Service level constraints

Hopp, W.J., M.L. Roof 2000. Quoting Manufacturing Due Dates Subject to a Service Level Constraint. HE Transactions 32(9), 771-784. 

The paper is organized as follows. In Section 1, we discuss the characteristics of a DDM problem, including decisions, modeling dimensions, objectives and solution approaches. In Section 2, we discuss commonly used scheduling rules in DDM policies. Offline DDM models, which assume that the demand and other input about the problem are available at the beginning of the planning horizon, are discussed in Section 3. Online models, which consider dynamic arrivals of orders over time, are presented in Section 4. Models for DDM in the presence of service level constraints are discussed in Section 5. We review the DDM models with order acceptance and pricing decisions in Section 6. We conclude with future research directions in Section 7. 

Service level constraints Commonly used service level constraints include an upper bound on (1) the fraction (or percentage) of orders which are completed after their due dates, (2) the average tardiness, and (3) the average order flow time. 

Average/total (weighted) due date (subject to service level constraints) [1] [6] [61] [109]... 

In the remaining part of this section, we discuss the papers with online DDM models in more detail. We use the term machine to refer to any type of resource. We say that due date management policy A dominates B, if both policies satisfy the same service level constraints and policy A achieves a better objective function than policy B. 

The first two of these rules are parametric and the parameters a and (3 are chosen (based on simulation experiments) such that the service level constraints are satisfied. These rules apply to both problems I and II. The third and fourth rules set the shortest possible due date at any time to satisfy the service level constraints of the maximum fraction of tardy jobs and the maximum average tardiness, and apply to problems I and II, respectively. The proposed due date management policies use these rules with SPT sequencing between different classes, and FCFS sequencing within each class. 

Note that the rules in Equations (12.1)-(12.4) do not consider the previously set due dates. Therefore, utilizing WEIN-NONPAR I and WEIN-NONPAR II, Wein proposes two other rules, WEIN-HOT-I and WEIN-HOT-II, for problems I and II, respectively. Under these rules, if there is enough slack in the system, a new job can be quoted a shorter lead time and scheduled ahead of some previous jobs of the same class. The sequencing policy is still SPT for different classes, but EDD (rather than FCFS) within each class. Although these rules may result in shorter due dates, they may violate the service level constraints. 

The first two terms in equations (12.7) and (12.8) estimate the flow time, and the last term is a waiting time allowance based on the forecast error. Normal probability tables can be used to choose the 7 value to satisfy the service level constraint on the maximum number of tardy jobs. 

Another study that considers DDM with 100% service guarantee is [65]. In addition to due date setting and scheduling, the authors consider order acceptance decisions and take a profit maximization perspective hence, their model and results are discussed in Section 6.1. Other papers that consider service level constraints along with pricing decisions in DDM include [75] and [97], which are discussed in Section 6.2. 

J.H. Bookbinder and A.I. Noor. Setting job-shop due-dates with service-level constraints. Journal of the Operational Research Society, 36(11) 1017-1026, 1985. 

W.J. Hopp and M.L. Roof Sturgis. Quoting manufacturing due dates subject to a service level constraint. HE Transactions, 32 771-784,2000. 

In the first section we discussed random demand. Then we calculated the conditional demand and now finally we define conditional random service and conditional random shortage. These concepts are very important for optimization of service levels under capacity constraints. 

Push-based ATP models must take into account very specific customer-related constraints such as customer priorities, sales channel characteristics, variations in customer service levels and so on. Inventory control and planning models usually operate at a more aggregate level. 

Thus, an important issue in our formulation will be how we specify the service constraint on our optimization problem. From our earlier discussion of in-stock probability and fill rate, recall that the probability distribution of demand figured prominently in measuring the service level. The most general case is the one in which both demand per unit time period (where the time period is typically specified as days or weeks) and replenishment lead time (correspondingly expressed in days or weeks) are random variables. Let us, therefore, assume that the lead time L follows a normal distribution with mean Pl variance al. Further, let us assume that the distribution of the demand also follows a normal distribution, such that its mean and variance, Po Od, are expressed in time units (i.e., demand per unit time) that are consistent with the time units used to express lead time L (e.g., days or weeks). 

The level of validation to be undertaken must be chosen considering scientific and economic constraints. All data have some value, and results from the development phase can all be pressed into service for validation. Separate planned experiments might lead to better and more statistically defensible results, but when this cannot be done, then whatever data are at hand must be used. The best use can be made of experiments to be done by understanding what is required. For example, in a precision study, if the goal is to know the day-to-day variability of an analysis, then duplicate measurements over 5 days would give more useful information than 5 replicates on day 1, and another 5 on day 5. The strategy would be reversed if variations within a day were expected to be greater than between days. 

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