Prescriptive Analytics for Demand Surge on Home Delivery Services

Abstract

This study develops mixed-integer programming (MIP) models for workforce allocation and delivery service design under delivery-date commitment requirements in third-party logistics (3PL) systems facing demand surge conditions. Existing research on delivery commitments has largely focused on customer behavior or simplified operational settings, with limited attention to integrated optimization frameworks that jointly consider workforce assignment, service scheduling, and service differentiation in realistic logistics environments. To address this gap, two MIP models are proposed for free and fee-based delivery services, respectively, incorporating customer delivery-date preferences, workforce heterogeneity, multi-skilled labor allocation, and capacity constraints within a unified decision-making framework. A real-world case study from a Chinese 3PL provider is used to evaluate the models. Computational results show that the fee-based service design improves delivery commitment reliability, workforce utilization, and profitability compared with the free-delivery setting, particularly under high-demand and capacity-constrained conditions. The findings highlight the operational value of service differentiation and workforce flexibility, and provide a prescriptive analytics framework to support integrated delivery planning in modern logistics systems.

1. Introduction

The rapid growth of e-commerce has significantly increased operational pressure on third-party logistics (3PL) providers. Rising online retail demand has led to higher order volumes, tighter delivery requirements, and more complex workforce planning needs [1,2,3]. As a result, logistics service providers must simultaneously ensure cost efficiency, timely delivery, and flexible resource utilization.

Recent disruptions such as the COVID-19 pandemic have further intensified these challenges by introducing workforce shortages, safety constraints, and demand uncertainty. These issues highlight the need for adaptive logistics systems capable of supporting reliable delivery services under dynamic operating conditions.

In practice, many firms have adopted differentiated delivery strategies to balance cost and service quality. A common approach is to offer customers both free standard delivery and fee-based priority delivery. For example, IKEA China provides free-delivery services using either insourced logistics teams or crowdsourced platforms depending on capacity conditions, while companies such as Alibaba and JD.com offer both free and paid delivery services, typically supported by crowdsourced fulfillment systems. These real-world practices demonstrate the importance of service differentiation in modern logistics operations.

A key feature of such systems is delivery-date commitment, which plays a critical role in customer satisfaction and operational planning. Reliable delivery commitments improve customer loyalty and enable better resource allocation through early demand visibility [4,5]. Accordingly, delivery service with date commitment (DSDC) has become an important mechanism for improving competitiveness in online retail logistics. From a managerial perspective, DSDC is increasingly supported by digital logistics platforms, real-time tracking systems, and omni-channel operations. These technologies enable better coordination of inventory, workforce, and transportation resources, improving both efficiency and service reliability. Moreover, customers are often willing to pay a premium for faster or more reliable delivery services, motivating firms to design hybrid systems combining free and paid delivery options [6,7].

Despite its practical relevance, there remains limited research on how logistics providers can jointly optimize workforce allocation, delivery scheduling, and service differentiation within a unified framework. Existing studies often consider these decisions separately or rely on simplified settings that do not fully reflect real-world 3PL operations. Motivated by these gaps, this study develops a mixed-integer programming framework for delivery service design under delivery-date commitment. The model jointly optimizes workforce assignment and delivery scheduling while explicitly incorporating free and fee-based service options.

The rest of this paper is organized as follows. Section 2 provides the literature review. Section 3 presents the problem description and mathematical formulations for delivery service without fee and with fee. Section 4 reports computational results from a small illustrative example and a real-world six-week case study, along with managerial insights. Section 5 concludes the paper and discusses future research directions.

2. Literature Review

Research on logistics service systems, delivery commitment, and workforce planning spans multiple streams, including service operations, behavioral logistics, and optimization-based scheduling. However, despite extensive work in these areas, there remains a lack of integrated models that jointly consider delivery-date commitments, workforce allocation, and service differentiation in large-scale logistics environments.

The first stream of the literature focuses on service operations and delivery performance from a customer satisfaction perspective. These studies emphasize that on-time delivery, service reliability, and flexibility are key drivers of customer loyalty and perceived service quality. Workforce flexibility, cross-trained labor, and coordinated task allocation have been identified as important factors influencing delivery performance [8,9,10]. However, many of these studies remain conceptual or partially quantitative and do not fully integrate operational decision-making mechanisms.

