Managing Production-Inventory Systems with Scarce Resources

Abstract

We consider the problem of managing production in a production-inventory system where a firm is subject to an allowance (a limit) on either the amount of input it can use or the amount of output it can produce over a specified compliance period (in addition to being subject to a constraint on the production capacity). Examples of such settings are numerous and include those where limits are placed on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. We study the structure of the optimal production policy for such systems and show that it is determined by dynamic thresholds that depend only on the sum of the on-hand inventory level and the remaining allowance. We provide an effective approximate solution approach that can compute these thresholds efficiently while retaining their essential properties. We examine the differences between how an allowance constraint and a constraint on production capacity affect production decisions and show that they exhibit opposite effects over time. We also examine, in the context of an extended version of the problem where both the allowance amount and the production capacity are endogenous, optimal investments in allowance and production capacity and the impact of both on firm profit. We also consider the optimal demand fulfillment policy in settings where the firm can decide whether to back-order or to reject demand that cannot be satisfied from on-hand inventory. The online appendix is available at https://doi.org/10.1287/msom.2016.0603 .

Multiseason production planning under export quotas

“…The constraint can also be due to reasons other than production capacity and it may be imposed on the total quantity in multiple periods. For example, Benjaafar, Chen, and Wang (2017) study a capacitated production‐inventory system where the total production output quantity over the planning horizon is upper bounded, which can be due to limit on the use of scarce natural resources as input or on the amount of waste or harmful pollution generated by production as output. In Gong and Zhou (2013), the limit is on the amount of emission allowances, and the firm has the options of trading emission allowances and choosing different production technologies, besides planning production.…”

Essays on blood supply management

“…A special case of regenerative capacity, and closest to this chapter, is the study by Benjaafar et al (2017) where they likened capacity to a scarce resource. Capacity in this case can be thought of as a resource that needs to be rationed in order to satisfy demand.…”

“…We can also say that the incoming capacity is zero for all periods except for the first period, making the first period's incoming capacity be the total capacity that needs to be rationed. This is precisely the model that Benjaafar et al (2017) considered. They use the setting of production limits/quotas in fisheries, logging, and carbon emissions and other harmful pollutants as the motivation to their model, and it supports our generalization further, indicating that problems with production limits fall under the larger class of problems with regenerative capacity.…”

“…They use the setting of production limits/quotas in fisheries, logging, and carbon emissions and other harmful pollutants as the motivation to their model, and it supports our generalization further, indicating that problems with production limits fall under the larger class of problems with regenerative capacity. In fact, Benjaafar et al's (2017) model (although they maximize revenue) is a special case of the model discussed in this paper.…”

“…At the same time, capacitated inventory systems, more complex inventory systems in existing literature (Benjaafar et al, 2017), and the motivational examples mentioned can be expressed as cases of regenerative capacity. More concretely, these are summarized in Table 3.1.…”