1212 / t 1 A SHORT TERM CAPACITY ADJUSTMENT POLICY FOR MINIMIZING LATENESS IN JOB SHOP PODUCTION SYSTEMS Henny P.G. van Ooijen J.Will M. Bertrand

1212 / t 2 Overview Introduction Literature review Research question Policy for capacity adjustment Evaluation Future research

1212 / t 3 Introduction Job shop (functionally organized work centers) –Dynamic, stochastic arrival pattern –Stochastic behaviour on the shop floor Highly fluctuating throughput times => Poor performance Fixed lead times –“Adjust” demand –Adjust available capacity Small change of capacity => big impact on the performance Setting cost optimal due dates –Prediction of throughput times

1212 / t 4 Literature (I) Palaka et al. –Customers sensitive to quoted lead times (fixed capacity/ marginal expansion) So and Song –Demands are sensitive to both price and delivery time (optimal setting of price/delivery time/capacity expansion) Ray and Jewkes –Demand is function of delivery time and price, and price is a function of delivery time

1212 / t 5 Literature (II) Barut and Shridharan –Allocation (dynamically) of capacity to multiple product classes Van Mieghem –Review strategic capacity management literature Setting capacity levels on medium or long term for “average” orders, based on average lead times and/or average delivery reliability

1212 / t 6 Research question Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an (economically justified) as high as possible delivery reliability?

1212 / t 7 Research question Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an (economically justified) as high as possible delivery reliability? ADJUST THE CAPACITIES AROUND A GIVEN LEVEL

1212 / t 8 Research question Given fixed, realistic short, lead times, and given dynamic, stochastic demand, then how can we obtain an (economically justified) as high as possible delivery reliability? ADJUST THE CAPACITIES AROUND A GIVEN LEVEL HOW MUCH?

1212 / t 9 Research question Given fixed, realistic short, lead times, and given dynamic, stochastic demand, what can we do to obtain a (economically justified) high delivery reliability? ADJUST THE CAPACITIES AROUND A GIVEN LEVEL HOW MUCH? Estimate the lateness given certain capacity levels

1212 / t 10 Forecasting throughput times (I) Empirically constructed routing normalized waiting time distribution functions F g (.) per order category g Upon arrival an order with g operations and a required reliability of  gets due date:

1212 / t 11 Forecasting throughput times (II) In this research: Estimate of remaining waiting time of an order with g remaining operations, reliability  :

1212 / t 12 Policy for capacity adjustment (I) If n tj is the actual load at a certain work center j at time t, then the total expected lateness is:

1212 / t 13 Policy for capacity adjustment (II) Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity “Adjusting” the load can be done by adjusting the capacity.

1212 / t 14 Policy for capacity adjustment (II) Conjecture: the load at a certain work center can be interpreted as load in relation to the installed capacity “Adjusting” the load can be done by adjusting the capacity.

1212 / t 15 Policy for capacity adjustment (III) We assume : Capacity costs for adjusting the load with 1 unit is equal to c 1 ; lateness costs is c 2 per unit late.

1212 / t 16 Policy for capacity adjustment (IV) After some rewriting this leads to an equation of the form: This is a Constrained Least Squares problem

1212 / t 17 Evaluation Simulation study –Ideal job-shop; 5 work centers; 90% utilization; First Come First Serve –Capacities can be varied weekly or monthly –The same lead time for all orders/Different lead times for orders of different categories

1212 / t 18 Future research Evaluation study How to determine capacity adjustment costs How to find the empirical distribution functions Other priority rules