Scheduling with a due-window for acceptable lead-times
ISS & MLB︱September 24-26, 2013
Scheduling with a due-window for acceptable lead-times Enrique Gerstl and Gur Mosheiov
School of Business Administration, The Hebrew University, Jerusalem 91905, Israel Phone: 972-2-588-3108, Fax: 972-2-588-1341, Email: [email protected]
Abstract Due-dates are often determined during sales negotiations between customers and the sales team of the firm. In the preliminary (pre-sale) stage, the customer provides a time interval (due-window) of his preferred due-dates. This interval reflects acceptable leadtimes, which are functions of the customer resource constraints (e.g. storage or personnel limitations). If the due-dates are assigned either prior to or after the due-window, the firm is penalized accordingly. The final contract refers to the penalties of the actual delivery times as well. Thus, for given (realized) due-dates, the firm is also penalized according to the earliness/tardiness of the delivery time of the products. The model introduced in this paper considers both parts of the sales negotiations (i.e., determination of the time interval for acceptable due-dates, and earliness/tardiness penalties of the actual delivery times). Scheduling literature contains three major procedures for assigning due-dates to jobs: ( ) assigning a common due-date for all the jobs (also known as CON), ( ) assigning jobdependent due-dates which are (linear) functions of the job processing times (also known as SLK), and ( ) assigning job-dependent due-dates which are penalized if exceed prespecified deadlines (also known as DIF). One extension of these models is to a setting of due-window. In this setting, jobs completed within a time interval (rather than at a time point) are not penalized. Jobs completed prior to or after this time interval (window) are penalized according to their earliness/tardiness. The extensions of CON to a setting of common due-window (also known as CONW), and that of SLK to a due-window (SLKW) have been solved and published. The extension of DIF to a due-window is presented in this paper.
MLB 157
ISS & MLB︱September 24-26, 2013
The original DIF model reflects the fact that there exists "lead time that customers consider to be reasonable and expected". Thus, no cost is incurred when the due-date is assigned to be smaller than the maximum acceptable lead-time, and it is a linear function of the difference between the due-date and the maximum acceptable lead-time, otherwise. In our new more general model, a lower bound on the interval of acceptable lead times is assumed as well. As a result, if the due-date is assigned to be within a given interval of acceptable lead times (which is bounded both from above and from below), no cost is incurred. Otherwise, the cost is a function of the deviation of the due-date from this interval. While the original DIF model was shown to be solved in polynomial time in the number of jobs, the extension to a due-window setting is shown here to be NP-hard in the ordinary sense. We prove several properties of an optimal schedule, and consequently propose a very efficient dynamic programming algorithm. Our proposed algorithm is shown to be able to solve to optimality instances of up to 1000 jobs in reasonable time.
MLB 158
Scheduling with a due-window for acceptable lead-times Enrique Gerstl and Gur Mosheiov
School of Business Administration, The Hebrew University, Jerusalem 91905, Israel Phone: 972-2-588-3108, Fax: 972-2-588-1341, Email: [email protected]
Abstract Due-dates are often determined during sales negotiations between customers and the sales team of the firm. In the preliminary (pre-sale) stage, the customer provides a time interval (due-window) of his preferred due-dates. This interval reflects acceptable leadtimes, which are functions of the customer resource constraints (e.g. storage or personnel limitations). If the due-dates are assigned either prior to or after the due-window, the firm is penalized accordingly. The final contract refers to the penalties of the actual delivery times as well. Thus, for given (realized) due-dates, the firm is also penalized according to the earliness/tardiness of the delivery time of the products. The model introduced in this paper considers both parts of the sales negotiations (i.e., determination of the time interval for acceptable due-dates, and earliness/tardiness penalties of the actual delivery times). Scheduling literature contains three major procedures for assigning due-dates to jobs: ( ) assigning a common due-date for all the jobs (also known as CON), ( ) assigning jobdependent due-dates which are (linear) functions of the job processing times (also known as SLK), and ( ) assigning job-dependent due-dates which are penalized if exceed prespecified deadlines (also known as DIF). One extension of these models is to a setting of due-window. In this setting, jobs completed within a time interval (rather than at a time point) are not penalized. Jobs completed prior to or after this time interval (window) are penalized according to their earliness/tardiness. The extensions of CON to a setting of common due-window (also known as CONW), and that of SLK to a due-window (SLKW) have been solved and published. The extension of DIF to a due-window is presented in this paper.
MLB 157
ISS & MLB︱September 24-26, 2013
The original DIF model reflects the fact that there exists "lead time that customers consider to be reasonable and expected". Thus, no cost is incurred when the due-date is assigned to be smaller than the maximum acceptable lead-time, and it is a linear function of the difference between the due-date and the maximum acceptable lead-time, otherwise. In our new more general model, a lower bound on the interval of acceptable lead times is assumed as well. As a result, if the due-date is assigned to be within a given interval of acceptable lead times (which is bounded both from above and from below), no cost is incurred. Otherwise, the cost is a function of the deviation of the due-date from this interval. While the original DIF model was shown to be solved in polynomial time in the number of jobs, the extension to a due-window setting is shown here to be NP-hard in the ordinary sense. We prove several properties of an optimal schedule, and consequently propose a very efficient dynamic programming algorithm. Our proposed algorithm is shown to be able to solve to optimality instances of up to 1000 jobs in reasonable time.
MLB 158