A second stream examines logistics performance under uncertainty, with particular emphasis on information systems and digital technologies. Research in this area highlights that technologies such as IoT-based tracking, real-time monitoring systems, and integrated logistics platforms can significantly improve delivery reliability and reduce uncertainty [11]. Nevertheless, these studies generally focus on system-level improvements rather than optimization models for workforce and scheduling decisions.

A third stream applies agency theory and behavioral modeling to study delivery commitments and customer response. These works show that delivery delays negatively affect customer satisfaction and future purchasing behavior, emphasizing the importance of fulfillment reliability [12,13,14,15,16,17,18]. Game-theoretic approaches have also been used to study pricing strategies, service contracts, and policy interventions related to delivery performance [19,20,21,22]. While insightful, these studies typically abstract away detailed operational constraints such as workforce scheduling and capacity limitations.

A smaller but important stream of research develops optimization-based models for delivery service systems. Some studies propose profit-oriented or performance-driven optimization models incorporating delivery constraints and solve them using heuristic algorithms such as genetic algorithms [23]. Other studies formulate multi-objective optimization models to improve delivery efficiency and service quality [24]. However, these models are often limited in scale and do not fully capture realistic workforce structures, service differentiation mechanisms, or large-scale 3PL operational settings.

In parallel, mixed-integer programming (MIP) formulations have been widely applied to home delivery and last-mile logistics problems, including vehicle routing with time windows, order batching, delivery time-slot management, and integrated routing and scheduling decisions [25,26,27]. Despite these advances, workforce assignment is typically assumed to be fixed or highly aggregated, while heterogeneous multi-skilled workers are rarely modeled explicitly in last-mile delivery systems [28]. Furthermore, existing MIP models generally optimize routing and scheduling decisions without jointly considering workforce activation, customer delivery-date commitments, and differentiated service policies such as free versus fee-based delivery options [29].

Overall, the existing literature lacks an integrated optimization framework that jointly considers delivery-date commitments, workforce assignment decisions, and service differentiation through free and fee-based delivery options. To bridge this gap, this study develops a mixed-integer programming (MIP) framework for delivery service design under delivery-date commitment requirements. The proposed model integrates workforce allocation, service scheduling, and service differentiation decisions within a unified optimization structure tailored to third-party logistics operations. In particular, the main contributions of this study include the development of an integrated MIP model for delivery service design under delivery-date commitments, the joint optimization of workforce assignment and delivery scheduling decisions, and the explicit modeling of service differentiation through free and fee-based delivery options. Together, these contributions provide a scalable decision-support framework for real-world 3PL operations.

3. Problem Description and Mathematical Model

3.1. Business Context and Problem Setting

In China, there are few home store retailers with sufficient economies of scale to compete with Alibaba (Alibaba.com) or JingDong (JD.com), and both companies outsource their delivery service from a pool of third party logistics (3PL) providers. The 3PL providers compete against each other in costs, and service quality. Unlike the delivery services offered by retailers in the U.S., the 3PL providers in China offer so-called ‘five-guarantees delivery service’ (JiaJuWuBao), which covers the logistics from manufacturers to individual customers. The five guarantees include:

• Take a shipment from manufacturers or retailers, and transport it to the distribution center near the shopper’s city.
• Provide last-mile delivery from the distribution center to the residential building of the shopper’s address based on the timeslot preferred by the shopper.
• Move the shipment from the downstairs entry to the shopper’s upstairs dwelling. Many old multi-story buildings in China do not have an elevator.
• Install furniture or electronic appliances using professional contractors.
• Retrieve unwanted old furniture or appliances, and repair any minor damage received during the shipping.

The collaborating 3PL provider operates through an integrated logistics network that combines long-haul transportation, collaborative outsourcing, crowdsourced labor, and multi-skilled contractors. Customer orders are processed through multiple operational stages, including shipment consolidation, delivery-date commitment, workforce assignment, and installation service coordination. Local delivery operations are supported through collaborative outsourcing partnerships among regional 3PL providers, where logistics resources and delivery responsibilities are shared to improve operational efficiency and reduce empty-mile transportation costs. In the final delivery stage, contractors possess heterogeneous skill sets, including loading, furniture assembly, appliance installation, and electrical work, while some workers are cross-trained to perform multiple sub-jobs. These operational characteristics create substantial workforce allocation and scheduling complexity, motivating the development of the proposed mixed-integer programming framework. The operational characteristics of the collaborating 3PL system are provided in Appendix A and Figure 1 illustrates the overall workflow of the delivery process.

