A two-stage stochastic optimization model for the retail multiskilled personnel scheduling problem: a k-chaining policy with $k \ge 2$

Abstract

<abstract> <p>Considering an uncertain demand, this study evaluates the potential benefits of using a multiskilled workforce through a k-chaining policy with $k \ge 2$. For the service sector and, particularly for the retail industry, we initially propose a deterministic mixed-integer linear programming model that determines how many employees should be multiskilled, in which and how many departments they should be trained, and how their weekly working hours will be assigned. Then, the deterministic model is reformulated using a two-stage stochastic optimization (TSSO) model to explicitly incorporate the uncertain personnel demand. The methodology is tested for a case study using real and simulated data derived from a Chilean retail store. We also compare the TSSO approach solutions with the myopic approaches' solutions (i.e., zero and total multiskilling). The case study is oriented to answer two key questions: how much multiskilling to add and how to add it. Results show that TSSO approach solutions always report maximum reliability for all levels of demand variability considered. It was also observed that, for high levels of demand variability, a k-chaining policy with $k \ge 2$ is more cost-effective than a 2-chaining policy. Finally, to evaluate the conservatism level in the solutions reported by the TSSO approach, two truncation types in the probability density function (pdf) associated with the personnel demand were considered. Results show that, if the pdf is only truncated at zero (more conservative truncation) the levels of required multiskilling are higher than when the pdf is truncated at 5th and 95th percentiles (less conservative truncation).</p> </abstract>

A benchmark dataset for the retail multiskilled personnel planning under uncertain demand

“…First, it can be noted that most articles used MIP models or a combination of MIP models and heuristic approaches as their chosen solution method. Notably, articles such as Henao et al [20], Henao et al [23], Abello et al [1], Fontalvo Echavez et al [16], Mercado and Henao [32], Mercado et al [33], and Henao et al [19] also incorporated optimization techniques such as RO, TSSO, or CF to address the challenge of uncertain demand.…”

“…Second, among the 17 articles listed in Table 2, twelve of them addressed a workforce training problem (i.e., [1,16,[19][20][21][22][23]32,33,41,44,54]). Therefore, in each of these articles, one of the objectives was to establish the optimal training plan for the staff.…”

“…Therefore, in each of these articles, one of the objectives was to establish the optimal training plan for the staff. However, 8 of these 12 articles specifically addressed a MPAP (i.e., [19][20][21]23,32,33,44,54]), which is identified in the table by the nomenclature A + WT. Remember that a MPAP simultaneously solves an assignment problem along with a workforce training problem.…”

“…Regarding the staff costs, it was assumed that each worker has a minimal cost of training (c = 1 US$− week/employee). Henao et al [19], Henao et al [20], Henao et al [23], Vergara et al [54], and Mercado et al [33] expressed that the outcomes found under this supposition represent an upper bound on the possible benefits of using multiskilled staff. In relation to the over/understaffing costs, it was assumed that these are the same across all departments.…”

“…Optimizing workforce composition, task and shift assignments, and ensuring cost-effectiveness are critical aspects of personnel scheduling for companies ( [22,24]). Comprehensive investigations conducted by Henao et al [19], Henao et al [21], and Mercado et al [33] have identified six primary personnel scheduling problems (PSPs): staffing, shift scheduling, days-off scheduling, tour scheduling, assignment, and workforce training. Staffing involves determining the required workforce for each task type and shift, while shift scheduling involves the daily allocation of work shifts to the hired workforce.…”