The Demand Forecast For The Next Four Periods Is 80 110 120

The Demand Forecast For The Next Four Periods Is 80 110 120 And

The demand forecast for the next four periods is 80, 110, 120, and 145 units respectively. The plant has a regular capacity of 100 units per period, an overtime capacity of 10 units per period, and a subcontractor capacity of 5 units per period. Costs per unit are: Regular production: $5, Overtime production: $8, Subcontracting: $9. Holding cost per unit per period: $3. No shortages are allowed, and the company has 5 units in inventory at the start of the planning period. The question is: How many units should be produced using overtime?

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Effective capacity planning is crucial for manufacturing firms striving to meet fluctuating demand while minimizing costs and avoiding stockouts. The scenario presented involves a production system with specific capacities, costs, and initial inventory, alongside a forecasted demand pattern over four periods. The core objective is to determine the optimal number of units to produce using overtime capacity in order to meet demand without shortages and at minimum cost.

In the given scenario, the firm has a regular capacity of 100 units per period but faces demand exceeding this capacity in some periods, specifically the latter two. Overtime capacity adds an additional 10 units per period at a higher cost; subcontractors can supply an additional 5 units at an even higher cost. Starting with 5 units in inventory, the firm needs to plan production to meet demand precisely in each period while incurring minimal costs related to production and holding inventory.

To begin, it is essential to analyze each period individually, considering demand, available capacity, and initial inventory, to determine the necessary overtime production. Since no shortages are allowed, production must meet or exceed demand in every period. If regular capacity plus initial inventory cannot cover demand, the firm must resort to overtime or subcontracting.

Period 1 (Demand 80 units): The firm starts with 5 units of inventory. The regular capacity of 100 units comfortably covers the demand of 80 units, so overtime and subcontracting are unnecessary in this period. Inventory after fulfilling demand: 5 + 100 (regular) – 80 (demand) = 25 units.

Period 2 (Demand 110 units): Starting with 25 units, the firm needs to produce additional units. The regular capacity of 100 units combined with existing inventory totals 125 units, which exceeds the demand of 110 units. To fulfill demand, the firm can produce 110 units, possibly reducing inventory, or produce extra units and hold surplus. Since inventory after demand satisfaction: 25 + 100 – 110 = 15 units, production occurs at regular capacity with no overtime needed.

Period 3 (Demand 120 units): Inventory at the start of this period is 15 units. Regular capacity is 100 units, which, combined with initial inventory, totals 115 units, just short of 120 units. To meet this demand, the firm must use additional capacity. Overtime capacity is 10 units at a higher cost. Producing 100 units at regular capacity plus 10 units of overtime yields 110 units, reaching only 125 units including inventory. After fulfilling demand, inventory balances at 15 + 100 + 10 – 120 = 5 units, so production of 110 units suffices, with 10 units of overtime used.

Period 4 (Demand 145 units): The start with 5 units, and maximum regular plus overtime production per period is 100 + 10 = 110 units. To meet the demand of 145 units, the firm must employ subcontracting or additional overtime. Subcontracting capacity is 5 units at a cost of $9 per unit, which is more expensive but necessary here. Producing 100 units at regular time, 10 units of overtime, and 5 units subcontracted sums to 115 units, which meets demand, leaving no gap. Inventory after demand: 5 + 100 + 10 + 5 – 145 = -25, but since shortages are not allowed, the firm must increase overtime to 35 units or subcontract more.

Therefore, in period 4, the firm needs to produce an additional 35 units in overtime or subcontracting to meet demand without shortages. Given that subcontracting is more expensive ($9), it is optimal to utilize overtime capacity as much as possible within the limits. Since overtime capacity is just 10 units per period, and the total shortfall is 35 units, the firm will need to supplement the overtime with subcontracting options.

Conclusion: The critical decision revolves around period 4, where the demand surpasses the sum of regular and overtime capacities. To meet demand without shortages, the firm should produce 10 units of overtime per period (for periods 3 and 4) and utilize subcontracting as needed in period 4. Specifically, in period 4, 10 units of overtime should be produced, and the remaining shortfall (25 units) will be addressed by subcontracting. This approach minimizes higher-cost subcontracting by maximizing overtime use within capacity limits.

In summary, the optimal utilization of overtime occurs in periods where demand exceeds regular capacity but not beyond the overtime limit. The firm should produce 10 units of overtime in period 4, complementing regular capacity, and use subcontracting for the remaining shortfall, ensuring demand fulfillment without shortages and at the lowest combined cost.

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