3.2. Notations

We address the general setting of e-commerce customer service, where online big-box retailers depend on 3PL service providers to deliver big-box items to customers on their preferred delivery dates. The schedule arises by assigning n customers to a subset of m workers in the planning horizon of T periods. Each customer contains $N_j$ sub-jobs, and each sub-job requires a particular skill k. Each sub-job must be assigned to one worker, where the set of workers who possess the skills to perform the sub-job is denoted by $M_k$, and total time available for worker i in time period t is denoted by $q_{it}$. Sub-jobs can be executed at different efficiency levels $d_{jki}$ with different costs $C_{jkit}$ during time period t. Customer service priorities are reflected through revenues $P_{jt}$, which depend on the customer’s preferred delivery period. In addition, customers may specify a blocking date, defined as the latest acceptable delivery date. Deliveries scheduled after the blocking date incur a substantial penalty or may become infeasible. Blocking dates typically arise from customer availability constraints, such as work schedules, access restrictions, or other time-sensitive requirements, and therefore represent an important practical consideration in delivery planning. If a service provider needs to hire a new worker or deliver a new product, there is fixed cost $f_{it}$ of hiring and training worker i if the work starts in a period t. The fixed cost $f_{it}$ can vary according to the worker’s experience (number of completed jobs), technical quality (number of insurance claims), and customer satisfaction (ranked evaluation and commented feedback). We include the following notations that will be used throughout the remainder of this paper:

Input Parameters
Nj	Set of sub-jobs to be done for customer j, (j = 1, …, n) by qualified workers available in each period of the planning horizon (we use 8 in this study)
K	Set of all skill-types needed to do all customers’ jobs
Mk	Set of workers who possess the skill to perform sub-job $k\in N_j$
Djk	Set of standard workload of sub-jobs $k\in N_j$ needed to be done for customer j, (j = 1, …, n), (where the manufacturer provides a training video and recommends man-hours for service provider installation based on the minimum skill required)
Lj	Set of dates when customer j prefers its job to be performed
n	Number of customers served over the planning horizon
m	Number of skilled workers (with different skills) who can work on the sub-jobs over the planning horizon
T	Number of periods in the planning horizon (e.g., 7 days per week, or 8 h per day)
$d_{jki}$	Time (demand) required to do sub-job $k\in N_j$ of job j by worker $i\in M_k$
$q_{it}$	Total time available for worker i during time period $t \in T$
$C_{jkit}$	Cost to do sub-job $k\in N_j$ for customer j by worker $i\in M_k$ during period $t\in L_j$
$f_{it}$	Fixed cost of hiring and training worker i if the worker starts in a period $\in T$ (this cost is incurred only one time during the horizon, and is determined by the worker’s skills, experience level, and technical quality and customer satisfaction of the worker’s completed projects)
$P_{jt}$	Price charged to customer j if served in period $t\in L_j$ if the retailer offers service with a fee (if the retailer offer service without a fee, the customer is given an option to pay for service before the designated delivery time planned by the retailer)
Decision Variables:
$x_{jkit}$	Equal to 1 if sub-job $k\in N_j$ for customer j is done by worker $i\in M_k$ during period $t\in L_j,$ and 0 otherwise
$z_{jt}$	Equal to 1 if customer j is served in period $t\in L_j,$ and 0 otherwise
$v_{it}$	Equal to 1 if worker i works in a period $t \in T,$ and 0 otherwise
$w_{it}$	Equal to 1 if worker i starts work in a period $t \in T,$ and 0 otherwise

3.3. Mathematical Model

In this section we present the 3PL delivery models for the popular cases of delivery service without fee and the alternative delivery service with fee scenario. As shown below, the two models differ only in their objective function.

