult for the manufacturer to predict future orders. In such settings, manufacturers are often forced to hold high safety stock levels to limit the number of product shortages and/or to reschedule production to respond to unexpected demands.

Motivated by this context, we propose and analyze a new multi-product (R, T) inventory policy with short-shipping in which an order is placed every T time units and the distributor aims to raise the inventory position of each product i to its respective Ri (produce-up-to) value, but short-shipping (shipping less than the unconstrained optimal order quantities) occurs when the aggregate order would exceed a truckload. By allowing short-shipments, it is possible to maintain both a fixed ordering interval which manufacturers often prefer because it facilitates their production planning, as well as relatively high utilization of truck capacity which distributors prefer due to economies of scale in transportation. We also evaluate how much benefit the manufacturer can obtain from the use of our proposed (R, T) policy which, due to its periodic review form, facilitates balancing of orders from distributors over time. To do so, we quantify the potential benefit to the manufacturer of having all of the distributors switch from their current mode of operation, which we approximate by a continuous-review full-truckload (Q, S) policy, to our proposed (R, T) policy. For both policies, we construct analytical models and develop accurate approximations that enable us to estimate the required base stock levels for the manufacturer to maintain a specified service level for a set of potentially non-identical distributors. Very few articles in the literature have developed systematic analytical models to address this issue for the case of non-identical distributors (or retailers). We conduct a numerical study to compare a system in which all distributors use an (R, T) policy with short-shipments to one in which they all use a (Q, S) policy. From our numerical study, we observe percentage reductions in the manufacturer's base stock level of 2% to 40% and safety stock reductions of 38% to 95% when the distributors switch from a (Q, S) policy to an (R, T) policy with short-shipping, representing substantial savings for the manufacturer.

There are two major contributions from the research presented in Chapters 2 and 3. First, our proposed (R, T) policy with short-shipping contributes to the literature on the stochastic joint replenishment problem (SJRP). Much of the past research on this topic has focused on finding optimal replenishment policies for the buyer (distributor or retailer), but these policies may have an adverse effect on the upstream supplier by increasing uncertainty in the order timing and quantities, thereby exacerbating the bullwhip effect. Our proposed policy, on the other hand, is designed to find a solution that is near-optimal for the distributors and simultaneously has the potential for making production planning easier for the manufacturer, thereby offering the potential for improving supply chain performance. Second, our work contributes to the literature on optimal or near-optimal policies, as well as performance evaluation of specific inventory policies for single-manufacturer (warehouse), multi-retailer (distributor) systems. Although much work has been done in this area, to the best of our knowledge, ours is the first to consider a supply chain in which the upstream stage uses a fixed-cycle (or discrete-time) production schedule and the downstream retailers (distributors) use a continuous-time ordering policy. One reason for the absence of such research in the literature may be that the literature has focused on situations in which the upstream location is a warehouse, which typically has fewer constraints on ordering than a manufacturer faces in planning its production. It is this feature of our problem that makes it distinctive, and is also the main reason why the manufacturer faces a challenge.

In the second study (Chapter 4), we seek to optimize production and inventory decisions of a manufacturer of seasonal products in a capital-intensive industry when demands are uncertain and the production yields of new products are also uncertain. Due to the capital-intensive nature of the industry, the manufacturer sets capacity levels far below peak demand and utilizes slack capacity during off-peak periods to build inventory in anticipation of peak demands. In such a setting, the manufacturer faces the difficult decision of whether to start production of new products well before the selling season (when spare capacity may be available) in order to ``work the bugs out" early, or minimally, to learn about achievable production yields, or to wait until closer to the selling season when capacity may be tight but more accurate demand forecasts may be available.

Motivated by this setting, we construct a parsimonious model to analyze production and inventory decisions for a manufacturer who introduces a new product to be produced in the same facility with existing products, and faces uncertainty in both demands and in the production yield of the new product.

We derive optimal policies for this setting and use these results as the basis for understanding conditions in which the manufacturer should make an early production run to learn the yield of the new product. We also perform comparative static analysis to investigate the effects of demand parameters (mean and range), production capacity, and yield parameters (mean and range) on the manufacturer's optimal decisions. We find not only that the optimal production quantity for the new product may be non-monotonic in the expected demand of the new product, but the decision of whether to learn the yield may also be non-monotonic in the expected demand. Furthermore, we find that, under some conditions, increased aggregate uncertainty about the demand and yield of the new product may deter the manufacturer from learning about the yield, contrary to the common wisdom that early resolution of uncertainty is advantageous.

Our model differs from those in the literature on demand updating in several key respects. First, unlike most papers in the literature, we incorporate capacity constraints and setup times in a context where products share capacity. Although these factors complicate the analysis and lead to a non-convex optimization model, they are critical practical considerations in our motivating context. Second, and perhaps more importantly, we consider yield learning along with demand forecast updating. In our setting, the manufacturer has the option to reduce his uncertainty about the yield of the new product by making an early production run. This gives the manufacturer an incentive to produce the new product early, an incentive which does not exist in models with only demand forecast updating.