Modeling Lean and Agile Approaches: A Western Canadian Forest Company Case Study

Materials and Methods

For better understanding, this section was divided into three sections. First is the case study, where we explain its singularities and sources of data. Second, the formulation of models was conceptually addressed, where we translate the manufacturing drivers into mathematical programming models. Third, we explain how the lumber demand scenarios were developed, which helped to recreate lumber demand behaviors based on order sizes and variability inside the order.

The Case Study

The forest-to-lumber SC planning problem was formulated keeping in mind an integrated BC Coastal forest SC, where harvesting, sort-yarding, and sawmilling operations do not always happen simultaneously. A year-based forest operation begins with logging, and then the logs for sawmilling are sorted by species, grade, and hauled by ground or water directly to forest industries. Downstream, sawmills extract the highest lumber grades possible from logs to produce commodities and customized lumber products. In terms of sales, when construction lumber grades are traded, wholesalers tend to be tolerant of an over/under fulfillment of orders. However, when trading high-grade lumber, industrial and wholesaler customers are less tolerant (i.e., there are high penalizations for missing targets). The focus in coastal BC is to create value while maintaining high volume and value recoveries and capacity utilization. Consequently, for the purpose of this study, a year of operation was considered as the time window. Accordingly, a planning horizon of one year divided into four periods was chosen (four quarters). The problem can be divided into procurement planning and lumber planning, where loggers carry out harvesting plans in advance and push stems and logs to sort yards. Then, sawmills buy log sorts depending on lumber sales orders, which is why the decoupling point of this SC is located at the sort yards (Figure 1).

Figure 1. Forest to lumber British Columbia (BC) coastal supply chain case study.

A case study provides the data for forest inventory yields, harvesting costs, log-to-lumber yields, manufacturing costs, lumber prices, and sales orders, and such information was extracted from publicly available annual financial reports from a British Columbia (BC) coastal forest integrated company.

Formulation of Models

The soft drivers of manufacturing principles were translated into hard drivers to model the problem. The SC strategy driver of the ME was considered as the central driver and used as the objective function. The manufacturing focus and inventory policy were translated into capacity usage penalty policies. The backorder and lead time focus were translated into demand satisfaction penalty policies. Product attributes, volume, and variety were considered as lumber demand scenarios. The agile, lean and BC-SC formulations included the possibility of lumber interchanges between sawmills and sawmilling outsourcing. The lean approach used a level manufacturing strategy, which was applied as a capacity constraint to ensure that at least a minimum level of capacity must be utilized. The agile approach used a chase manufacturing strategy, which was applied as a capacity constraint to ensure a higher flexibility of capacity usage. The BC-SC used mixed capacity constraints, which was a level strategy for the timber supply problem, and a chase strategy for the lumber manufacturing problem (Table 2). Two additional features were added: (1) applied penalties when lumber production was below or exceeded demand, and (2) applied penalties when capacity (i.e., time availability) was exceeded or was not completely used over a period by loggers, sort yards, and sawmills. In terms of demand satisfaction, over and under demand were heavily penalized under the agile approach, moderately penalized under the BC-SC approach, and lightly penalized under the lean approach. In terms of capacity, over and underproduction capacity was heavily penalized under the lean approach, moderately penalized under the BC-SC approach, and lightly penalized under the agile approach.

Table 2. Summary of manufacturing environment model formulations. ME: manufacturing environment.

ME Formulation	Central Manufacturing Principle Applied	Demand Satisfaction Penalty Policy	Capacity Usage Penalty Policy	Objective Function
Agile	Reduces the cost of variety to create the highest possible value.	Allows a tiny % of lumber demand to be over or under demand.	Emulates a time flexibility policy and production is set to match the demand and does not carry any leftover products (CHASE strategy).	Creating maximum value. Thus, we applied a profit max. objective function.
Hybrid: BC-SC	Profit max by harvesting the highest value forest resources and satisfying lumber demand.	BC-SC assumed to be middle ground, because it produces a mixed portfolio of lumber.	LEVEL Production is a strategy that produces the same number of units equally. LEVEL for procurement, and CHASE for sawmilling.	DP at sort-yards; thus, harvesting and sort-yards minimize costs, satisfying log demand. Sawmills max. Profit, satisfying lumber demand.
Lean	SC cost minimization reduces all forms of waste (i.e., Muda) through the SC.	Allows the highest % of lumber demand, which can be over or under demand.	The penalization emulates a LEVEL strategy.	Focused on cost min.; thus, a cost minimization objective function was applied.

The objective function for agile maximizes profit (1^A). Its components are: lumber and chip incomes, penalized incomes for overproduction, less operational costs, and cost penalties for below-demand lumber production, and cost penalties for over/under capacity usage. The objective function for lean minimizes cost (1^L) and contains the same components as the objective function for the agile approach. The BC-SC was divided into two problems: (1) timber supply and (2) lumber manufacturing. In order to compare this formulation with the other two, it was assumed that procurement areas transfer logs to the lumber production area with no profits. The timber supply problem satisfies a forecasted log demand; the log production solution was used to solve the lumber manufacturing problem. The objective function of the timber supply problem minimized cost (1^T). Its components were: operational costs and cost penalties for over/under capacity usage in logging and sort yard operations. The lumber manufacturing problem had a profit maximization objective function (1^W), and solved the lumber planning problem. The components of the objective function were: lumber and chip incomes, penalized incomes for overproduction, log costs, operational costs, cost penalties for under-demand lumber production, and cost penalties for over/under capacity in sawmilling operations (please see Table A1, Table A2, Table A3, Table A4, Table A5, Table A6 and Table A7 in Appendix A for full formulations).

Lumber Demand Scenarios	Description of the Scenario
i. Base_LD: Base lumber products demand.	Lumber demand by grades and species, based on BC companies’ public annual reports.
ii. LB_LV: Large batches and low variation of lumber products demanded.	Large batch and low variety of lumber products demanded, obtained by multiplying the original lumber demand data by a random binary number. This arrangement ensures large values similar to Base_LD, but when multiplied by a random binary number, the variation was reduced, because when the binary random number takes a zero value, it makes demand zero as well.
iii. LB_HV: Large batches and high variation of lumber products demanded.	Large batch and high variety of lumber products demanded, obtained by multiplying the original lumber demand data by a continuous random number generated between 0 and 1 plus 0.25. This arrangement ensured large values similar to Base_LD, or even bigger, but all are non-zero values, because continuous random numbers were used. This means that all of the values exist, thus ensuring high variation.
iv. SB_LV: Small batches and low variation of lumber products demanded	Small batch and low variety of lumber products demanded, obtained by multiplying the original lumber demand data by a random binary number, and by a continuous random number generated between 0 and 1. This arrangement ensured lower values in comparison with Base_LD, or at most the same, but the variation was reduced.
v. SB_HV: Small batches and high variation of lumber products demanded.	Small batch and high variety of lumber product demanded, obtained by multiplying the original lumber demand data by a continuous random number generated between 0 and 1. This arrangement ensured lower values in comparison with Base_LD, or at most the same, but all are non-zero values ensuring high variety