3.3.1. Delivery Service Without Fee

$$Minimize TC={\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{t=1}^T}{f}_{it}{w}_{it}+{\displaystyle {\sum }_{j=1}^n}{\sum }_{k\in N_j}{\displaystyle {\sum }_{t=1}^T}{\displaystyle {\sum }_{i\in M_k}}{c}_{jkit}{x}_{jkit}$$

(1)

$$s.t.{\displaystyle {\sum }_{t=1}^T}{Z}_{jt}=1 \forall j$$

(2)

$${\displaystyle {\sum }_{i\in M_k}}{x}_{jkit}=z_{jt} \forall j,k\in N_j,t$$

(3)

$$v_{it}\le {\displaystyle {\sum }_{l=1}^t}{w}_{il} \forall i,t$$

(4)

$${\displaystyle {\sum }_{j=1}^n}{\sum }_{ k\in N_j}{d}_{jki}{x}_{jkit}\le q_{it}{v}_{it} \forall i,t$$

(5)

$$z_{jt},x_{jkit}\in \left\{\mathrm{0,1}\right\} \forall j,k\in N_j,i\in M_k,t$$

(6)

$$w_{it}\in \left\{\mathrm{0,1}\right\},v_{it}\ge 0 \forall i,t$$

(7)

The objective function (1) includes the total fixed and variable costs with delivery date determined by the 3PL service provider (which can be any day during the week). The value of TC is the total cost to be minimized over the horizon. Constraints (2) enforce each customer (job) be served in only one period each day. Constraints (3) ensure all sub-jobs of the customer (job) j are served together in one period. Constraints (4) ensure that if worker i works in a period t, then they must have been trained earlier or during time t. Combined with the fixed cost in the objective function, the constraint implies that the worker will incur some fixed cost f_it, e.g., hiring and training cost, upon starting work. The fixed cost f_it is also related to the worker’s experience, technical ability, and customer satisfaction. Constraints (5) ensure a worker may be hired or deployed to work in period t, and the worker’s total assigned workload will not exceed their capacity. The proposed mixed-integer programming (MIP) formulation is computationally challenging because it integrates customer assignment, delivery scheduling, worker activation, and multi-skilled workforce allocation decisions within a unified optimization framework. In particular, when delivery periods and worker activation decisions are fixed, the model reduces to a capacity-constrained assignment problem equivalent to the classical Generalized Assignment Problem (GAP), which is NP-hard [30]. Since GAP is a special case of the proposed formulation, the proposed model is also NP-hard. Moreover, the formulation contains O(nmKT) binary assignment variables. Additional worker activation and scheduling variables further increase the combinatorial search space as the problem size grows.

In this model, the service provider decides which day to deliver to the customer based on the lowest cost over the planning horizon. Some providers offer customers several possible delivery dates and confirm the delivery beforehand.

3.3.2. Delivery Service with Fee

If a customer prefers an early delivery date or an alternative date, and is willing to pay for receiving a delivery on this date, then the provider switches to the model that offers delivery service with a fee as follows:

$$Minimize TC={\displaystyle {\sum }_{i=1}^m}{\displaystyle {\sum }_{t=1}^T}{f}_{it}{w}_{it}+{\displaystyle {\sum }_{j=1}^n}{\sum }_{k\in N_j}{\displaystyle {\sum }_{t\in L_j}}{\displaystyle {\sum }_{i\in M_k}}{c}_{jkit}{x}_{jkit}-{\displaystyle {\sum }_{j=1}^n}{\displaystyle {\sum }_{t\in L_j}}{P}_{jt}{z}_{jt}$$

(1′)

$$s.t.{\displaystyle {\sum }_{t\in L_j}}{Z}_{jt}=1 \forall j$$

(2′)

$${\displaystyle {\sum }_{i\in M_k}}{x}_{jkit}=z_{jt} \forall j,k\in N_j,t\in L_j$$

(3′)

$$v_{it}\le {\displaystyle {\sum }_{l=1}^t}{w}_{il} \forall i,t \in T$$

(4′)

$${\displaystyle {\sum }_{j=1}^n}{\sum }_{ k\in N_j}{d}_{jki}{x}_{jkit}\le q_{it}{v}_{it} \forall i,t\in L_j$$

(5′)

$$z_{jt},x_{jkit}\in \left\{\mathrm{0,1}\right\} \forall j,k\in N_j,i\in M_k,t\in L_j$$

(6′)

$$w_{it}\in \left\{0, 1\right\}, v_{it}\ge 0 \forall i,t \in T$$

(7′)

