*3.1.2.2 Operational planning model*

As shown in **Figure 4**, the operational horizon ranges from 8 to 11 weeks. The length of this horizon is defined according to the position of the first week in the month.

**Figure 4.** *Variable operational planning horizon.*

*Enhancement of Textile Supply Chain Performance through Optimal Capacity Planning DOI: http://dx.doi.org/10.5772/intechopen.96292*

For example, if the first week of the planning horizon corresponds to the second week of the month ϴ, then the length of the planning horizon is set to 11 weeks because tactical decisions related to the month ϴ + 2 must also be taken into account.

We denote by a couple (t, s) the weeks in the operational planning model, where s is the position of the week in month t. Operational planning includes a set of periods TSӨ<sup>δ</sup> and takes place at the beginning of week δ of month Ө (as detailed in appendix B).

For the operational planning model, detailed in appendix C, the length of the planning horizon is justified by the fact that POs resulting from tactical planning should be reliably detailed at the operational level. Hence, to properly place decisions made at the tactical level, the operational planning horizon must reach the end of the month.

#### **3.2 Data collection plan**

Based on company reports translating historical data, Gemba walks and after meetings and team benchmarking, we were able to collect the necessary information to set the required parameters for the proposed models.

Before detailing experimental data, it is important to identify the established planning assumptions:


#### *3.2.1 Experimental data*

The relevant company delivers about 200 references of products to 30 retailers per year through 3 knitting manufacturing plants located in Tunisia. Products are transferred to customers through two local warehouses storing finished products ordered by local and overseas retailers. These warehouses are characterized by their limited storage capacity and a storage cost of approximately 5% of the unit production cost per unit.

The shipments can be carried out by trucks, for local deliveries, or by aircraft and by ships, for overseas connections. Our mathematical models decide on the mode of transport to be adopted according to the delivery times involved. Indeed, a delay of at least 5 weeks is necessary to deliver the products by ship. However, aircraft shipments are made within the same week. The considered transportation costs are composed of fixed costs, depending on the number of shipments made, and variable costs depending on the shipped quantities.

Considering the 200 variety of manufactured products, the internal production costs vary from 3 to 35 euros. In order to accommodate the limited internal capacity, flexibility is ensured by scheduling overtime. However, overtime activity is limited to 25% of production capacity after regular working hours and costs 40% more. The internal flexibility is reinforced by a subcontracting activity with 10 local subcontractors and one overseas one located in China. The local subcontractors have

enough capacity to meet the ordered quantities and fill the limited capacity of the internal production sites. The latter offer products at prices 20% higher than the cost of internal production. As for the Chinese subcontractor, it can manufacture large volumes of products but with delivery times exceeding 2 months. The latter offers basic products at costs that are about half the internal production cost. Our planning models decide on production allocations based on available capacities and assigned lead times. The overall focus is to meet customer orders on time and at lower cost.

Our proposed approach is run over 6 months, generating a weekly production schedule identifying the quantities to be manufactured, stored and distributed. The proposed models are solved using the package ILOG OPL Studio V6.3/ Cplex 11 and are run on an intel Core i5 PC with a 2.3 Ghz processor and 512 MB of memory. The planning model at the tactical level takes into account approximately 122,000 constraints and 66,000 variables, of which more than 5,000 are binary. However, the operational model contains 55,000 constraints and 3,000 binary variables among the 25,000 considered variables in the model. An almost optimal solution, with a deviation of 10–<sup>4</sup> from optimality, is obtained for all the executed models.

#### **3.3 Current situation and the gap with the desired one**

Our approach evaluates the current situation of the apparel manufacturer who incurs a logistic cost equal to 2864 k€ obtained for the 6 months.

In order to improve the situation, we aim at considering additional flexibility at the tactical planning level in order to better accommodate the unpredictable orders that will be placed at the operational level. A decrease of the overall logistic cost is expected.
