W e analyze the problem faced by companies that rely on TL (Truckload) and LTL (Less than Truckload) carriers for the distribution of products across their supply chain. Our goal is to design simple inventory policies and transportation strategies to satisfy timevarying demands over a finite horizon, while minimizing systemwide cost by taking advantage of quantity discounts in the transportation cost structures. For this purpose, we study the cost effectiveness of restricting the inventory policies to the class of zero-inventory-ordering (ZIO) policies in a single-warehouse multiretailer scenario in which the warehouse serves as a cross-dock facility. In particular, we demonstrate that there exists a ZIO inventory policy whose total inventory and transportation cost is no more than 4/3 (5.6/4.6 if transportation costs are stationary) times the optimal cost. However, finding the best ZIO policy is an NPhard problem as well. Thus, we propose two algorithms to find an effective ZIO policy: An exact algorithm whose running time is polynomial for any fixed number of retailers, and a linear-programming-based heuristic whose effectiveness is demonstrated in a series of computational experiments. Finally, we extend the worst-case results developed in this paper to systems in which the warehouse does hold inventory.

We consider two substitutable products and compare two alternative measures of product substitutability for linear demand functions that are commonly used in the literature. While one leads to unrealistically high prices and profits as products become more substitutable, the results obtained using the other measure are in line with intuition. Using the more appropriate measure of product substitutability, we study the optimal investment mix in flexible and dedicated capacities in both monopoly and oligopoly settings. We find that the optimal investment in manufacturing flexibility tends to decrease as the products become closer substitutes; this is because (1) pricing can be used more effectively to balance supply and demand, and (2) the gains obtained by shifting production to the more profitable product are reduced due to increased correlation between the price potentials of the substitutable products. The value of flexibility always increases with demand variability. We also show that, as long as the optimal investments in dedicated capacity for both products are positive, the optimal expected prices and production quantities do not depend on the cost of the flexible capacity. Manufacturing flexibility simply allows the firm to achieve those expected values with lower capacity, while leading to higher expected profits.

Flexible capacity has been shown to be very effective to hedge against forecast errors at the investment stage. In a make-to-order environment, this flexibility can also be used to hedge against variability in customer orders in the short term. For that purpose, production levels must be adjusted each period to match current demands, to give priority to the higher margin product, or to satisfy the closest customer. However, this will result in swings in production, inducing larger order variability at upstream suppliers and significantly higher component inventory levels at the manufacturer. Through a stylized two-plant, two-product capacitated manufacturing setting, we show that the performance of the system depends heavily on the allocation mechanism used to assign products to the available capacity. Although managers would be inclined to give priority to higher-margin products or to satisfy customers from their closest production site, these practices lead to greater swings in production, result in higher operational costs, and may reduce profits.resource flexibility, capacity allocation, supply chain performance, demand uncertainty, operational hedging

Investments in dedicated and flexible capacity have traditionally been based on demand forecasts obtained under the assumption of a predetermined product price. However, the impact on revenue of poor capacity and flexibility decisions can be mitigated by appropriately changing prices. While investment decisions need to be made years before demand is realized, pricing decisions can easily be postponed until product launch, when more accurate demand information is available. We study the effect of this price decision delay on the optimal investments on dedicated and flexible capacity. Computational experiments show that considering price postponement at the planning stage leads to a large reduction in capacity investments, especially in the more expensive flexible capacity, and a significant increase in profits. Its impact depends on demand correlation, elasticity and diversion, ratio of fixed to variable capacity costs, and uncertainty remaining at the times the pricing and production decisions are made.

We consider an economic lot-sizing problem with a special class of piecewise linear ordering costs, which we refer to as the class of modified all-unit discount cost functions. Such an ordering cost function represents transportation costs charged by many less-thantruckload carriers. We show that even special cases of the lot-sizing problem are NP-hard and therefore analyze the effectiveness of easily implementable policies. In particular, we demonstrate that there exists a zero-inventory-ordering (ZIO) policy, i.e., a policy in which an order is placed only when the inventory level drops to zero, whose total inventory and ordering cost is no more than 4/3 times the optimal cost. Furthermore, if the ordering cost function does not vary over time, then the cost of the best ZIO policy is no more than 5 6 4 6 times the optimal cost. These results hold for any transportation and holding cost functions that satisfy the following properties: (i) they are nondecreasing functions, and (ii) the associated cost per unit is nonincreasing. Finally, we report on a numerical study that shows the effectiveness of ZIO policies on a set of test problems.

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As manufacturers in various industries evolve toward predominantly make-to-order production to better serve their customers' needs, increasing product mix flexibility emerges as a necessary strategy to provide adequate market responsiveness. However, the implications of increased flexibility on overall system performance are widely unknown. We develop analytical models and an optimization-based simulation tool to study the impact of increasing flexibility on shortages, production variability, component inventories, and order variability induced at upstream suppliers in general multiplant multiproduct make-to-order manufacturing systems. Our results show that (1) Partial flexibility leads to a considerable increase in production variability, and consequently in higher component inventory levels and upstream order variability. Although a modest increase in flexibility yields most of the sales benefits, production variability is reduced as more flexibility is added to the system. Consequently, investments in additional flexibility may be justified when component inventories are expensive, or simply by the benefits associated with the smoother production. (2) The performance of flexible systems is highly dependent on the capacity allocation policies implemented. Policies that evenly distribute product demands to the available plants lead to consistently better performance because they avoid the misplacement of inventories by replicating the performance of a single-plant system. These insights and the simulation tool can be used by practitioners to guide the design of their flexible production systems, trading off the initial capital outlay versus the sales benefits and the expected operational costs.manufacturing capacity and flexibility planning, production variability, demand allocation, make-to-order manufacturing systems

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