The objective function (1′) includes the price paid by customers, according to their preferred time, as well as the total fixed and variable costs. By assigning a large negative cost for deliveries on dates that are blocked by the customer (as undeliverable or not preferred), the objective function can enforce that work will be done on the committed date. The value of TC is thus again the total cost to be minimized over the horizon. In this model, if the value of $P_{jt}$ is set to zero, the formulation becomes effectively the same as the model for delivery service without fee. Using different sets of values for $P_{jt}$ allows us to address various demands and customer preferences. Note that the last term in (1′) represents revenue earned so that a negative value of the objective function corresponds to a contribution to profits. Constraint (2′) ensures each customer (job) is served exactly once during the planning horizon. Constraint (3′) requires all sub-jobs belonging to the same customer to be completed simultaneously to avoid fragmented service visits. Constraint (4′) links worker deployment to worker activation and training decisions. Constraint (5′) ensures assigned workload does not exceed worker capacity.

One note is that relaxing these assumptions would significantly increase computational complexity.

To illustrate the relationship between operational inputs, optimization decisions, and computational outputs, Figure 2 presents the overall optimization framework of the proposed delivery service scheduling model.

As shown in Figure 2, customer demand information, worker availability, delivery preferences, and service structures are integrated into the mixed-integer programming framework to jointly determine workforce assignment, delivery scheduling, and service selection decisions while minimizing operational cost.

4. Computational Experiments and Results

4.1. Small Benchmark Example

Before presenting an actual case study, we illustrate the main features of the model with a small example. For this purpose, consider a big-box retailer with three workers (one driver and two assistants) to serve six customers over a 3-day planning horizon. The sub-jobs and man-hour requirements of each sub-job for six customers, and price offered by the customers for the 3-day delivery window, are given in

Table 1. Customer Workload and Price Data.

Workload				Customer	Price Offered
N1	N2	N3	N4	j	T1	T2	T3
1		5		1		180
5	3	1	1	2			160
1	5			3	170
1		3	5	4		145
	1		5	5			185
5			1	6	165

. In Table 1, the standard workload is measured in man-hours based on the lowest level of experiences. The price offered by the customer is based on the report of a recent empirical study. Each customer chooses one day as the preferred delivery date, and the 3PL service provider plans its services to meet these requests. In Table 1, we combine the information on sub-jobs and workload of sub-jobs together. The workload values represent standard labor hours required for each sub-job based on manufacturer installation guidelines and historical completion records for entry-level workers. The prices offered by customers are used to infer their preferred service dates, with higher prices indicating stronger preferences for earlier service.

In

Table 2. Level of worker experience, and their availability each period.

Level of Experience				Workers	Availability
M1	M2	M3	M4	i	T1	T2	T3
5	1	5	5	1	8	8	7
3	5		3	2	8	8	8
	5	5	3	3	7	8	7

, the skills and experience level of skill for three workers as well as their availability for the 3 days are given. In the insourcing approach, workers have high levels of experience, and high availability per day because they are employees of the retailer. This sample represents the insourcing approach with a high level of experience. In the crowdsourcing approach, workers have varying availability each day, and they might work for several providers at the same time as independent contractors. In Table 2, the data for Level of Experience gives the rating from 0 to 5 for each worker, and each sub-job as well as worker availability in hours over the 3-day period.

The fixed costs of hiring and training workers along with data about each worker’s past performance are given in

Table 3. Fixed cost of each worker on each period.

Technical Quality			Workers	Fixed Cost
Completion of Project	Insurance Claim	Customer Satisfaction
			i	T1	T2	T3
2200	1	4	1	15	15	15
1400	0	4	2	18	18	18
400	0	3	3	26	26	26

. The fixed costs are estimated by the worker’s experience, technical quality, and customer feedback. There are different ways to estimate the fixed costs based on historical data, and data analytics tools. For this, a five-level category is used to evaluate each criterion, and cost is assigned based on the level. Training here is minimal, and costs are in RMBs.

The time and cost to complete each sub-job by the worker each period is shown in

Table 4. Time and cost for each sub-job by a qualified worker in each period.

Djki			jk	Cjkit
I				T1			T2			T3
1	2	3		i = 1	i = 2	i = 3	i = 1	i = 2	i = 3	i = 1	i = 2	i = 3
0.56	0.71		11				16	14
2.78		2.78	13				61		67
2.78	3.57		21							78	74
3.00	1.67	1.67	22							47	43	47
0.56		0.56	23							13		13
0.56	0.71	0.71	24							12	15	16
0.56	0.71		31	13	16
5.00	2.78	2.78	32	66	78	78
0.56	0.71		41				13	13
1.67		1.67	43				37		40
2.78	3.57	3.57	44				78	63	63
1.00	0.56	0.56	52							17	12	12
2.78	3.57	3.57	54							78	69	74
2.78	3.57		61	78	74
0.56	0.71	0.71	64	12	16	14

. The time to complete the job is calculated by the level of experience. The cost of a sub-job by qualified workers is calculated based on a salary survey. In China, the hourly rate for an entry-level delivery worker is between 16.5 and 21 RMB per hour, according to the Human Resources and Social Security Bureau, an official Chinese agency [31].

Table 5. Results of sample problem for service with fee.

Xjkit				Cjkit	Zjt		Pjt
j	k	i	T		j	t
1	1	2	2	14	1	2	180
1	3	1	2	61	2	3	160
2	1	1	3	78	3	1	170
2	2	2	3	43	4	2	145
2	3	1	3	13	5	3	185
2	4	1	3	12	6	1	165
3	1	1	1	13	wit		Fit
3	2	1	1	66	i	t
4	1	2	2	13	1	1	15
4	3	1	2	37	2	1	18
4	4	2	2	63
5	2	2	3	12	Solution
5	4	2	3	69	TC = −392
6	1	2	1	74
6	4	1	1	12

presents the optimal solution of delivery service in this small example. The values of decision variables in the objective function are reported in the table along with the value of objective function, which is −392, which means profit of 392. The model was solved in less than 0.0001 s using IBM ILOG CPLEX Optimization Studio 20.1 on a desktop PC with an 11th Gen Intel Core i9-11900H processor (2.50 GHz) and 32 GB of RAM.

The results provide several managerial insights. First, although three workers were available, the model determined that only two workers were required to complete all six customer deliveries, demonstrating the model’s ability to efficiently utilize labor resources while satisfying delivery commitments. Second, the solution illustrates how delivery timing and worker assignment decisions are jointly optimized to maximize profitability. Customers with different preferred delivery dates and service fees are assigned to workers and time periods in a coordinated manner, balancing workforce capacity and revenue opportunities.

Note that the model can also be used for scenario or what-if analysis. For example, suppose customers 3 and 5 both changed their delivery date to day 2. Re-solving the model quickly reveals that the new delivery schedule is in fact doable, but profits decline slightly from 392 to 364. Likewise, if all six customers prefer the same delivery date, the model quickly discloses that there is no feasible solution with the current workforce, and additional workers would have to be hired.

4.2. Real-World Case Study

In this section, we consider a large-scale delivery operation by a Chinese 3PL service provider for the largest online big-box retailer in China. Here, we give an overview of the problem, and the usefulness of the optimization model in planning and executing customer deliveries. Note that in Appendix A we describe the complete order fulfillment process for a typical customer of a big-box retailer by a 3PL service provider.

The online big-box retailer considered several models of omni-channel fulfillment operations, choosing crowdsourcing to staff their delivery service. Unlike the insourcing approach, the online retailer’s planning horizon depends on the distance between manufacturing, and customer since they often use an intermodal transportation approach. The local 3PL service provider where the customer is located will manage the door-to-door delivery with worker and task assignments. The policy of the local 3PL here usually states that workers assigned to the customers are limited to a 10 min driving distance from those customers. We retrieved the data from a dedicated server via an ODBC connection. The primary attributes of the data include customer address and their preferred service time; shipment information such as item description, costs, and planned arrival time; and manufacturer-recommended man-hour requirements for installation. Worker information lists skills, their related skill levels, number of completed projects, customers’ ratings, training history, and third-party service provider information, noting the number of contractors, workers, and warehouse location. For training purposes, manufacturers provide a training video for installation and handling. They also provide man-hour requirements for various tasks. For the market opportunities at hand, sub-jobs are classified into eight categories including lamps, lanterns, curtains, drying racks, furniture category, flooring, wallpaper category, door, appliances, and locks.

The company plans deliveries 6 weeks in advance, solving the optimization model for each week to organize planning.

Table 6. Customer information on workload (standard man-hours unit) and crowdsourcing workers information.

ID	Total Workload	Workload Range	Daily Minimum Workload	Daily Maximum Workload	Total Capacity	Capacity Range	Daily Minimum Capacity	Daily Maximum Capacity
W1	1628	1 to 6 h	122	295	1574	4 to 6 h	221	240
W2	1619	1 to 4 h	187	280	2227	4 to 7 h	310	324
W3	2310	1 to 8 h	212	431	3050	6 to 8 h	427	445
W4	2728	1 to 5 h	227	548	2895	7 to 8 h	411	415
W5	3284	1 to 4 h	415	560	3957	7 to 8 h	557	570
W6	3761	1 to 6 h	397	608	4447	7 to 8 h	628	641

details the weekly operational scale of the case by tracking total workload demands and crowdsourcing workers in formation over the 6-week planning horizon. The data shows a progressive demand surge, with total workload requirements escalating from a low of 1619 standard man-hours in week 2 to a peak of 3761 standard man-hours by week 6. Over this same period, individual customer order requirements remain consistently bound within a workload range of 1 to 8 h per order. To accommodate these shifting demands, the third-party logistics (3PL) provider dynamically scales its total available labor capacity from 1574 h in week 1 to a maximum of 4447 h in week 6, utilizing independent contractors who provide flexible daily shifts ranging between 4 and 8 h.

The results of the optimization runs are shown in

Table 7. Computational results of case study on delivery with fee.

ID	Number of Customers	Number of Available Workers	Number of Variables	Number of Constraints	Number of Deployed Workers	Cost of Deployed Workers	Total Cost of Service	Labor Utilization Efficiency
W1	110	45	10,439	1190	36	22,276	−3861	0.823
W2	164	57	19,611	1622	28	21,335	1956	0.881
W3	133	63	18,482	1548	38	30,226	−15,631	0.762
W4	235	55	26,675	1931	45	35,820	−3943	0.752
W5	317	75	49,824	2673	74	44,451	4709	0.868
W6	258	85	45,630	2529	49	48,668	−11,074	0.882

. Table 7 reports the number of workers deployed, total cost and labor efficiency each week in the planning horizon. Operation logs show that worker availability ranged from 45 to 85 workers during weeks 1 to 6, and that over this time they were to service from 110 to 317 customers. Given these plans, the firm is on track to earn a profit in weeks 1, 3, 4, and 6, but to lose money in weeks 2 and 5. Note that Table 7 also gives the size of the models solved where the six instances range in size from 10,439 to 45,630 variables, and from 1190 to 2529 constraints. The large number of variables is primarily driven by the combinatorial nature of workforce assignment and delivery scheduling decisions, while the constraints represent operational, capacity, scheduling, and logical consistency requirements. These dimensions illustrate the computational complexity of solving realistic large-scale home delivery scheduling problems. All six problems were solved within 1 h by CPLEX.

For evaluating the labor utilization efficiency, we use the ratio between the total adjusted workload demanded by the customer ${\displaystyle {\sum }_{i\in M_k}}{\displaystyle {\sum }_{t\in L_j}}{\displaystyle {\sum }_{j=1}^n}{\sum }_{k\in N_j}{d}_{jki}{x}_{jkit}$ and the total occupied worker capacity ${\displaystyle {\sum }_{i\in M_k}}{\displaystyle {\sum }_{t\in L_j}}{q}_{it}{v}_{it}$.

These ratios are high, indicating limited flexibility in response to possible changes in customer demands and worker availability. For example, if the availability of workers declined by 5% in week 5, which has the highest ratio of customer/worker (317/75) and the highest ratio of deployed/available workers (74/75), then the solver cannot find a feasible solution, implying that the schedule is not workable. Workforce flexibility is key to the crowdsourcing business model when customer demand is uncertain.

Note that if the provider chose to switch to the service without fee model, rather than the service with fee model considered above, it could take control of delivery dates. This, in turn, would likely lead to changes in both the cost of deployed workers as well as labor utilization efficiency, with a resulting impact on profits. To test the impact of such a change here, we took the same data on workload demand, and worker availability used above, and allowed the possible delivery day to be relaxed to any day of the week. The results obtained by running the service without a fee model are shown in

Table 8. Computational results of case study on delivery without fee.

ID	Number of Customers	Number of Available Workers	Number of Variables	Number of Constraints	Number of Deployed Workers	Total Cost of Service/Deployed Workers	Labor Utilization Efficiency
W1	110	45	69,293	3890	29	21,394	0.932
W2	164	57	132,489	5582	24	20,855	0.947
W3	133	63	124,082	4746	32	29,515	0.903
W4	235	55	182,105	7487	32	34,845	0.924
W5	317	75	342,468	10,509	63	43,667	0.92
W6	258	85	312,270	9015	47	48,480	0.89

. Note that by allowing delivery any day of the week, the size of the model grows substantially, resulting in much longer run times. The free-delivery setting introduces greater scheduling flexibility, which substantially increases the number of feasible delivery and workforce assignment combinations, resulting in significantly larger mixed-integer programming models. Of the six solutions shown in Table 8, the shortest solution time was 4 h and the longest was 10 h. To evaluate labor utilization efficiency in this case, we use the ratio between the total adjusted workload demanded by the customer ${\displaystyle {\sum }_{i\in M_k}}{\displaystyle {\sum }_{t=1}^T}{\displaystyle {\sum }_{j=1}^n}{\sum }_{k\in N_j}{d}_{jki}{x}_{jkit}$ and the total occupied worker capacity ${\displaystyle {\sum }_{i\in M_k}}{\displaystyle {\sum }_{t=1}^T}{q}_{it}{v}_{it}$.

The results show that labor utilization increased by an average of 12% and the number of workers was reduced by 16% on average, leading to a total labor cost reduction of 2.2%. However, considering the entire process (see Appendix A) these changes, considering total revenue and production costs, actually led to lower profitability than was realized under the ‘with fee’ model.

Using the without fee model to test additional alternatives, we found that the worker’s availability can be reduced up to 50% and still allow feasible solutions. However, if the minimum worker capacity of any given day is less than the maximum total adjusted workload by a single customer, the problem is infeasible. The service-without-fee model showcases the trade-offs between the total cost of delivery and the value of schedule flexibility to commit to customer delivery dates.

The recent pandemic sheds some light on the trade-off of service without fees and with a fee. For example, for service without a fee, companies cannot meet the sudden jump in customer demand or disruption of logistics. Amazon must halt delivery service on some items due to its capacity bottleneck, and warehouse closings [32]. For service with a fee, companies must plan a hiring spree of crowdsourcing workers in a short period to meet a surge of customer demand. Some 3PL delivery service companies, such as Instacart and Shipt, use flexible tipping as incentive to the crowdsourcing workers for fast delivery service.

5. Conclusions and Future Study

This study develops mixed-integer programming models for delivery service design under delivery-date commitment requirements in a third-party logistics (3PL) environment. The proposed framework jointly determines workforce allocation, delivery scheduling, and service differentiation decisions under both free-delivery and fee-based delivery policies. Using data from a large-scale Chinese 3PL provider, the models demonstrate how delivery commitments and workforce constraints interact to influence operational efficiency and profitability.

The computational results show that fee-based delivery services provide greater control over delivery commitments and can improve profitability by aligning customer preferences with operational capacity. In contrast, free-delivery services offer greater scheduling flexibility, leading to improved labor utilization and reduced workforce requirements, but may not maximize overall profitability. The results also highlight the importance of workforce flexibility, particularly under demand surges, where worker availability becomes a critical determinant of service feasibility and delivery performance.

From a managerial perspective, the proposed framework provides a practical decision-support tool for evaluating trade-offs among service levels, workforce utilization, and operating costs. The results suggest that service differentiation can serve as an effective demand-management mechanism, while flexible workforce deployment can improve the resilience of delivery operations during periods of fluctuating demand.

Several limitations provide opportunities for future research. First, the proposed models focus on workforce assignment and delivery scheduling and do not explicitly incorporate vehicle routing decisions. Second, the models assume deterministic demand, service times, and worker availability, whereas actual logistics systems operate under considerable uncertainty. Third, customer preferences are represented through delivery commitments and pricing structures without explicitly modeling customer behavioral responses. Future research may address these limitations by integrating routing decisions, stochastic or robust optimization approaches, and customer choice models within a unified framework.

Future studies may also investigate the use of real-time operational data from digital logistics platforms and IoT-enabled tracking systems to support dynamic rescheduling and workforce allocation. In addition, systematic sensitivity analyses on key parameters, such as workforce capacity, demand intensity, delivery fee levels, and service-time estimates, would provide further insights into the robustness of delivery policies and their managerial implications. Finally, validation across multiple logistics providers and geographic regions would help assess the broader applicability of the proposed framework and enhance its practical relevance.